13458:
209:
4361:
3956:
13444:
50:
13482:
6449:
13470:
193:
4356:{\displaystyle \operatorname {R} _{\mathbf {X} \mathbf {X} }={\begin{bmatrix}\operatorname {E} &\operatorname {E} &\cdots &\operatorname {E} \\\\\operatorname {E} &\operatorname {E} &\cdots &\operatorname {E} \\\\\vdots &\vdots &\ddots &\vdots \\\\\operatorname {E} &\operatorname {E} &\cdots &\operatorname {E} \\\\\end{bmatrix}}}
8170:
5305:
5119:
6180:
2086:
8001:
5637:
5124:
4938:
4923:
4835:
9959:
at the satellites, and the point of time at the receiver on the ground. This is done by the receiver generating a replica signal of the 1,023-bit C/A (Coarse/Acquisition) code, and generating lines of code chips in packets of ten at a time, or 10,230 chips (1,023 Ă 10), shifting slightly as it goes
8448:
the autocorrelation for other lag values being zero. In this calculation we do not perform the carry-over operation during addition as is usual in normal multiplication. Note that we can halve the number of operations required by exploiting the inherent symmetry of the autocorrelation. If the signal
8877:
9560:, then form a function which is a valid autocorrelation in the sense that it is possible to define a theoretical process having exactly that autocorrelation. Other estimates can suffer from the problem that, if they are used to calculate the variance of a linear combination of the
1191:
2343:
6120:
6444:{\displaystyle {\begin{aligned}R_{ff}(\tau )&=\lim _{T\rightarrow \infty }{\frac {1}{T}}\int _{0}^{T}f(t+\tau ){\overline {f(t)}}\,{\rm {d}}t\\R_{yy}(\ell )&=\lim _{N\rightarrow \infty }{\frac {1}{N}}\sum _{n=0}^{N-1}y(n)\,{\overline {y(n-\ell )}}.\end{aligned}}}
1783:
9658:. The Durbin-Watson can be linearly mapped however to the Pearson correlation between values and their lags. A more flexible test, covering autocorrelation of higher orders and applicable whether or not the regressors include lags of the dependent variable, is the
1196:
Note that this expression is not well defined for all-time series or processes, because the mean may not exist, or the variance may be zero (for a constant process) or infinite (for processes with distribution lacking well-behaved moments, such as certain types of
10941:
Kalvani, Payam Rajabi; Jahangiri, Ali Reza; Shapouri, Samaneh; Sari, Amirhossein; Jalili, Yousef Seyed (August 2019). "Multimode AFM analysis of aluminum-doped zinc oxide thin films sputtered under various substrate temperatures for optoelectronic applications".
2924:
5914:
The above definitions work for signals that are square integrable, or square summable, that is, of finite energy. Signals that "last forever" are treated instead as random processes, in which case different definitions are needed, based on expected values. For
1695:
3581:
3329:
1349:: the autocovariance depends only on the time-distance between the pair of values but not on their position in time. This further implies that the autocovariance and autocorrelation can be expressed as a function of the time-lag, and that this would be an
3457:
3204:
2516:
9178:
3885:
6877:
6750:
5319:, the above definition is often used without the normalization, that is, without subtracting the mean and dividing by the variance. When the autocorrelation function is normalized by mean and variance, it is sometimes referred to as the
4465:
2601:
8694:
5461:
2688:
4840:
4752:
7730:
8165:{\displaystyle {\begin{array}{rrrrrr}&2&3&-1\\\times &2&3&-1\\\hline &-2&-3&1\\&&6&9&-3\\+&&&4&6&-2\\\hline &-2&3&14&3&-2\end{array}}}
6886:
In the following, we will describe properties of one-dimensional autocorrelations only, since most properties are easily transferred from the one-dimensional case to the multi-dimensional cases. These properties hold for
2171:
5924:
812:
9943:
that results from the motion of the particles. Autocorrelation of the signal can be analyzed in terms of the diffusion of the particles. From this, knowing the viscosity of the fluid, the sizes of the particles can be
5300:{\displaystyle \operatorname {K} _{\mathbf {Z} \mathbf {Z} }=\operatorname {E} )(\mathbf {Z} -\operatorname {E} )^{\rm {H}}]=\operatorname {R} _{\mathbf {Z} \mathbf {Z} }-\operatorname {E} \operatorname {E} ^{\rm {H}}}
5114:{\displaystyle \operatorname {K} _{\mathbf {X} \mathbf {X} }=\operatorname {E} )(\mathbf {X} -\operatorname {E} )^{\rm {T}}]=\operatorname {R} _{\mathbf {X} \mathbf {X} }-\operatorname {E} \operatorname {E} ^{\rm {T}}}
5909:
1497:
9627:. Problematic autocorrelation of the errors, which themselves are unobserved, can generally be detected because it produces autocorrelation in the observable residuals. (Errors are also known as "error terms" in
4582:
11130:
7998:) by hand, we first recognize that the definition just given is the same as the "usual" multiplication, but with right shifts, where each vertical addition gives the autocorrelation for particular lag values:
916:
7569:
7838:
2747:
4616:
3791:
3664:
3463:
3210:
6453:
These definitions have the advantage that they give sensible well-defined single-parameter results for periodic functions, even when those functions are not the output of stationary ergodic processes.
9534:
1758:
8618:
3342:
9454:
3091:
9024:
8699:
6185:
5929:
8530:
7131:
2402:
9031:
7254:
7033:
6960:
1512:
2730:
2081:{\displaystyle \rho _{XX}(t_{1},t_{2})={\frac {\operatorname {K} _{XX}(t_{1},t_{2})}{\sigma _{t_{1}}\sigma _{t_{2}}}}={\frac {\operatorname {E} \left}{\sigma _{t_{1}}\sigma _{t_{2}}}}.}
11010:
8446:
7959:
8367:
3047:
2393:
6759:
6632:
10413:
8244:
10232:
4396:
2521:
1242:
413:
9819:
7438:
5678:
4723:
835:
2613:
1397:
9738:(MA), the autocorrelation function is used to determine the appropriate number of lagged error terms to be included. This is based on the fact that for an MA process of order
589:
9775:
7596:
10282:
8292:
7477:
5400:
4495:
4385:
3916:
3712:
9314:
9253:
1293:
9880:
9854:
7885:
2118:
151:
10314:
9713:
4642:
3946:
3690:
6533:
3815:
1775:. However, in other disciplines (e.g. engineering) the normalization is usually dropped and the terms "autocorrelation" and "autocovariance" are used interchangeably.
554:
282:
7992:
6553:
2965:
9206:
7352:
3080:
338:
Different fields of study define autocorrelation differently, and not all of these definitions are equivalent. In some fields, the term is used interchangeably with
7288:
7180:
5779:
5453:
4674:
3005:
1347:
1320:
908:
881:
687:
660:
496:
9662:. This involves an auxiliary regression, wherein the residuals obtained from estimating the model of interest are regressed on (a) the original regressors and (b)
9287:
9226:
5808:
5711:
5632:{\displaystyle R_{ff}(\tau )=\int _{-\infty }^{\infty }f(t+\tau ){\overline {f(t)}}\,{\rm {d}}t=\int _{-\infty }^{\infty }f(t){\overline {f(t-\tau )}}\,{\rm {d}}t}
5433:
5361:
1266:
9353:
256:
8641:
7734:
When mean values are subtracted from signals before computing an autocorrelation function, the resulting function is usually called an auto-covariance function.
4918:{\displaystyle \mathbf {a} ^{\mathrm {H} }\operatorname {R} _{\mathbf {Z} \mathbf {Z} }\mathbf {a} \geq 0\quad {\text{for all }}\mathbf {a} \in \mathbb {C} ^{n}}
4830:{\displaystyle \mathbf {a} ^{\mathrm {T} }\operatorname {R} _{\mathbf {X} \mathbf {X} }\mathbf {a} \geq 0\quad {\text{for all }}\mathbf {a} \in \mathbb {R} ^{n}}
10194:
10170:
9578:
9558:
9373:
8956:
7372:
7318:
7151:
7053:
6625:
6510:
6490:
6166:
6146:
5759:
5731:
2985:
629:
609:
524:
453:
433:
6605:
2153:
311:
as a function of the time lag between them. The analysis of autocorrelation is a mathematical tool for finding repeating patterns, such as the presence of a
179:
2348:
The normalization is important both because the interpretation of the autocorrelation as a correlation provides a scale-free measure of the strength of
11138:
7482:
8872:{\displaystyle {\begin{aligned}F_{R}(f)&=\operatorname {FFT} \\S(f)&=F_{R}(f)F_{R}^{*}(f)\\R(\tau )&=\operatorname {IFFT} \end{aligned}}}
10141:). In particular, it is possible to have serial dependence but no (linear) correlation. In some fields however, the two terms are used as synonyms.
6175:, the expectation can be replaced by the limit of a time average. The autocorrelation of an ergodic process is sometimes defined as or equated to
695:
5816:
12579:
9609:
11003:
10978:
10620:
Colberg, P.; Höfling, F. (2011). "Highly accelerated simulations of glassy dynamics using GPUs: caveats on limited floating-point precision".
8006:
13084:
10732:
Percival, Donald B. (1993). "Three
Curious Properties of the Sample Variance and Autocovariance for Stationary Processes with Unknown Mean".
10034:, is used by X-ray diffractionists to help recover the "Fourier phase information" on atom positions not available through diffraction alone.
1705:
1408:
4507:
1186:{\displaystyle \operatorname {K} _{XX}(t_{1},t_{2})=\operatorname {E} \left=\operatorname {E} \left-\mu _{t_{1}}{\overline {\mu }}_{t_{2}}}
13234:
9631:.) Autocorrelation of the errors violates the ordinary least squares assumption that the error terms are uncorrelated, meaning that the
12858:
11499:
2338:{\displaystyle \rho _{XX}(\tau )={\frac {\operatorname {K} _{XX}(\tau )}{\sigma ^{2}}}={\frac {\operatorname {E} \left}{\sigma ^{2}}}}
7757:
6115:{\displaystyle {\begin{aligned}R_{ff}(\tau )&=\operatorname {E} \left\\R_{yy}(\ell )&=\operatorname {E} \left.\end{aligned}}}
12632:
4587:
172:
17:
3727:
3600:
13071:
141:
228:
is 1.0, the value of the result at 5 different points is indicated by the shaded area below each point. Also, the symmetry of
106:
9971:
intensity of a nanostructured system is the
Fourier transform of the spatial autocorrelation function of the electron density.
11083:
11059:
10925:
10786:
10716:
10529:
10487:
10456:
10372:
9899:
9459:
9655:
9623:(OLS), the adequacy of a model specification can be checked in part by establishing whether there is autocorrelation of the
8539:
116:
11494:
11194:
9385:
5916:
12098:
11246:
9605:
8961:
165:
8452:
7162:
The continuous autocorrelation function reaches its peak at the origin, where it takes a real value, i.e. for any delay
2919:{\displaystyle \left|\operatorname {R} _{XX}(t_{1},t_{2})\right|^{2}\leq \operatorname {E} \left\operatorname {E} \left}
10683:
10604:
10579:
10554:
10482:
Kun Il Park, Fundamentals of
Probability and Stochastic Processes with Applications to Communications, Springer, 2018,
9624:
6888:
111:
7064:
12881:
12773:
11147:
7840:
can be used when the signal size is small. For example, to calculate the autocorrelation of the real signal sequence
1690:{\displaystyle \operatorname {K} _{XX}(\tau )=\operatorname {E} \left=\operatorname {E} \left-\mu {\overline {\mu }}}
3576:{\displaystyle S_{XX}(f)=\int _{-\infty }^{\infty }\operatorname {R} _{XX}(\tau )\cos(2\pi f\tau )\,{\rm {d}}\tau .}
3324:{\displaystyle S_{XX}(f)=\int _{-\infty }^{\infty }\operatorname {R} _{XX}(\tau )e^{-i2\pi f\tau }\,{\rm {d}}\tau .}
13486:
13059:
12933:
10398:
10382:
7185:
10759:
6971:
6898:
13117:
12778:
12523:
11894:
11484:
10622:
10019:
effect or to fix intonation). When applied at time scales larger than a second, autocorrelation can identify the
5733:
in the integral is a dummy variable and is only necessary to calculate the integral. It has no specific meaning.
1772:
377:
307:
with a delayed copy of itself as a function of delay. Informally, it is the similarity between observations of a
10100:) it can be used to compute an autocorrelation seismic attribute, out of a 3D seismic survey of the underground.
2693:
13168:
12380:
12187:
12076:
12034:
10346:
10111:
7270:
The autocorrelation of the sum of two completely uncorrelated functions (the cross-correlation is zero for all
3452:{\displaystyle \operatorname {R} _{XX}(\tau )=\int _{-\infty }^{\infty }S_{XX}(f)\cos(2\pi f\tau )\,{\rm {d}}f}
2352:, and because the normalization has an effect on the statistical properties of the estimated autocorrelations.
2163:
12108:
8372:
7890:
3199:{\displaystyle \operatorname {R} _{XX}(\tau )=\int _{-\infty }^{\infty }S_{XX}(f)e^{i2\pi f\tau }\,{\rm {d}}f}
13518:
13411:
12370:
11273:
8296:
3022:
2741:
2368:
1245:
320:
9964:
in the incoming satellite signal, until the receiver replica signal and the satellite signal codes match up.
9540:
The advantage of estimates of the last type is that the set of estimated autocorrelations, as a function of
12962:
12911:
12896:
12886:
12755:
12627:
12594:
12420:
12375:
12205:
10387:
9968:
9683:
8177:
6461:
4746:
10202:
9536:
separately and calculating separate sample means and/or sample variances for use in defining the estimate.
1212:
383:
13474:
13306:
13107:
13031:
12332:
12086:
11755:
11219:
9780:
9651:
9640:
8671:
3334:
3333:
For real-valued functions, the symmetric autocorrelation function has a real symmetric transform, so the
3016:
380:
between values of the process at different times, as a function of the two times or of the time lag. Let
304:
9982:, autocorrelation is used to establish a link between surface morphology and functional characteristics.
7377:
5645:
4679:
820:
13513:
13191:
13163:
13158:
12906:
12665:
12571:
12551:
12459:
12170:
11988:
11471:
11343:
10138:
9932:
2511:{\displaystyle \operatorname {R} _{XX}(t_{1},t_{2})={\overline {\operatorname {R} _{XX}(t_{2},t_{1})}}}
1356:
41:
9173:{\displaystyle {\hat {R}}(k)={\frac {1}{(n-k)\sigma ^{2}}}\sum _{t=1}^{n-k}(X_{t}-\mu )(X_{t+k}-\mu )}
12923:
12691:
12412:
12337:
12266:
12195:
12115:
12103:
11973:
11961:
11954:
11662:
11383:
10393:
10336:
10012:
9979:
9724:
3715:
562:
499:
316:
9745:
6460:
can be treated by a short-time autocorrelation function analysis, using finite time integrals. (See
13508:
13406:
13173:
13036:
12721:
12686:
12650:
12435:
11877:
11786:
11745:
11657:
11348:
11187:
10988:
10708:
10241:
10173:
10086:
10038:
9928:
9687:
9659:
9632:
8249:
7443:
7257:
5366:
349:
71:
4472:
4368:
3893:
3695:
13315:
12928:
12868:
12805:
12443:
12427:
12165:
12027:
12017:
11867:
11781:
10377:
10331:
9921:
9292:
9231:
7584:
3880:{\displaystyle \operatorname {R} _{\mathbf {X} \mathbf {X} }\triangleq \ \operatorname {E} \left}
3692:
matrix containing as elements the autocorrelations of all pairs of elements of the random vector
1271:
146:
81:
11051:
11044:
9859:
9824:
8536:) where the left and right tails of the previous autocorrelation sequence will overlap and give
7843:
2093:
13353:
13283:
13076:
13013:
12768:
12655:
11652:
11549:
11456:
11335:
11234:
10861:"Analytical form of the autocorrelation function for the fluorescence correlation spectroscopy"
10326:
10287:
9691:
9620:
8882:
8686:
7747:
6872:{\displaystyle R_{ff}(\tau )\triangleq \int _{t_{0}}^{t_{0}+T}f(t){\overline {f(t-\tau )}}\,dt}
6745:{\displaystyle R_{ff}(\tau )\triangleq \int _{t_{0}}^{t_{0}+T}f(t+\tau ){\overline {f(t)}}\,dt}
4621:
3925:
3669:
2349:
357:
353:
66:
10703:
Spectral
Analysis for Physical Applications: Multitaper and Conventional Univariate Techniques
6515:
1295:
are time-independent, and further the autocovariance function depends only on the lag between
532:
261:
13378:
13320:
13263:
13089:
12982:
12891:
12617:
12501:
12360:
12352:
12242:
12234:
12049:
11945:
11923:
11882:
11847:
11814:
11760:
11735:
11690:
11629:
11589:
11391:
11214:
11139:
Quantitative Data
Processing in Scanning Probe Microscopy: SPM Applications for Nanometrology
10284:
would imply that there is statistical dependence between all pairs of values at the same lag
9613:
7964:
6538:
4460:{\displaystyle \operatorname {R} _{\mathbf {Z} \mathbf {Z} }\triangleq \ \operatorname {E} .}
4388:
2944:
2596:{\displaystyle \operatorname {R} _{XX}(\tau )={\overline {\operatorname {R} _{XX}(-\tau )}}.}
503:
10700:
9185:
7327:
3055:
13301:
12876:
12825:
12801:
12763:
12681:
12660:
12612:
12491:
12469:
12438:
12347:
12224:
12175:
12093:
12066:
12022:
11978:
11740:
11516:
11396:
11106:
10872:
10815:
10640:
10352:
10137:
is closely linked to the notion of autocorrelation, but represents a distinct concept (see
9735:
9635:
does not apply, and that OLS estimators are no longer the Best Linear
Unbiased Estimators (
9601:
9597:
9593:
8533:
7273:
7165:
5764:
5438:
5332:
4647:
2990:
2938:
1768:
1325:
1298:
886:
859:
665:
638:
474:
9316:
are replaced by the standard formulae for sample mean and sample variance, then this is a
9272:
9211:
5784:
5687:
5409:
5337:
2683:{\displaystyle \left|\operatorname {R} _{XX}(\tau )\right|\leq \operatorname {R} _{XX}(0)}
1251:
8:
13448:
13373:
13296:
12977:
12741:
12734:
12696:
12604:
12584:
12556:
12289:
12155:
12150:
12140:
12132:
11950:
11911:
11801:
11791:
11700:
11479:
11435:
11353:
11278:
11180:
10701:
9986:
9589:
9332:
4498:
842:
235:
11110:
10876:
10819:
10644:
10082:, spatial autocorrelation refers to correlation of a variable with itself through space.
10056:
to score the similarity of an observed spectrum to an idealized spectrum representing a
10037:
In statistics, spatial autocorrelation between sample locations also helps one estimate
8623:
13462:
13273:
13127:
13023:
12972:
12848:
12745:
12729:
12706:
12483:
12217:
12200:
12160:
12071:
11966:
11928:
11899:
11859:
11819:
11765:
11682:
11368:
11363:
11131:
Signal design for good correlation: for wireless communication, cryptography, and radar
10959:
10836:
10803:
10656:
10630:
10408:
10403:
10235:
10179:
10155:
10104:
10031:
10016:
9666:
lags of the residuals, where 'k' is the order of the test. The simplest version of the
9563:
9543:
9376:
9358:
8941:
7751:
7725:{\displaystyle R(j,k,\ell )=\sum _{n,q,r}x_{n,q,r}\,{\overline {x}}_{n-j,q-k,r-\ell }.}
7357:
7303:
7136:
7059:
7038:
6610:
6495:
6475:
6151:
6131:
6125:
5744:
5716:
2970:
614:
594:
509:
438:
418:
9902:
to provide quantitative insight into molecular-level diffusion and chemical reactions.
6558:
2123:
13457:
13368:
13338:
13330:
13150:
13141:
13066:
12997:
12853:
12838:
12813:
12701:
12642:
12508:
12496:
12122:
12039:
11983:
11906:
11750:
11672:
11451:
11325:
11158:
11155:
11143:
11079:
11055:
10963:
10921:
10898:
10890:
10841:
10782:
10712:
10679:
10600:
10575:
10550:
10525:
10483:
10452:
10362:
10053:
9952:
8886:
7294:
7264:
5681:
5403:
5316:
3083:
328:
213:
208:
76:
9686:. Under the null hypothesis of no autocorrelation, this statistic is asymptotically
8659:, several efficient algorithms exist which can compute the autocorrelation in order
13393:
13348:
13112:
13099:
12992:
12967:
12901:
12833:
12711:
12319:
12212:
12145:
12058:
12005:
11824:
11695:
11489:
11373:
11288:
11255:
11114:
10951:
10880:
10831:
10823:
10745:
10741:
10660:
10648:
10011:, autocorrelation (when applied at time scales smaller than a second) is used as a
9913:
9906:
9318:
9257:
7154:
4739:
4735:
3050:
2156:
27:
Correlation of a signal with a time-shifted copy of itself, as a function of shift
13310:
12916:
12843:
12518:
12392:
12365:
12342:
12311:
11938:
11933:
11887:
11617:
11268:
11073:
10983:
10149:
10122:
10089:
data, autocorrelation must be taken into account for correct error determination.
9975:
9940:
9647:
overestimated) when the autocorrelations of the errors at low lags are positive.
8935:
7743:
7588:
6172:
468:
312:
308:
12800:
10067:, autocorrelation is used to study and characterize the spatial distribution of
9596:, autocorrelation in a variable of interest is typically modeled either with an
13259:
13254:
11717:
11647:
11293:
11094:
10955:
10341:
10196:. A series is serially independent if there is no dependence between any pair.
10115:
9956:
9667:
8651:
8643:
The procedure can be regarded as an application of the convolution property of
3798:
3794:
838:
373:
339:
10827:
10652:
7746:
sequence, it is frequently necessary to compute the autocorrelation with high
13502:
13416:
13383:
13246:
13207:
13018:
12987:
12451:
12405:
12010:
11712:
11539:
11303:
11298:
11118:
11069:
10894:
10125:, autocorrelation has been used to accurately measure power system frequency.
10049:
9961:
6966:
3722:
3595:
2396:
1778:
The definition of the autocorrelation coefficient of a stochastic process is
1350:
460:
296:
9650:
The traditional test for the presence of first-order autocorrelation is the
807:{\displaystyle \operatorname {R} _{XX}(t_{1},t_{2})=\operatorname {E} \left}
13358:
13291:
13268:
13183:
12513:
11809:
11707:
11642:
11584:
11569:
11506:
11461:
10902:
10845:
10072:
10064:
10020:
9644:
9628:
846:
5904:{\displaystyle R_{yy}(\ell )=\sum _{n\in Z}y(n)\,{\overline {y(n-\ell )}}}
1204:
13401:
13363:
13046:
12947:
12809:
12622:
12589:
12081:
11998:
11993:
11637:
11594:
11574:
11554:
11544:
11313:
11004:"A New Method for Fast Frequency Measurement for Protection Applications"
10357:
10145:
10093:
9326:
8644:
7321:
2934:
464:
332:
300:
201:
4928:
All eigenvalues of the autocorrelation matrix are real and non-negative.
12247:
11727:
11427:
11358:
11308:
11283:
11203:
11126:
11039:
10885:
10860:
10097:
10079:
9985:
In optics, normalized autocorrelations and cross-correlations give the
9728:
369:
34:
10449:
Probability and Random
Processes for Electrical and Computer Engineers
10118:
can affect the optimal portion of the portfolio to hold in that asset.
9955:, or time shift, between the point of time at the transmission of the
9654:
or, if the explanatory variables include a lagged dependent variable,
8896:
correlation can be performed by using brute force calculation for low
6962:, which is easy to prove from the definition. In the continuous case,
1492:{\displaystyle \operatorname {R} _{XX}(\tau )=\operatorname {E} \left}
12400:
12252:
11872:
11667:
11579:
11564:
11559:
11524:
11163:
9997:
9993:
8912:
7580:
4577:{\displaystyle \mathbf {X} =\left(X_{1},X_{2},X_{3}\right)^{\rm {T}}}
3919:
1198:
345:
11095:"Computational Design of Sequences with Good Correlation Properties"
9375:. This estimate is always biased; however, it usually has a smaller
9026:, an estimate of the autocorrelation coefficient may be obtained as
11916:
11534:
11411:
11406:
11401:
9262:
3802:
1771:) to normalize the autocovariance function to get a time-dependent
557:
324:
10635:
9939:
suspended in a fluid. A laser shining into the mixture produces a
9382:
Other possibilities derive from treating the two portions of data
2155:, with 1 indicating perfect correlation and â1 indicating perfect
49:
13421:
13122:
10071:
in the universe and in multi-wavelength observations of low mass
10057:
10045:
9936:
7290:) is the sum of the autocorrelations of each function separately.
456:
7564:{\displaystyle R_{ff}(\tau )=(f*g_{-1}({\overline {f}}))(\tau )}
13343:
12324:
12298:
12278:
11529:
11320:
10068:
10001:
7833:{\displaystyle R_{xx}(j)=\sum _{n}x_{n}\,{\overline {x}}_{n-j}}
1767:
It is common practice in some disciplines (e.g. statistics and
10804:"Fluorescence Correlation Spectroscopy: Past, Present, Future"
9265:
of the process are not known there are several possibilities:
3594:(also called second moment) of a (potentially time-dependent)
136:
11172:
10367:
10024:
10008:
9917:
9910:
9905:
Another application of autocorrelation is the measurement of
9639:). While it does not bias the OLS coefficient estimates, the
4611:{\displaystyle \operatorname {R} _{\mathbf {X} \mathbf {X} }}
196:
Above: A plot of a series of 100 random numbers concealing a
101:
10940:
10859:
HoĆyst, Robert; Poniewierski, Andrzej; Zhang, Xuzhu (2017).
5326:
3786:{\displaystyle \mathbf {X} =(X_{1},\ldots ,X_{n})^{\rm {T}}}
3659:{\displaystyle \mathbf {X} =(X_{1},\ldots ,X_{n})^{\rm {T}}}
11263:
10114:, the presence or absence of autocorrelation in an asset's
9891:
9636:
6895:
A fundamental property of the autocorrelation is symmetry,
5310:
4728:
527:
197:
8938:
process with known mean and variance for which we observe
5736:
363:
192:
10522:
Measurement and Data
Analysis for Engineering and Science
10107:
imaging, autocorrelation is used to visualize blood flow.
9948:
9580:'s, the variance calculated may turn out to be negative.
11153:
10698:
9890:
Autocorrelation's ability to find repeating patterns in
8915:
density to compute higher values, resulting in the same
10858:
10574:(3rd ed.). Upper Saddle River, NJ: PrenticeâHall.
9529:{\displaystyle \{X_{k+1},\,X_{k+2},\,\ldots ,\,X_{n}\}}
8674:
allows computing the autocorrelation from the raw data
7297:, it maintains all the properties of cross-correlation.
1753:{\displaystyle \operatorname {K} _{XX}(0)=\sigma ^{2}.}
1205:
Definition for wide-sense stationary stochastic process
10570:
Box, G. E. P.; Jenkins, G. M.; Reinsel, G. C. (1994).
10505:
Probability, Random variables and
Stochastic processes
10015:
for both instrument tuners and "Auto Tune" (used as a
8613:{\displaystyle R_{xx}=(\ldots ,14,1,1,14,1,1,\ldots )}
7583:
autocorrelation is defined similarly. For example, in
3985:
852:
Subtracting the mean before multiplication yields the
360:
are specific forms of processes with autocorrelation.
10290:
10244:
10205:
10182:
10158:
9862:
9827:
9783:
9748:
9731:(Heteroskedasticity and Autocorrelation Consistent).
9694:
9566:
9546:
9462:
9449:{\displaystyle \{X_{1},\,X_{2},\,\ldots ,\,X_{n-k}\}}
9388:
9361:
9335:
9295:
9275:
9234:
9214:
9188:
9034:
8964:
8944:
8697:
8626:
8542:
8455:
8375:
8299:
8252:
8180:
8004:
7967:
7893:
7846:
7760:
7599:
7485:
7446:
7380:
7360:
7330:
7306:
7276:
7188:
7168:
7139:
7067:
7041:
6974:
6901:
6762:
6635:
6613:
6561:
6541:
6518:
6498:
6478:
6183:
6154:
6134:
5927:
5819:
5787:
5767:
5747:
5719:
5690:
5648:
5464:
5441:
5412:
5369:
5340:
5127:
4941:
4843:
4755:
4682:
4650:
4624:
4590:
4510:
4475:
4399:
4371:
3959:
3928:
3896:
3818:
3730:
3698:
3672:
3603:
3466:
3345:
3213:
3094:
3058:
3025:
2993:
2973:
2947:
2750:
2696:
2616:
2524:
2405:
2371:
2174:
2126:
2096:
1786:
1708:
1515:
1411:
1359:
1328:
1301:
1274:
1254:
1215:
919:
889:
862:
823:
698:
668:
641:
617:
597:
565:
535:
512:
477:
441:
421:
386:
331:
for analyzing functions or series of values, such as
264:
238:
13085:
Autoregressive conditional heteroskedasticity (ARCH)
7574:
4935:
is related to the autocorrelation matrix as follows:
3585:
10030:Autocorrelation in space rather than time, via the
9019:{\displaystyle \{X_{1},\,X_{2},\,\ldots ,\,X_{n}\}}
8532:then we get a circular autocorrelation (similar to
4391:, the autocorrelation matrix is instead defined by
3337:can be re-expressed in terms of real cosines only:
12547:
11043:
10779:An Introduction to Modern Econometrics Using Stata
10308:
10276:
10226:
10188:
10164:
9874:
9848:
9813:
9769:
9707:
9572:
9552:
9528:
9448:
9367:
9347:
9308:
9281:
9247:
9220:
9200:
9172:
9018:
8950:
8871:
8635:
8612:
8525:{\displaystyle x=(\ldots ,2,3,-1,2,3,-1,\ldots ),}
8524:
8440:
8361:
8286:
8238:
8164:
7986:
7953:
7879:
7832:
7724:
7563:
7471:
7432:
7366:
7346:
7312:
7282:
7248:
7174:
7145:
7125:
7047:
7027:
6954:
6871:
6744:
6619:
6599:
6547:
6527:
6504:
6484:
6467:
6443:
6160:
6140:
6114:
5903:
5802:
5773:
5753:
5725:
5705:
5672:
5631:
5447:
5427:
5394:
5355:
5299:
5113:
4917:
4829:
4717:
4668:
4636:
4610:
4576:
4489:
4459:
4379:
4355:
3940:
3910:
3879:
3785:
3706:
3684:
3658:
3575:
3451:
3323:
3198:
3074:
3041:
2999:
2979:
2959:
2918:
2724:
2682:
2595:
2510:
2387:
2337:
2147:
2112:
2080:
1752:
1689:
1491:
1391:
1341:
1314:
1287:
1260:
1236:
1185:
902:
875:
829:
806:
681:
654:
623:
603:
583:
548:
518:
490:
447:
427:
407:
276:
250:
11092:
11050:(Second ed.). New York: Macmillan. pp.
10569:
10052:makes use of autocorrelation in conjunction with
9931:data, which notably enables determination of the
9612:(ARIMA). With multiple interrelated data series,
8620:which has the same period as the signal sequence
2937:signal will have a strong peak (represented by a
2928:
2120:is well defined, its value must lie in the range
200:function. Below: The sine function revealed in a
13500:
10152:has serial dependence if the value at some time
9608:(ARMA), or an extension of the latter called an
8926:efficiency, but with lower memory requirements.
7126:{\displaystyle R_{ff}(-\tau )=R_{ff}^{*}(\tau )}
6342:
6218:
3714:. The autocorrelation matrix is used in various
12633:Multivariate adaptive regression splines (MARS)
10547:Communication Systems Engineering (2nd Edition)
10349:(transformation for autocorrelated error terms)
10238:, then statistical dependence between the pair
10699:Percival, Donald B.; Andrew T. Walden (1993).
10619:
9610:autoregressive integrated moving average model
8174:Thus the required autocorrelation sequence is
11188:
11068:
10920:(Third ed.). CRC Press. pp. 18â19.
10595:Frenkel, D.; Smit, B. (2002). "chap. 4.4.2".
10572:Time Series Analysis: Forecasting and Control
9723:Responses to nonzero autocorrelation include
7354:is a function which manipulates the function
7260:. The same result holds in the discrete case.
7249:{\displaystyle |R_{ff}(\tau )|\leq R_{ff}(0)}
6555:is replaced by integration over any interval
1399:. This gives the more familiar forms for the
173:
11093:Soltanalian, Mojtaba; Stoica, Petre (2012).
9898:Autocorrelation analysis is used heavily in
9523:
9463:
9443:
9389:
9013:
8965:
7293:Since autocorrelation is a specific type of
7028:{\displaystyle R_{ff}(-\tau )=R_{ff}(\tau )}
6955:{\displaystyle R_{ff}(\tau )=R_{ff}(-\tau )}
6492:is a continuous periodic function of period
2735:
10594:
10478:
10476:
10474:
10472:
10470:
10468:
9909:and the measurement of very-short-duration
8900:values, and then progressively binning the
4837:for a real random vector, and respectively
2365:The fact that the autocorrelation function
372:, the autocorrelation of a real or complex
11233:
11195:
11181:
11142:(Second ed.). Elsevier. pp. 108â112
10915:
10499:
10497:
10495:
7754:based on the signal processing definition
7267:is, itself, periodic with the same period.
3010:
2725:{\displaystyle \operatorname {R} _{XX}(0)}
180:
166:
11846:
11001:
10979:"Auto-Tune: Why Pop Music Sounds Perfect"
10976:
10884:
10835:
10673:
10634:
10414:Unbiased estimation of standard deviation
10041:when sampling a heterogeneous population.
9512:
9505:
9485:
9426:
9419:
9405:
9002:
8995:
8981:
7806:
7671:
7587:the autocorrelation of a square-summable
6862:
6735:
6406:
6297:
6072:
5873:
5618:
5547:
5327:Autocorrelation of continuous-time signal
4905:
4817:
3559:
3438:
3307:
3185:
2933:The autocorrelation of a continuous-time
220:. For the operations involving function
10731:
10599:(2nd ed.). London: Academic Press.
10465:
10442:
10440:
10438:
10436:
10434:
10432:
10430:
8441:{\displaystyle R_{xx}(-2)=R_{xx}(2)=-2,}
7954:{\displaystyle x_{0}=2,x_{1}=3,x_{2}=-1}
7737:
5402:is most often defined as the continuous
5311:Autocorrelation of deterministic signals
5121:Respectively for complex random vectors:
4729:Properties of the autocorrelation matrix
207:
191:
11009:. Schweitzer Engineering Laboratories.
10707:. Cambridge University Press. pp.
10544:
10492:
8362:{\displaystyle R_{xx}(-1)=R_{xx}(1)=3,}
5737:Autocorrelation of discrete-time signal
3042:{\displaystyle \operatorname {R} _{XX}}
2744:, inequality for stochastic processes:
2388:{\displaystyle \operatorname {R} _{XX}}
845:. Note that the expectation may not be
364:Autocorrelation of stochastic processes
14:
13501:
13159:KaplanâMeier estimator (product limit)
11099:IEEE Transactions on Signal Processing
11038:
10515:
10513:
10446:
9960:along in order to accommodate for the
9583:
5919:, the autocorrelations are defined as
5917:wide-sense-stationary random processes
13232:
12799:
12546:
11845:
11615:
11232:
11176:
11154:
10801:
10427:
10373:Fluorescence correlation spectroscopy
9900:fluorescence correlation spectroscopy
9894:yields many applications, including:
8239:{\displaystyle R_{xx}=(-2,3,14,3,-2)}
3019:relates the autocorrelation function
13469:
13169:Accelerated failure time (AFT) model
10776:
10678:. London, New York: Academic Press.
10549:(2 ed.). Pearson. p. 168.
10519:
10227:{\displaystyle \left\{X_{t}\right\}}
10129:
9996:, autocorrelation can determine the
2360:
1237:{\displaystyle \left\{X_{t}\right\}}
408:{\displaystyle \left\{X_{t}\right\}}
13481:
12764:Analysis of variance (ANOVA, anova)
11616:
11133:. Cambridge University Press, 2005.
10510:
9927:Autocorrelation is used to analyze
9814:{\displaystyle \tau =0,1,\ldots ,q}
9643:tend to be underestimated (and the
9606:autoregressive-moving-average model
8650:While the brute force algorithm is
4925:in case of a complex random vector.
24:
12859:CochranâMantelâHaenszel statistics
11485:Pearson product-moment correlation
11032:
10802:Elson, Elliot L. (December 2011).
10597:Understanding Molecular Simulation
9670:from this auxiliary regression is
9616:(VAR) or its extensions are used.
7433:{\displaystyle g_{-1}(f)(t)=f(-t)}
6542:
6522:
6352:
6300:
6228:
6128:, these will also be functions of
6049:
5961:
5673:{\displaystyle {\overline {f(t)}}}
5621:
5574:
5569:
5550:
5503:
5498:
5291:
5271:
5254:
5235:
5222:
5199:
5168:
5148:
5129:
5105:
5085:
5068:
5049:
5036:
5013:
4982:
4962:
4943:
4859:
4852:
4771:
4764:
4718:{\displaystyle \operatorname {E} }
4683:
4592:
4568:
4481:
4445:
4423:
4401:
4310:
4271:
4237:
4173:
4134:
4100:
4061:
4022:
3988:
3961:
3902:
3866:
3842:
3820:
3777:
3650:
3562:
3511:
3505:
3500:
3441:
3387:
3382:
3347:
3310:
3258:
3252:
3247:
3188:
3136:
3131:
3096:
3027:
2866:
2816:
2758:
2698:
2656:
2623:
2605:
2557:
2526:
2458:
2407:
2373:
2247:
2204:
1925:
1836:
1710:
1622:
1544:
1517:
1440:
1413:
1082:
968:
921:
830:{\displaystyle \operatorname {E} }
824:
747:
700:
212:Visual comparison of convolution,
25:
13530:
10944:Superlattices and Microstructures
10676:Spectral Analysis and Time Series
10545:Proakis, John (August 31, 2001).
7575:Multi-dimensional autocorrelation
5363:, the continuous autocorrelation
4738:for complex random vectors and a
3590:The (potentially time-dependent)
3586:Autocorrelation of random vectors
2166:(WSS) process, the definition is
1392:{\displaystyle \tau =t_{2}-t_{1}}
327:frequencies. It is often used in
13480:
13468:
13456:
13443:
13442:
13233:
11002:Kasztenny, Bogdan (March 2016).
10383:Partial autocorrelation function
10332:Autocorrelation of a formal word
9935:of nanometer-sized particles or
5281:
5264:
5245:
5240:
5209:
5192:
5178:
5161:
5139:
5134:
5095:
5078:
5059:
5054:
5023:
5006:
4992:
4975:
4953:
4948:
4896:
4879:
4869:
4864:
4846:
4808:
4791:
4781:
4776:
4758:
4745:The autocorrelation matrix is a
4734:The autocorrelation matrix is a
4602:
4597:
4512:
4439:
4433:
4411:
4406:
4373:
3971:
3966:
3860:
3854:
3830:
3825:
3732:
3700:
3605:
2518:respectively for a WSS process:
1762:
841:operator and the bar represents
48:
13118:Least-squares spectral analysis
11016:from the original on 2022-10-09
10995:
10970:
10934:
10909:
10852:
10795:
10770:
10760:"Serial correlation techniques"
10752:
10725:
10692:
9885:
8881:where IFFT denotes the inverse
7256:. This is a consequence of the
6889:wide-sense stationary processes
6881:
6468:Definition for periodic signals
4889:
4801:
1773:Pearson correlation coefficient
584:{\displaystyle \sigma _{t}^{2}}
526:. Suppose that the process has
284:are identical in this example.
12099:Mean-unbiased minimum-variance
11202:
11075:A Guide to Modern Econometrics
10977:Tyrangiel, Josh (2009-02-05).
10746:10.1080/00031305.1993.10475997
10667:
10613:
10588:
10563:
10538:
10451:. Cambridge University Press.
10271:
10245:
10112:intertemporal portfolio choice
9837:
9831:
9770:{\displaystyle R(\tau )\neq 0}
9758:
9752:
9604:(MA), their combination as an
9167:
9142:
9139:
9120:
9077:
9065:
9053:
9047:
9041:
8862:
8859:
8853:
8847:
8831:
8825:
8815:
8809:
8791:
8785:
8765:
8759:
8749:
8746:
8740:
8734:
8718:
8712:
8607:
8559:
8516:
8462:
8423:
8417:
8398:
8389:
8347:
8341:
8322:
8313:
8272:
8266:
8233:
8197:
7874:
7853:
7780:
7774:
7621:
7603:
7558:
7552:
7549:
7546:
7533:
7511:
7505:
7499:
7466:
7460:
7427:
7418:
7409:
7403:
7400:
7394:
7243:
7237:
7217:
7213:
7207:
7190:
7120:
7114:
7090:
7081:
7022:
7016:
6997:
6988:
6949:
6940:
6921:
6915:
6853:
6841:
6832:
6826:
6782:
6776:
6726:
6720:
6711:
6699:
6655:
6649:
6594:
6562:
6425:
6413:
6403:
6397:
6349:
6331:
6325:
6288:
6282:
6273:
6261:
6225:
6207:
6201:
6091:
6079:
6069:
6063:
6039:
6033:
6002:
5990:
5981:
5975:
5951:
5945:
5892:
5880:
5870:
5864:
5839:
5833:
5797:
5791:
5700:
5694:
5661:
5655:
5609:
5597:
5588:
5582:
5538:
5532:
5523:
5511:
5484:
5478:
5422:
5416:
5389:
5383:
5350:
5344:
5286:
5277:
5268:
5260:
5228:
5217:
5213:
5205:
5188:
5185:
5182:
5174:
5157:
5154:
5100:
5091:
5082:
5074:
5042:
5031:
5027:
5019:
5002:
4999:
4996:
4988:
4971:
4968:
4712:
4689:
4663:
4651:
4451:
4429:
4339:
4316:
4300:
4277:
4266:
4243:
4202:
4179:
4163:
4140:
4129:
4106:
4090:
4067:
4051:
4028:
4017:
3994:
3772:
3739:
3645:
3612:
3556:
3541:
3532:
3526:
3486:
3480:
3435:
3420:
3411:
3405:
3368:
3362:
3279:
3273:
3233:
3227:
3160:
3154:
3117:
3111:
2929:Autocorrelation of white noise
2901:
2878:
2851:
2828:
2799:
2773:
2719:
2713:
2677:
2671:
2644:
2638:
2581:
2572:
2547:
2541:
2499:
2473:
2448:
2422:
2308:
2289:
2283:
2258:
2225:
2219:
2194:
2188:
2142:
2127:
2022:
1982:
1976:
1936:
1877:
1851:
1826:
1800:
1731:
1725:
1605:
1586:
1580:
1555:
1538:
1532:
1434:
1428:
1065:
1025:
1019:
979:
962:
936:
741:
715:
13:
1:
13412:Geographic information system
12628:Simultaneous equations models
10777:Baum, Christopher F. (2006).
10420:
10277:{\displaystyle (X_{t},X_{s})}
10176:on the value at another time
8929:
8449:happens to be periodic, i.e.
8287:{\displaystyle R_{xx}(0)=14,}
7472:{\displaystyle R_{ff}(\tau )}
5741:The discrete autocorrelation
5395:{\displaystyle R_{ff}(\tau )}
2355:
1246:wide-sense stationary process
631:. Then the definition of the
321:missing fundamental frequency
224:, and assuming the height of
12595:Coefficient of determination
12206:Uniformly most powerful test
10399:PraisâWinsten transformation
10388:Phylogenetic autocorrelation
9989:of an electromagnetic field.
9969:small-angle X-ray scattering
9684:coefficient of determination
9255:are known, this estimate is
7813:
7678:
7541:
6857:
6730:
6462:short-time Fourier transform
6456:Alternatively, signals that
6429:
6292:
6171:For processes that are also
6095:
6006:
5896:
5665:
5613:
5542:
5323:or autocovariance function.
4747:positive semidefinite matrix
4490:{\displaystyle {}^{\rm {H}}}
4380:{\displaystyle \mathbf {Z} }
3911:{\displaystyle {}^{\rm {T}}}
3707:{\displaystyle \mathbf {X} }
2585:
2503:
2312:
2026:
1682:
1655:
1609:
1473:
1165:
1116:
1069:
781:
204:produced by autocorrelation.
7:
13164:Proportional hazards models
13108:Spectral density estimation
13090:Vector autoregression (VAR)
12524:Maximum posterior estimator
11756:Randomized controlled trial
10319:
10023:, for example to determine
9933:particle size distributions
9309:{\displaystyle \sigma ^{2}}
9248:{\displaystyle \sigma ^{2}}
6124:For processes that are not
5781:for a discrete-time signal
5321:autocorrelation coefficient
1288:{\displaystyle \sigma ^{2}}
323:in a signal implied by its
10:
13535:
12924:Multivariate distributions
11344:Average absolute deviation
10956:10.1016/j.spmi.2019.106173
10347:CochraneâOrcutt estimation
10139:Correlation and dependence
9951:system to correct for the
9875:{\displaystyle \tau >q}
9849:{\displaystyle R(\tau )=0}
9355:in the above formula with
8892:Alternatively, a multiple
7880:{\displaystyle x=(2,3,-1)}
6965:the autocorrelation is an
5713:. Note that the parameter
2113:{\displaystyle \rho _{XX}}
350:trend-stationary processes
142:Cross-correlation function
107:Cross-correlation function
42:Correlation and covariance
13438:
13392:
13329:
13282:
13245:
13241:
13228:
13200:
13182:
13149:
13140:
13098:
13045:
13006:
12955:
12946:
12912:Structural equation model
12867:
12824:
12820:
12795:
12754:
12720:
12674:
12641:
12603:
12570:
12566:
12542:
12482:
12391:
12310:
12274:
12265:
12248:Score/Lagrange multiplier
12233:
12186:
12131:
12057:
12048:
11858:
11854:
11841:
11800:
11774:
11726:
11681:
11663:Sample size determination
11628:
11624:
11611:
11515:
11470:
11444:
11426:
11382:
11334:
11254:
11245:
11241:
11228:
11210:
10828:10.1016/j.bpj.2011.11.012
10734:The American Statistician
10674:Priestley, M. B. (1982).
10653:10.1016/j.cpc.2011.01.009
10524:. New York: McGrawâHill.
10520:Dunn, Patrick F. (2005).
10394:Pitch detection algorithm
10337:Autocorrelation technique
10309:{\displaystyle \tau =s-t}
10013:pitch detection algorithm
9980:scanning probe microscopy
9725:generalized least squares
9708:{\displaystyle \chi ^{2}}
9329:-based estimate replaces
9182:for any positive integer
7263:The autocorrelation of a
7058:the autocorrelation is a
4637:{\displaystyle 3\times 3}
4584:is a random vector, then
3941:{\displaystyle n\times n}
3716:digital signal processing
3685:{\displaystyle n\times n}
2742:CauchyâSchwarz inequality
2736:CauchyâSchwarz inequality
1700:In particular, note that
415:be a random process, and
152:Cross-covariance function
130:For deterministic signals
117:Cross-covariance function
13407:Environmental statistics
12929:Elliptical distributions
12722:Generalized linear model
12651:Simple linear regression
12421:HodgesâLehmann estimator
11878:Probability distribution
11787:Stochastic approximation
11349:Coefficient of variation
11119:10.1109/TSP.2012.2186134
11046:Elements of Econometrics
10916:Van Sickle, Jan (2008).
10447:Gubner, John A. (2006).
10087:Markov chain Monte Carlo
10048:algorithm for analyzing
10039:mean value uncertainties
9929:dynamic light scattering
9729:NeweyâWest HAC estimator
7994:for all other values of
7748:computational efficiency
7742:For data expressed as a
7258:rearrangement inequality
6528:{\displaystyle -\infty }
6464:for a related process.)
4742:for real random vectors.
3951:Written component-wise:
1504:auto-covariance function
1401:autocorrelation function
854:auto-covariance function
633:autocorrelation function
549:{\displaystyle \mu _{t}}
358:moving average processes
354:autoregressive processes
277:{\displaystyle f\star g}
137:Autocorrelation function
102:Autocorrelation function
95:For stochastic processes
72:Cross-correlation matrix
18:Autocorrelation function
13067:Cross-correlation (XCF)
12675:Non-standard predictors
12109:LehmannâScheffĂ© theorem
11782:Adaptive clinical trial
11136:Klapetek, Petr (2018).
11125:Solomon W. Golomb, and
10378:Optical autocorrelation
10174:statistically dependent
9922:optical autocorrelators
9734:In the estimation of a
9678:is the sample size and
9652:DurbinâWatson statistic
9261:. If the true mean and
8885:. The asterisk denotes
8687:fast Fourier transforms
8672:WienerâKhinchin theorem
7987:{\displaystyle x_{i}=0}
7055:is a real function, and
6754:which is equivalent to
6548:{\displaystyle \infty }
6512:, the integration from
3335:WienerâKhinchin theorem
3017:WienerâKhinchin theorem
3011:WienerâKhinchin theorem
2960:{\displaystyle \tau =0}
506:of the process at time
147:Autocovariance function
112:Autocovariance function
82:Cross-covariance matrix
13463:Mathematics portal
13284:Engineering statistics
13192:NelsonâAalen estimator
12769:Analysis of covariance
12656:Ordinary least squares
12580:Pearson product-moment
11984:Statistical functional
11895:Empirical distribution
11728:Controlled experiments
11457:Frequency distribution
11235:Descriptive statistics
10918:GPS for Land Surveyors
10503:Papoulis, Athanasius,
10327:Autocorrelation matrix
10310:
10278:
10228:
10190:
10166:
9876:
9850:
9815:
9771:
9709:
9621:ordinary least squares
9574:
9554:
9530:
9450:
9369:
9349:
9310:
9283:
9249:
9222:
9202:
9201:{\displaystyle k<n}
9174:
9119:
9020:
8952:
8883:fast Fourier transform
8873:
8647:of a discrete signal.
8637:
8614:
8526:
8442:
8363:
8288:
8240:
8166:
7988:
7955:
7881:
7834:
7726:
7565:
7473:
7434:
7368:
7348:
7347:{\displaystyle g_{-1}}
7314:
7284:
7250:
7176:
7147:
7127:
7049:
7029:
6956:
6873:
6746:
6621:
6601:
6549:
6529:
6506:
6486:
6445:
6393:
6162:
6142:
6116:
5905:
5804:
5775:
5755:
5727:
5707:
5674:
5633:
5449:
5429:
5396:
5357:
5301:
5115:
4933:auto-covariance matrix
4919:
4831:
4719:
4670:
4638:
4612:
4578:
4491:
4461:
4381:
4357:
3942:
3912:
3881:
3807:autocorrelation matrix
3787:
3708:
3686:
3660:
3592:autocorrelation matrix
3577:
3453:
3325:
3200:
3076:
3075:{\displaystyle S_{XX}}
3051:power spectral density
3043:
3001:
2981:
2961:
2920:
2726:
2684:
2597:
2512:
2389:
2350:statistical dependence
2339:
2149:
2114:
2082:
1754:
1691:
1493:
1393:
1343:
1316:
1289:
1262:
1238:
1187:
904:
877:
831:
808:
683:
656:
625:
605:
585:
550:
520:
502:) produced by a given
492:
449:
435:be any point in time (
429:
409:
285:
278:
252:
205:
77:Auto-covariance matrix
67:Autocorrelation matrix
13379:Population statistics
13321:System identification
13055:Autocorrelation (ACF)
12983:Exponential smoothing
12897:Discriminant analysis
12892:Canonical correlation
12756:Partition of variance
12618:Regression validation
12462:(JonckheereâTerpstra)
12361:Likelihood-ratio test
12050:Frequentist inference
11962:Locationâscale family
11883:Sampling distribution
11848:Statistical inference
11815:Cross-sectional study
11802:Observational studies
11761:Randomized experiment
11590:Stem-and-leaf display
11392:Central limit theorem
10991:on February 10, 2009.
10623:Comput. Phys. Commun.
10311:
10279:
10229:
10191:
10167:
9877:
9851:
9816:
9772:
9710:
9614:vector autoregression
9575:
9555:
9531:
9451:
9370:
9350:
9311:
9284:
9250:
9223:
9208:. When the true mean
9203:
9175:
9093:
9021:
8953:
8874:
8638:
8615:
8527:
8443:
8364:
8289:
8241:
8167:
7989:
7956:
7882:
7835:
7738:Efficient computation
7727:
7566:
7474:
7440:, the definition for
7435:
7369:
7349:
7315:
7285:
7283:{\displaystyle \tau }
7251:
7177:
7175:{\displaystyle \tau }
7148:
7128:
7050:
7030:
6957:
6874:
6747:
6622:
6602:
6550:
6530:
6507:
6487:
6446:
6367:
6163:
6143:
6117:
5906:
5805:
5776:
5774:{\displaystyle \ell }
5756:
5728:
5708:
5675:
5634:
5450:
5448:{\displaystyle \tau }
5430:
5397:
5358:
5302:
5116:
4920:
4832:
4720:
4671:
4669:{\displaystyle (i,j)}
4639:
4613:
4579:
4492:
4462:
4389:complex random vector
4382:
4358:
3943:
3922:matrix of dimensions
3913:
3882:
3788:
3709:
3687:
3661:
3578:
3454:
3326:
3201:
3077:
3044:
3002:
3000:{\displaystyle \tau }
2982:
2962:
2921:
2727:
2685:
2598:
2513:
2390:
2340:
2164:wide-sense stationary
2150:
2115:
2083:
1755:
1692:
1494:
1394:
1344:
1342:{\displaystyle t_{2}}
1317:
1315:{\displaystyle t_{1}}
1290:
1263:
1239:
1188:
905:
903:{\displaystyle t_{2}}
878:
876:{\displaystyle t_{1}}
832:
809:
684:
682:{\displaystyle t_{2}}
657:
655:{\displaystyle t_{1}}
626:
606:
586:
551:
521:
493:
491:{\displaystyle X_{t}}
450:
430:
410:
319:, or identifying the
291:, sometimes known as
279:
253:
211:
195:
13519:Time domain analysis
13302:Probabilistic design
12887:Principal components
12730:Exponential families
12682:Nonlinear regression
12661:General linear model
12623:Mixed effects models
12613:Errors and residuals
12590:Confounding variable
12492:Bayesian probability
12470:Van der Waerden test
12460:Ordered alternative
12225:Multiple comparisons
12104:RaoâBlackwellization
12067:Estimating equations
12023:Statistical distance
11741:Factorial experiment
11274:Arithmetic-Geometric
10353:Correlation function
10288:
10242:
10203:
10180:
10156:
9860:
9825:
9781:
9746:
9736:moving average model
9720:degrees of freedom.
9692:
9660:BreuschâGodfrey test
9656:Durbin's h statistic
9633:Gauss Markov theorem
9625:regression residuals
9602:moving average model
9598:autoregressive model
9564:
9544:
9460:
9386:
9359:
9333:
9293:
9282:{\displaystyle \mu }
9273:
9232:
9221:{\displaystyle \mu }
9212:
9186:
9032:
8962:
8942:
8695:
8624:
8540:
8534:circular convolution
8453:
8373:
8297:
8250:
8178:
8002:
7965:
7891:
7844:
7758:
7597:
7483:
7444:
7378:
7358:
7328:
7304:
7300:By using the symbol
7274:
7186:
7166:
7137:
7065:
7039:
6972:
6899:
6760:
6633:
6611:
6559:
6539:
6516:
6496:
6476:
6181:
6152:
6132:
5925:
5817:
5803:{\displaystyle y(n)}
5785:
5765:
5745:
5717:
5706:{\displaystyle f(t)}
5688:
5646:
5462:
5439:
5435:with itself, at lag
5428:{\displaystyle f(t)}
5410:
5367:
5356:{\displaystyle f(t)}
5338:
5125:
4939:
4841:
4753:
4680:
4648:
4622:
4588:
4508:
4473:
4397:
4369:
3957:
3926:
3894:
3816:
3728:
3696:
3670:
3601:
3464:
3343:
3211:
3092:
3056:
3023:
2991:
2971:
2967:and will be exactly
2945:
2939:Dirac delta function
2748:
2694:
2614:
2522:
2403:
2369:
2172:
2124:
2094:
1784:
1769:time series analysis
1706:
1513:
1409:
1357:
1326:
1299:
1272:
1261:{\displaystyle \mu }
1252:
1213:
917:
887:
860:
821:
696:
666:
639:
615:
595:
563:
533:
510:
475:
439:
419:
384:
262:
236:
33:Part of a series on
13374:Official statistics
13297:Methods engineering
12978:Seasonal adjustment
12746:Poisson regressions
12666:Bayesian regression
12605:Regression analysis
12585:Partial correlation
12557:Regression analysis
12156:Prediction interval
12151:Likelihood interval
12141:Confidence interval
12133:Interval estimation
12094:Unbiased estimators
11912:Model specification
11792:Up-and-down designs
11480:Partial correlation
11436:Index of dispersion
11354:Interquartile range
11111:2012ITSP...60.2180S
10877:2017SMat...13.1267H
10820:2011BpJ...101.2855E
10808:Biophysical Journal
10645:2011CoPhC.182.1120C
10507:, McGraw-Hill, 1991
9987:degree of coherence
9590:regression analysis
9584:Regression analysis
9348:{\displaystyle n-k}
8808:
8670:. For example, the
7113:
6822:
6695:
6257:
5578:
5507:
4499:Hermitian transpose
3509:
3391:
3256:
3140:
2610:For a WSS process:
843:complex conjugation
580:
378:Pearson correlation
251:{\displaystyle g*f}
13394:Spatial statistics
13274:Medical statistics
13174:First hitting time
13128:Whittle likelihood
12779:Degrees of freedom
12774:Multivariate ANOVA
12707:Heteroscedasticity
12519:Bayesian estimator
12484:Bayesian inference
12333:KolmogorovâSmirnov
12218:Randomization test
12188:Testing hypotheses
12161:Tolerance interval
12072:Maximum likelihood
11967:Exponential family
11900:Density estimation
11860:Statistical theory
11820:Natural experiment
11766:Scientific control
11683:Survey methodology
11369:Standard deviation
11156:Weisstein, Eric W.
11072:(10 August 2017).
10886:10.1039/C6SM02643E
10409:Triple correlation
10404:Scaled correlation
10390:(Galton's problem)
10306:
10274:
10224:
10186:
10162:
10105:medical ultrasound
10032:Patterson function
9872:
9846:
9811:
9767:
9705:
9570:
9550:
9526:
9446:
9377:mean squared error
9365:
9345:
9306:
9279:
9245:
9218:
9198:
9170:
9016:
8948:
8869:
8867:
8794:
8636:{\displaystyle x.}
8633:
8610:
8522:
8438:
8359:
8284:
8236:
8162:
8160:
7984:
7951:
7877:
7830:
7795:
7752:brute force method
7722:
7648:
7561:
7479:may be written as:
7469:
7430:
7374:and is defined as
7364:
7344:
7310:
7280:
7246:
7172:
7143:
7123:
7096:
7060:Hermitian function
7045:
7025:
6952:
6869:
6788:
6742:
6661:
6617:
6597:
6545:
6525:
6502:
6482:
6441:
6439:
6356:
6243:
6232:
6158:
6138:
6112:
6110:
5901:
5860:
5800:
5771:
5751:
5723:
5703:
5670:
5629:
5561:
5490:
5445:
5425:
5392:
5353:
5297:
5111:
4915:
4827:
4715:
4666:
4634:
4608:
4574:
4487:
4457:
4377:
4353:
4347:
3938:
3908:
3877:
3783:
3704:
3682:
3656:
3573:
3492:
3449:
3374:
3321:
3239:
3196:
3123:
3072:
3039:
2997:
2977:
2957:
2916:
2722:
2680:
2593:
2508:
2385:
2335:
2145:
2110:
2078:
1750:
1687:
1489:
1389:
1339:
1312:
1285:
1258:
1234:
1183:
900:
873:
827:
804:
679:
652:
621:
601:
581:
566:
546:
516:
488:
445:
425:
405:
293:serial correlation
286:
274:
248:
206:
60:For random vectors
13514:Signal processing
13496:
13495:
13434:
13433:
13430:
13429:
13369:National accounts
13339:Actuarial science
13331:Social statistics
13224:
13223:
13220:
13219:
13216:
13215:
13151:Survival function
13136:
13135:
12998:Granger causality
12839:Contingency table
12814:Survival analysis
12791:
12790:
12787:
12786:
12643:Linear regression
12538:
12537:
12534:
12533:
12509:Credible interval
12478:
12477:
12261:
12260:
12077:Method of moments
11946:Parametric family
11907:Statistical model
11837:
11836:
11833:
11832:
11751:Random assignment
11673:Statistical power
11607:
11606:
11603:
11602:
11452:Contingency table
11422:
11421:
11289:Generalized/power
11159:"Autocorrelation"
11085:978-1-119-40110-0
11061:978-0-02-365070-3
10927:978-0-8493-9195-8
10814:(12): 2855â2870.
10788:978-1-59718-013-9
10764:Statistical Ideas
10718:978-0-521-43541-3
10531:978-0-07-282538-1
10488:978-3-319-68074-3
10458:978-0-521-86470-1
10363:Cross-correlation
10199:If a time series
10189:{\displaystyle s}
10172:in the series is
10165:{\displaystyle t}
10135:Serial dependence
10130:Serial dependence
10096:(specifically in
10054:cross-correlation
9953:propagation delay
9573:{\displaystyle X}
9553:{\displaystyle k}
9368:{\displaystyle n}
9091:
9044:
8951:{\displaystyle n}
8887:complex conjugate
7816:
7786:
7681:
7627:
7544:
7367:{\displaystyle f}
7313:{\displaystyle *}
7295:cross-correlation
7265:periodic function
7146:{\displaystyle f}
7048:{\displaystyle f}
6860:
6733:
6620:{\displaystyle T}
6505:{\displaystyle T}
6485:{\displaystyle f}
6432:
6365:
6341:
6295:
6241:
6217:
6161:{\displaystyle n}
6141:{\displaystyle t}
6098:
6009:
5899:
5845:
5754:{\displaystyle R}
5726:{\displaystyle t}
5682:complex conjugate
5668:
5616:
5545:
5404:cross-correlation
5317:signal processing
4893:
4805:
4422:
3841:
3084:Fourier transform
2980:{\displaystyle 0}
2588:
2506:
2399:can be stated as
2361:Symmetry property
2333:
2315:
2239:
2073:
2029:
1917:
1685:
1658:
1612:
1476:
1268:and the variance
1168:
1119:
1072:
784:
624:{\displaystyle t}
604:{\displaystyle t}
519:{\displaystyle t}
498:is the value (or
448:{\displaystyle t}
428:{\displaystyle t}
329:signal processing
214:cross-correlation
190:
189:
16:(Redirected from
13526:
13484:
13483:
13472:
13471:
13461:
13460:
13446:
13445:
13349:Crime statistics
13243:
13242:
13230:
13229:
13147:
13146:
13113:Fourier analysis
13100:Frequency domain
13080:
13027:
12993:Structural break
12953:
12952:
12902:Cluster analysis
12849:Log-linear model
12822:
12821:
12797:
12796:
12738:
12712:Homoscedasticity
12568:
12567:
12544:
12543:
12463:
12455:
12447:
12446:(KruskalâWallis)
12431:
12416:
12371:Cross validation
12356:
12338:AndersonâDarling
12285:
12272:
12271:
12243:Likelihood-ratio
12235:Parametric tests
12213:Permutation test
12196:1- & 2-tails
12087:Minimum distance
12059:Point estimation
12055:
12054:
12006:Optimal decision
11957:
11856:
11855:
11843:
11842:
11825:Quasi-experiment
11775:Adaptive designs
11626:
11625:
11613:
11612:
11490:Rank correlation
11252:
11251:
11243:
11242:
11230:
11229:
11197:
11190:
11183:
11174:
11173:
11169:
11168:
11122:
11089:
11065:
11049:
11026:
11025:
11023:
11021:
11015:
11008:
10999:
10993:
10992:
10987:. Archived from
10974:
10968:
10967:
10938:
10932:
10931:
10913:
10907:
10906:
10888:
10871:(6): 1267â1275.
10856:
10850:
10849:
10839:
10799:
10793:
10792:
10774:
10768:
10767:
10756:
10750:
10749:
10729:
10723:
10722:
10706:
10696:
10690:
10689:
10671:
10665:
10664:
10638:
10629:(5): 1120â1129.
10617:
10611:
10610:
10592:
10586:
10585:
10567:
10561:
10560:
10542:
10536:
10535:
10517:
10508:
10501:
10490:
10480:
10463:
10462:
10444:
10315:
10313:
10312:
10307:
10283:
10281:
10280:
10275:
10270:
10269:
10257:
10256:
10233:
10231:
10230:
10225:
10223:
10219:
10218:
10195:
10193:
10192:
10187:
10171:
10169:
10168:
10163:
10123:numerical relays
9947:Utilized in the
9881:
9879:
9878:
9873:
9855:
9853:
9852:
9847:
9820:
9818:
9817:
9812:
9776:
9774:
9773:
9768:
9714:
9712:
9711:
9706:
9704:
9703:
9594:time series data
9579:
9577:
9576:
9571:
9559:
9557:
9556:
9551:
9535:
9533:
9532:
9527:
9522:
9521:
9501:
9500:
9481:
9480:
9455:
9453:
9452:
9447:
9442:
9441:
9415:
9414:
9401:
9400:
9374:
9372:
9371:
9366:
9354:
9352:
9351:
9346:
9315:
9313:
9312:
9307:
9305:
9304:
9288:
9286:
9285:
9280:
9254:
9252:
9251:
9246:
9244:
9243:
9227:
9225:
9224:
9219:
9207:
9205:
9204:
9199:
9179:
9177:
9176:
9171:
9160:
9159:
9132:
9131:
9118:
9107:
9092:
9090:
9089:
9088:
9060:
9046:
9045:
9037:
9025:
9023:
9022:
9017:
9012:
9011:
8991:
8990:
8977:
8976:
8957:
8955:
8954:
8949:
8925:
8910:
8899:
8895:
8878:
8876:
8875:
8870:
8868:
8807:
8802:
8784:
8783:
8711:
8710:
8684:
8669:
8658:
8642:
8640:
8639:
8634:
8619:
8617:
8616:
8611:
8555:
8554:
8531:
8529:
8528:
8523:
8447:
8445:
8444:
8439:
8416:
8415:
8388:
8387:
8368:
8366:
8365:
8360:
8340:
8339:
8312:
8311:
8293:
8291:
8290:
8285:
8265:
8264:
8245:
8243:
8242:
8237:
8193:
8192:
8171:
8169:
8168:
8163:
8161:
8127:
8106:
8105:
8079:
8078:
8054:
8008:
7997:
7993:
7991:
7990:
7985:
7977:
7976:
7960:
7958:
7957:
7952:
7941:
7940:
7922:
7921:
7903:
7902:
7886:
7884:
7883:
7878:
7839:
7837:
7836:
7831:
7829:
7828:
7817:
7809:
7805:
7804:
7794:
7773:
7772:
7731:
7729:
7728:
7723:
7718:
7717:
7682:
7674:
7670:
7669:
7647:
7585:three dimensions
7570:
7568:
7567:
7562:
7545:
7537:
7532:
7531:
7498:
7497:
7478:
7476:
7475:
7470:
7459:
7458:
7439:
7437:
7436:
7431:
7393:
7392:
7373:
7371:
7370:
7365:
7353:
7351:
7350:
7345:
7343:
7342:
7319:
7317:
7316:
7311:
7289:
7287:
7286:
7281:
7255:
7253:
7252:
7247:
7236:
7235:
7220:
7206:
7205:
7193:
7181:
7179:
7178:
7173:
7155:complex function
7152:
7150:
7149:
7144:
7132:
7130:
7129:
7124:
7112:
7107:
7080:
7079:
7054:
7052:
7051:
7046:
7034:
7032:
7031:
7026:
7015:
7014:
6987:
6986:
6961:
6959:
6958:
6953:
6939:
6938:
6914:
6913:
6878:
6876:
6875:
6870:
6861:
6856:
6836:
6821:
6814:
6813:
6803:
6802:
6801:
6775:
6774:
6751:
6749:
6748:
6743:
6734:
6729:
6715:
6694:
6687:
6686:
6676:
6675:
6674:
6648:
6647:
6626:
6624:
6623:
6618:
6606:
6604:
6603:
6600:{\displaystyle }
6598:
6587:
6586:
6574:
6573:
6554:
6552:
6551:
6546:
6534:
6532:
6531:
6526:
6511:
6509:
6508:
6503:
6491:
6489:
6488:
6483:
6450:
6448:
6447:
6442:
6440:
6433:
6428:
6408:
6392:
6381:
6366:
6358:
6355:
6324:
6323:
6304:
6303:
6296:
6291:
6277:
6256:
6251:
6242:
6234:
6231:
6200:
6199:
6167:
6165:
6164:
6159:
6147:
6145:
6144:
6139:
6121:
6119:
6118:
6113:
6111:
6104:
6100:
6099:
6094:
6074:
6032:
6031:
6015:
6011:
6010:
6005:
5985:
5944:
5943:
5910:
5908:
5907:
5902:
5900:
5895:
5875:
5859:
5832:
5831:
5809:
5807:
5806:
5801:
5780:
5778:
5777:
5772:
5760:
5758:
5757:
5752:
5732:
5730:
5729:
5724:
5712:
5710:
5709:
5704:
5679:
5677:
5676:
5671:
5669:
5664:
5650:
5638:
5636:
5635:
5630:
5625:
5624:
5617:
5612:
5592:
5577:
5572:
5554:
5553:
5546:
5541:
5527:
5506:
5501:
5477:
5476:
5454:
5452:
5451:
5446:
5434:
5432:
5431:
5426:
5401:
5399:
5398:
5393:
5382:
5381:
5362:
5360:
5359:
5354:
5306:
5304:
5303:
5298:
5296:
5295:
5294:
5284:
5267:
5250:
5249:
5248:
5243:
5227:
5226:
5225:
5212:
5195:
5181:
5164:
5144:
5143:
5142:
5137:
5120:
5118:
5117:
5112:
5110:
5109:
5108:
5098:
5081:
5064:
5063:
5062:
5057:
5041:
5040:
5039:
5026:
5009:
4995:
4978:
4958:
4957:
4956:
4951:
4924:
4922:
4921:
4916:
4914:
4913:
4908:
4899:
4894:
4891:
4882:
4874:
4873:
4872:
4867:
4857:
4856:
4855:
4849:
4836:
4834:
4833:
4828:
4826:
4825:
4820:
4811:
4806:
4803:
4794:
4786:
4785:
4784:
4779:
4769:
4768:
4767:
4761:
4740:symmetric matrix
4736:Hermitian matrix
4724:
4722:
4721:
4716:
4711:
4710:
4701:
4700:
4675:
4673:
4672:
4667:
4643:
4641:
4640:
4635:
4617:
4615:
4614:
4609:
4607:
4606:
4605:
4600:
4583:
4581:
4580:
4575:
4573:
4572:
4571:
4565:
4561:
4560:
4559:
4547:
4546:
4534:
4533:
4515:
4504:For example, if
4496:
4494:
4493:
4488:
4486:
4485:
4484:
4478:
4466:
4464:
4463:
4458:
4450:
4449:
4448:
4442:
4436:
4420:
4416:
4415:
4414:
4409:
4386:
4384:
4383:
4378:
4376:
4362:
4360:
4359:
4354:
4352:
4351:
4345:
4338:
4337:
4328:
4327:
4299:
4298:
4289:
4288:
4265:
4264:
4255:
4254:
4233:
4208:
4201:
4200:
4191:
4190:
4162:
4161:
4152:
4151:
4128:
4127:
4118:
4117:
4096:
4089:
4088:
4079:
4078:
4050:
4049:
4040:
4039:
4016:
4015:
4006:
4005:
3976:
3975:
3974:
3969:
3947:
3945:
3944:
3939:
3917:
3915:
3914:
3909:
3907:
3906:
3905:
3899:
3886:
3884:
3883:
3878:
3876:
3872:
3871:
3870:
3869:
3863:
3857:
3839:
3835:
3834:
3833:
3828:
3792:
3790:
3789:
3784:
3782:
3781:
3780:
3770:
3769:
3751:
3750:
3735:
3713:
3711:
3710:
3705:
3703:
3691:
3689:
3688:
3683:
3665:
3663:
3662:
3657:
3655:
3654:
3653:
3643:
3642:
3624:
3623:
3608:
3582:
3580:
3579:
3574:
3566:
3565:
3522:
3521:
3508:
3503:
3479:
3478:
3458:
3456:
3455:
3450:
3445:
3444:
3404:
3403:
3390:
3385:
3358:
3357:
3330:
3328:
3327:
3322:
3314:
3313:
3306:
3305:
3269:
3268:
3255:
3250:
3226:
3225:
3205:
3203:
3202:
3197:
3192:
3191:
3184:
3183:
3153:
3152:
3139:
3134:
3107:
3106:
3081:
3079:
3078:
3073:
3071:
3070:
3048:
3046:
3045:
3040:
3038:
3037:
3006:
3004:
3003:
2998:
2986:
2984:
2983:
2978:
2966:
2964:
2963:
2958:
2925:
2923:
2922:
2917:
2915:
2911:
2910:
2909:
2904:
2898:
2897:
2896:
2895:
2881:
2865:
2861:
2860:
2859:
2854:
2848:
2847:
2846:
2845:
2831:
2812:
2811:
2806:
2802:
2798:
2797:
2785:
2784:
2769:
2768:
2732:is always real.
2731:
2729:
2728:
2723:
2709:
2708:
2689:
2687:
2686:
2681:
2667:
2666:
2651:
2647:
2634:
2633:
2602:
2600:
2599:
2594:
2589:
2584:
2568:
2567:
2554:
2537:
2536:
2517:
2515:
2514:
2509:
2507:
2502:
2498:
2497:
2485:
2484:
2469:
2468:
2455:
2447:
2446:
2434:
2433:
2418:
2417:
2394:
2392:
2391:
2386:
2384:
2383:
2344:
2342:
2341:
2336:
2334:
2332:
2331:
2322:
2321:
2317:
2316:
2311:
2301:
2300:
2287:
2276:
2275:
2245:
2240:
2238:
2237:
2228:
2215:
2214:
2201:
2187:
2186:
2157:anti-correlation
2154:
2152:
2151:
2148:{\displaystyle }
2146:
2119:
2117:
2116:
2111:
2109:
2108:
2090:If the function
2087:
2085:
2084:
2079:
2074:
2072:
2071:
2070:
2069:
2068:
2054:
2053:
2052:
2051:
2036:
2035:
2031:
2030:
2025:
2021:
2020:
2019:
2018:
2001:
2000:
1999:
1998:
1980:
1975:
1974:
1973:
1972:
1955:
1954:
1953:
1952:
1923:
1918:
1916:
1915:
1914:
1913:
1912:
1898:
1897:
1896:
1895:
1880:
1876:
1875:
1863:
1862:
1847:
1846:
1833:
1825:
1824:
1812:
1811:
1799:
1798:
1759:
1757:
1756:
1751:
1746:
1745:
1721:
1720:
1696:
1694:
1693:
1688:
1686:
1678:
1670:
1666:
1665:
1664:
1659:
1651:
1648:
1647:
1618:
1614:
1613:
1608:
1598:
1597:
1584:
1573:
1572:
1528:
1527:
1498:
1496:
1495:
1490:
1488:
1484:
1483:
1482:
1477:
1469:
1466:
1465:
1424:
1423:
1398:
1396:
1395:
1390:
1388:
1387:
1375:
1374:
1348:
1346:
1345:
1340:
1338:
1337:
1321:
1319:
1318:
1313:
1311:
1310:
1294:
1292:
1291:
1286:
1284:
1283:
1267:
1265:
1264:
1259:
1243:
1241:
1240:
1235:
1233:
1229:
1228:
1192:
1190:
1189:
1184:
1182:
1181:
1180:
1179:
1169:
1161:
1158:
1157:
1156:
1155:
1138:
1134:
1133:
1132:
1131:
1130:
1120:
1112:
1109:
1108:
1107:
1106:
1078:
1074:
1073:
1068:
1064:
1063:
1062:
1061:
1044:
1043:
1042:
1041:
1023:
1018:
1017:
1016:
1015:
998:
997:
996:
995:
961:
960:
948:
947:
932:
931:
909:
907:
906:
901:
899:
898:
882:
880:
879:
874:
872:
871:
836:
834:
833:
828:
813:
811:
810:
805:
803:
799:
798:
797:
796:
795:
785:
777:
774:
773:
772:
771:
740:
739:
727:
726:
711:
710:
688:
686:
685:
680:
678:
677:
661:
659:
658:
653:
651:
650:
630:
628:
627:
622:
610:
608:
607:
602:
590:
588:
587:
582:
579:
574:
555:
553:
552:
547:
545:
544:
525:
523:
522:
517:
497:
495:
494:
489:
487:
486:
454:
452:
451:
446:
434:
432:
431:
426:
414:
412:
411:
406:
404:
400:
399:
283:
281:
280:
275:
257:
255:
254:
249:
231:
227:
223:
182:
175:
168:
52:
30:
29:
21:
13534:
13533:
13529:
13528:
13527:
13525:
13524:
13523:
13509:Autocorrelation
13499:
13498:
13497:
13492:
13455:
13426:
13388:
13325:
13311:quality control
13278:
13260:Clinical trials
13237:
13212:
13196:
13184:Hazard function
13178:
13132:
13094:
13078:
13041:
13037:BreuschâGodfrey
13025:
13002:
12942:
12917:Factor analysis
12863:
12844:Graphical model
12816:
12783:
12750:
12736:
12716:
12670:
12637:
12599:
12562:
12561:
12530:
12474:
12461:
12453:
12445:
12429:
12414:
12393:Rank statistics
12387:
12366:Model selection
12354:
12312:Goodness of fit
12306:
12283:
12257:
12229:
12182:
12127:
12116:Median unbiased
12044:
11955:
11888:Order statistic
11850:
11829:
11796:
11770:
11722:
11677:
11620:
11618:Data collection
11599:
11511:
11466:
11440:
11418:
11378:
11330:
11247:Continuous data
11237:
11224:
11206:
11201:
11086:
11062:
11035:
11033:Further reading
11030:
11029:
11019:
11017:
11013:
11006:
11000:
10996:
10975:
10971:
10939:
10935:
10928:
10914:
10910:
10857:
10853:
10800:
10796:
10789:
10781:. Stata Press.
10775:
10771:
10758:
10757:
10753:
10730:
10726:
10719:
10697:
10693:
10686:
10672:
10668:
10618:
10614:
10607:
10593:
10589:
10582:
10568:
10564:
10557:
10543:
10539:
10532:
10518:
10511:
10502:
10493:
10481:
10466:
10459:
10445:
10428:
10423:
10418:
10322:
10289:
10286:
10285:
10265:
10261:
10252:
10248:
10243:
10240:
10239:
10214:
10210:
10206:
10204:
10201:
10200:
10181:
10178:
10177:
10157:
10154:
10153:
10150:random variable
10132:
10085:In analysis of
9976:surface science
9941:speckle pattern
9907:optical spectra
9888:
9861:
9858:
9857:
9826:
9823:
9822:
9782:
9779:
9778:
9747:
9744:
9743:
9699:
9695:
9693:
9690:
9689:
9688:distributed as
9641:standard errors
9586:
9565:
9562:
9561:
9545:
9542:
9541:
9517:
9513:
9490:
9486:
9470:
9466:
9461:
9458:
9457:
9431:
9427:
9410:
9406:
9396:
9392:
9387:
9384:
9383:
9360:
9357:
9356:
9334:
9331:
9330:
9319:biased estimate
9300:
9296:
9294:
9291:
9290:
9274:
9271:
9270:
9239:
9235:
9233:
9230:
9229:
9213:
9210:
9209:
9187:
9184:
9183:
9149:
9145:
9127:
9123:
9108:
9097:
9084:
9080:
9064:
9059:
9036:
9035:
9033:
9030:
9029:
9007:
9003:
8986:
8982:
8972:
8968:
8963:
8960:
8959:
8943:
8940:
8939:
8932:
8916:
8901:
8897:
8893:
8866:
8865:
8834:
8819:
8818:
8803:
8798:
8779:
8775:
8768:
8753:
8752:
8721:
8706:
8702:
8698:
8696:
8693:
8692:
8675:
8660:
8654:
8625:
8622:
8621:
8547:
8543:
8541:
8538:
8537:
8454:
8451:
8450:
8408:
8404:
8380:
8376:
8374:
8371:
8370:
8332:
8328:
8304:
8300:
8298:
8295:
8294:
8257:
8253:
8251:
8248:
8247:
8185:
8181:
8179:
8176:
8175:
8159:
8158:
8150:
8145:
8140:
8135:
8125:
8124:
8116:
8111:
8104:
8098:
8097:
8089:
8084:
8076:
8075:
8070:
8062:
8052:
8051:
8043:
8038:
8033:
8027:
8026:
8018:
8013:
8005:
8003:
8000:
7999:
7995:
7972:
7968:
7966:
7963:
7962:
7936:
7932:
7917:
7913:
7898:
7894:
7892:
7889:
7888:
7845:
7842:
7841:
7818:
7808:
7807:
7800:
7796:
7790:
7765:
7761:
7759:
7756:
7755:
7740:
7683:
7673:
7672:
7653:
7649:
7631:
7598:
7595:
7594:
7589:discrete signal
7577:
7536:
7524:
7520:
7490:
7486:
7484:
7481:
7480:
7451:
7447:
7445:
7442:
7441:
7385:
7381:
7379:
7376:
7375:
7359:
7356:
7355:
7335:
7331:
7329:
7326:
7325:
7305:
7302:
7301:
7275:
7272:
7271:
7228:
7224:
7216:
7198:
7194:
7189:
7187:
7184:
7183:
7167:
7164:
7163:
7138:
7135:
7134:
7108:
7100:
7072:
7068:
7066:
7063:
7062:
7040:
7037:
7036:
7007:
7003:
6979:
6975:
6973:
6970:
6969:
6931:
6927:
6906:
6902:
6900:
6897:
6896:
6884:
6837:
6835:
6809:
6805:
6804:
6797:
6793:
6792:
6767:
6763:
6761:
6758:
6757:
6716:
6714:
6682:
6678:
6677:
6670:
6666:
6665:
6640:
6636:
6634:
6631:
6630:
6612:
6609:
6608:
6582:
6578:
6569:
6565:
6560:
6557:
6556:
6540:
6537:
6536:
6517:
6514:
6513:
6497:
6494:
6493:
6477:
6474:
6473:
6470:
6438:
6437:
6409:
6407:
6382:
6371:
6357:
6345:
6334:
6316:
6312:
6309:
6308:
6299:
6298:
6278:
6276:
6252:
6247:
6233:
6221:
6210:
6192:
6188:
6184:
6182:
6179:
6178:
6153:
6150:
6149:
6133:
6130:
6129:
6109:
6108:
6075:
6073:
6059:
6055:
6042:
6024:
6020:
6017:
6016:
5986:
5984:
5971:
5967:
5954:
5936:
5932:
5928:
5926:
5923:
5922:
5912:
5876:
5874:
5849:
5824:
5820:
5818:
5815:
5814:
5786:
5783:
5782:
5766:
5763:
5762:
5746:
5743:
5742:
5739:
5718:
5715:
5714:
5689:
5686:
5685:
5680:represents the
5651:
5649:
5647:
5644:
5643:
5640:
5620:
5619:
5593:
5591:
5573:
5565:
5549:
5548:
5528:
5526:
5502:
5494:
5469:
5465:
5463:
5460:
5459:
5440:
5437:
5436:
5411:
5408:
5407:
5374:
5370:
5368:
5365:
5364:
5339:
5336:
5335:
5329:
5313:
5290:
5289:
5285:
5280:
5263:
5244:
5239:
5238:
5234:
5221:
5220:
5216:
5208:
5191:
5177:
5160:
5138:
5133:
5132:
5128:
5126:
5123:
5122:
5104:
5103:
5099:
5094:
5077:
5058:
5053:
5052:
5048:
5035:
5034:
5030:
5022:
5005:
4991:
4974:
4952:
4947:
4946:
4942:
4940:
4937:
4936:
4909:
4904:
4903:
4895:
4890:
4878:
4868:
4863:
4862:
4858:
4851:
4850:
4845:
4844:
4842:
4839:
4838:
4821:
4816:
4815:
4807:
4802:
4790:
4780:
4775:
4774:
4770:
4763:
4762:
4757:
4756:
4754:
4751:
4750:
4731:
4706:
4702:
4696:
4692:
4681:
4678:
4677:
4649:
4646:
4645:
4623:
4620:
4619:
4601:
4596:
4595:
4591:
4589:
4586:
4585:
4567:
4566:
4555:
4551:
4542:
4538:
4529:
4525:
4524:
4520:
4519:
4511:
4509:
4506:
4505:
4480:
4479:
4477:
4476:
4474:
4471:
4470:
4444:
4443:
4438:
4437:
4432:
4410:
4405:
4404:
4400:
4398:
4395:
4394:
4372:
4370:
4367:
4366:
4346:
4343:
4342:
4333:
4329:
4323:
4319:
4308:
4303:
4294:
4290:
4284:
4280:
4269:
4260:
4256:
4250:
4246:
4234:
4231:
4230:
4225:
4220:
4215:
4209:
4206:
4205:
4196:
4192:
4186:
4182:
4171:
4166:
4157:
4153:
4147:
4143:
4132:
4123:
4119:
4113:
4109:
4097:
4094:
4093:
4084:
4080:
4074:
4070:
4059:
4054:
4045:
4041:
4035:
4031:
4020:
4011:
4007:
4001:
3997:
3981:
3980:
3970:
3965:
3964:
3960:
3958:
3955:
3954:
3927:
3924:
3923:
3901:
3900:
3898:
3897:
3895:
3892:
3891:
3888:
3865:
3864:
3859:
3858:
3853:
3852:
3848:
3829:
3824:
3823:
3819:
3817:
3814:
3813:
3795:random elements
3776:
3775:
3771:
3765:
3761:
3746:
3742:
3731:
3729:
3726:
3725:
3699:
3697:
3694:
3693:
3671:
3668:
3667:
3649:
3648:
3644:
3638:
3634:
3619:
3615:
3604:
3602:
3599:
3598:
3588:
3561:
3560:
3514:
3510:
3504:
3496:
3471:
3467:
3465:
3462:
3461:
3440:
3439:
3396:
3392:
3386:
3378:
3350:
3346:
3344:
3341:
3340:
3309:
3308:
3286:
3282:
3261:
3257:
3251:
3243:
3218:
3214:
3212:
3209:
3208:
3187:
3186:
3167:
3163:
3145:
3141:
3135:
3127:
3099:
3095:
3093:
3090:
3089:
3063:
3059:
3057:
3054:
3053:
3030:
3026:
3024:
3021:
3020:
3013:
2992:
2989:
2988:
2972:
2969:
2968:
2946:
2943:
2942:
2931:
2905:
2900:
2899:
2891:
2887:
2886:
2882:
2877:
2876:
2872:
2855:
2850:
2849:
2841:
2837:
2836:
2832:
2827:
2826:
2822:
2807:
2793:
2789:
2780:
2776:
2761:
2757:
2756:
2752:
2751:
2749:
2746:
2745:
2738:
2701:
2697:
2695:
2692:
2691:
2659:
2655:
2626:
2622:
2621:
2617:
2615:
2612:
2611:
2608:
2606:Maximum at zero
2560:
2556:
2555:
2553:
2529:
2525:
2523:
2520:
2519:
2493:
2489:
2480:
2476:
2461:
2457:
2456:
2454:
2442:
2438:
2429:
2425:
2410:
2406:
2404:
2401:
2400:
2376:
2372:
2370:
2367:
2366:
2363:
2358:
2327:
2323:
2296:
2292:
2288:
2286:
2265:
2261:
2257:
2253:
2246:
2244:
2233:
2229:
2207:
2203:
2202:
2200:
2179:
2175:
2173:
2170:
2169:
2125:
2122:
2121:
2101:
2097:
2095:
2092:
2091:
2064:
2060:
2059:
2055:
2047:
2043:
2042:
2038:
2037:
2014:
2010:
2009:
2005:
1994:
1990:
1989:
1985:
1981:
1979:
1968:
1964:
1963:
1959:
1948:
1944:
1943:
1939:
1935:
1931:
1924:
1922:
1908:
1904:
1903:
1899:
1891:
1887:
1886:
1882:
1881:
1871:
1867:
1858:
1854:
1839:
1835:
1834:
1832:
1820:
1816:
1807:
1803:
1791:
1787:
1785:
1782:
1781:
1765:
1741:
1737:
1713:
1709:
1707:
1704:
1703:
1698:
1677:
1660:
1650:
1649:
1637:
1633:
1632:
1628:
1593:
1589:
1585:
1583:
1562:
1558:
1554:
1550:
1520:
1516:
1514:
1511:
1510:
1500:
1478:
1468:
1467:
1455:
1451:
1450:
1446:
1416:
1412:
1410:
1407:
1406:
1383:
1379:
1370:
1366:
1358:
1355:
1354:
1333:
1329:
1327:
1324:
1323:
1306:
1302:
1300:
1297:
1296:
1279:
1275:
1273:
1270:
1269:
1253:
1250:
1249:
1224:
1220:
1216:
1214:
1211:
1210:
1207:
1194:
1175:
1171:
1170:
1160:
1159:
1151:
1147:
1146:
1142:
1126:
1122:
1121:
1111:
1110:
1102:
1098:
1097:
1093:
1092:
1088:
1057:
1053:
1052:
1048:
1037:
1033:
1032:
1028:
1024:
1022:
1011:
1007:
1006:
1002:
991:
987:
986:
982:
978:
974:
956:
952:
943:
939:
924:
920:
918:
915:
914:
894:
890:
888:
885:
884:
867:
863:
861:
858:
857:
822:
819:
818:
815:
791:
787:
786:
776:
775:
767:
763:
762:
758:
757:
753:
735:
731:
722:
718:
703:
699:
697:
694:
693:
673:
669:
667:
664:
663:
646:
642:
640:
637:
636:
616:
613:
612:
596:
593:
592:
575:
570:
564:
561:
560:
540:
536:
534:
531:
530:
511:
508:
507:
482:
478:
476:
473:
472:
471:process). Then
469:continuous-time
440:
437:
436:
420:
417:
416:
395:
391:
387:
385:
382:
381:
366:
313:periodic signal
309:random variable
289:Autocorrelation
263:
260:
259:
237:
234:
233:
229:
225:
221:
218:autocorrelation
186:
157:
156:
132:
122:
121:
97:
87:
86:
62:
28:
23:
22:
15:
12:
11:
5:
13532:
13522:
13521:
13516:
13511:
13494:
13493:
13491:
13490:
13478:
13466:
13452:
13439:
13436:
13435:
13432:
13431:
13428:
13427:
13425:
13424:
13419:
13414:
13409:
13404:
13398:
13396:
13390:
13389:
13387:
13386:
13381:
13376:
13371:
13366:
13361:
13356:
13351:
13346:
13341:
13335:
13333:
13327:
13326:
13324:
13323:
13318:
13313:
13304:
13299:
13294:
13288:
13286:
13280:
13279:
13277:
13276:
13271:
13266:
13257:
13255:Bioinformatics
13251:
13249:
13239:
13238:
13226:
13225:
13222:
13221:
13218:
13217:
13214:
13213:
13211:
13210:
13204:
13202:
13198:
13197:
13195:
13194:
13188:
13186:
13180:
13179:
13177:
13176:
13171:
13166:
13161:
13155:
13153:
13144:
13138:
13137:
13134:
13133:
13131:
13130:
13125:
13120:
13115:
13110:
13104:
13102:
13096:
13095:
13093:
13092:
13087:
13082:
13074:
13069:
13064:
13063:
13062:
13060:partial (PACF)
13051:
13049:
13043:
13042:
13040:
13039:
13034:
13029:
13021:
13016:
13010:
13008:
13007:Specific tests
13004:
13003:
13001:
13000:
12995:
12990:
12985:
12980:
12975:
12970:
12965:
12959:
12957:
12950:
12944:
12943:
12941:
12940:
12939:
12938:
12937:
12936:
12921:
12920:
12919:
12909:
12907:Classification
12904:
12899:
12894:
12889:
12884:
12879:
12873:
12871:
12865:
12864:
12862:
12861:
12856:
12854:McNemar's test
12851:
12846:
12841:
12836:
12830:
12828:
12818:
12817:
12793:
12792:
12789:
12788:
12785:
12784:
12782:
12781:
12776:
12771:
12766:
12760:
12758:
12752:
12751:
12749:
12748:
12732:
12726:
12724:
12718:
12717:
12715:
12714:
12709:
12704:
12699:
12694:
12692:Semiparametric
12689:
12684:
12678:
12676:
12672:
12671:
12669:
12668:
12663:
12658:
12653:
12647:
12645:
12639:
12638:
12636:
12635:
12630:
12625:
12620:
12615:
12609:
12607:
12601:
12600:
12598:
12597:
12592:
12587:
12582:
12576:
12574:
12564:
12563:
12560:
12559:
12554:
12548:
12540:
12539:
12536:
12535:
12532:
12531:
12529:
12528:
12527:
12526:
12516:
12511:
12506:
12505:
12504:
12499:
12488:
12486:
12480:
12479:
12476:
12475:
12473:
12472:
12467:
12466:
12465:
12457:
12449:
12433:
12430:(MannâWhitney)
12425:
12424:
12423:
12410:
12409:
12408:
12397:
12395:
12389:
12388:
12386:
12385:
12384:
12383:
12378:
12373:
12363:
12358:
12355:(ShapiroâWilk)
12350:
12345:
12340:
12335:
12330:
12322:
12316:
12314:
12308:
12307:
12305:
12304:
12296:
12287:
12275:
12269:
12267:Specific tests
12263:
12262:
12259:
12258:
12256:
12255:
12250:
12245:
12239:
12237:
12231:
12230:
12228:
12227:
12222:
12221:
12220:
12210:
12209:
12208:
12198:
12192:
12190:
12184:
12183:
12181:
12180:
12179:
12178:
12173:
12163:
12158:
12153:
12148:
12143:
12137:
12135:
12129:
12128:
12126:
12125:
12120:
12119:
12118:
12113:
12112:
12111:
12106:
12091:
12090:
12089:
12084:
12079:
12074:
12063:
12061:
12052:
12046:
12045:
12043:
12042:
12037:
12032:
12031:
12030:
12020:
12015:
12014:
12013:
12003:
12002:
12001:
11996:
11991:
11981:
11976:
11971:
11970:
11969:
11964:
11959:
11943:
11942:
11941:
11936:
11931:
11921:
11920:
11919:
11914:
11904:
11903:
11902:
11892:
11891:
11890:
11880:
11875:
11870:
11864:
11862:
11852:
11851:
11839:
11838:
11835:
11834:
11831:
11830:
11828:
11827:
11822:
11817:
11812:
11806:
11804:
11798:
11797:
11795:
11794:
11789:
11784:
11778:
11776:
11772:
11771:
11769:
11768:
11763:
11758:
11753:
11748:
11743:
11738:
11732:
11730:
11724:
11723:
11721:
11720:
11718:Standard error
11715:
11710:
11705:
11704:
11703:
11698:
11687:
11685:
11679:
11678:
11676:
11675:
11670:
11665:
11660:
11655:
11650:
11648:Optimal design
11645:
11640:
11634:
11632:
11622:
11621:
11609:
11608:
11605:
11604:
11601:
11600:
11598:
11597:
11592:
11587:
11582:
11577:
11572:
11567:
11562:
11557:
11552:
11547:
11542:
11537:
11532:
11527:
11521:
11519:
11513:
11512:
11510:
11509:
11504:
11503:
11502:
11497:
11487:
11482:
11476:
11474:
11468:
11467:
11465:
11464:
11459:
11454:
11448:
11446:
11445:Summary tables
11442:
11441:
11439:
11438:
11432:
11430:
11424:
11423:
11420:
11419:
11417:
11416:
11415:
11414:
11409:
11404:
11394:
11388:
11386:
11380:
11379:
11377:
11376:
11371:
11366:
11361:
11356:
11351:
11346:
11340:
11338:
11332:
11331:
11329:
11328:
11323:
11318:
11317:
11316:
11311:
11306:
11301:
11296:
11291:
11286:
11281:
11279:Contraharmonic
11276:
11271:
11260:
11258:
11249:
11239:
11238:
11226:
11225:
11223:
11222:
11217:
11211:
11208:
11207:
11200:
11199:
11192:
11185:
11177:
11171:
11170:
11151:
11134:
11123:
11090:
11084:
11066:
11060:
11034:
11031:
11028:
11027:
10994:
10969:
10933:
10926:
10908:
10851:
10794:
10787:
10769:
10766:. 26 May 2014.
10751:
10740:(4): 274â276.
10724:
10717:
10691:
10685:978-0125649018
10684:
10666:
10612:
10606:978-0122673511
10605:
10587:
10581:978-0130607744
10580:
10562:
10556:978-0130617934
10555:
10537:
10530:
10509:
10491:
10464:
10457:
10425:
10424:
10422:
10419:
10417:
10416:
10411:
10406:
10401:
10396:
10391:
10385:
10380:
10375:
10370:
10365:
10360:
10355:
10350:
10344:
10342:Autocorrelator
10339:
10334:
10329:
10323:
10321:
10318:
10305:
10302:
10299:
10296:
10293:
10273:
10268:
10264:
10260:
10255:
10251:
10247:
10222:
10217:
10213:
10209:
10185:
10161:
10131:
10128:
10127:
10126:
10119:
10116:rate of return
10108:
10101:
10090:
10083:
10076:
10073:X-ray binaries
10061:
10042:
10035:
10028:
10005:
9990:
9983:
9972:
9965:
9957:carrier signal
9945:
9925:
9903:
9887:
9884:
9871:
9868:
9865:
9845:
9842:
9839:
9836:
9833:
9830:
9810:
9807:
9804:
9801:
9798:
9795:
9792:
9789:
9786:
9766:
9763:
9760:
9757:
9754:
9751:
9702:
9698:
9668:test statistic
9585:
9582:
9569:
9549:
9538:
9537:
9525:
9520:
9516:
9511:
9508:
9504:
9499:
9496:
9493:
9489:
9484:
9479:
9476:
9473:
9469:
9465:
9445:
9440:
9437:
9434:
9430:
9425:
9422:
9418:
9413:
9409:
9404:
9399:
9395:
9391:
9380:
9364:
9344:
9341:
9338:
9323:
9303:
9299:
9278:
9242:
9238:
9217:
9197:
9194:
9191:
9169:
9166:
9163:
9158:
9155:
9152:
9148:
9144:
9141:
9138:
9135:
9130:
9126:
9122:
9117:
9114:
9111:
9106:
9103:
9100:
9096:
9087:
9083:
9079:
9076:
9073:
9070:
9067:
9063:
9058:
9055:
9052:
9049:
9043:
9040:
9015:
9010:
9006:
9001:
8998:
8994:
8989:
8985:
8980:
8975:
8971:
8967:
8947:
8931:
8928:
8864:
8861:
8858:
8855:
8852:
8849:
8846:
8843:
8840:
8837:
8835:
8833:
8830:
8827:
8824:
8821:
8820:
8817:
8814:
8811:
8806:
8801:
8797:
8793:
8790:
8787:
8782:
8778:
8774:
8771:
8769:
8767:
8764:
8761:
8758:
8755:
8754:
8751:
8748:
8745:
8742:
8739:
8736:
8733:
8730:
8727:
8724:
8722:
8720:
8717:
8714:
8709:
8705:
8701:
8700:
8632:
8629:
8609:
8606:
8603:
8600:
8597:
8594:
8591:
8588:
8585:
8582:
8579:
8576:
8573:
8570:
8567:
8564:
8561:
8558:
8553:
8550:
8546:
8521:
8518:
8515:
8512:
8509:
8506:
8503:
8500:
8497:
8494:
8491:
8488:
8485:
8482:
8479:
8476:
8473:
8470:
8467:
8464:
8461:
8458:
8437:
8434:
8431:
8428:
8425:
8422:
8419:
8414:
8411:
8407:
8403:
8400:
8397:
8394:
8391:
8386:
8383:
8379:
8358:
8355:
8352:
8349:
8346:
8343:
8338:
8335:
8331:
8327:
8324:
8321:
8318:
8315:
8310:
8307:
8303:
8283:
8280:
8277:
8274:
8271:
8268:
8263:
8260:
8256:
8235:
8232:
8229:
8226:
8223:
8220:
8217:
8214:
8211:
8208:
8205:
8202:
8199:
8196:
8191:
8188:
8184:
8157:
8154:
8151:
8149:
8146:
8144:
8141:
8139:
8136:
8134:
8131:
8128:
8126:
8123:
8120:
8117:
8115:
8112:
8110:
8107:
8103:
8100:
8099:
8096:
8093:
8090:
8088:
8085:
8083:
8080:
8077:
8074:
8071:
8069:
8066:
8063:
8061:
8058:
8055:
8053:
8050:
8047:
8044:
8042:
8039:
8037:
8034:
8032:
8029:
8028:
8025:
8022:
8019:
8017:
8014:
8012:
8009:
8007:
7983:
7980:
7975:
7971:
7950:
7947:
7944:
7939:
7935:
7931:
7928:
7925:
7920:
7916:
7912:
7909:
7906:
7901:
7897:
7876:
7873:
7870:
7867:
7864:
7861:
7858:
7855:
7852:
7849:
7827:
7824:
7821:
7815:
7812:
7803:
7799:
7793:
7789:
7785:
7782:
7779:
7776:
7771:
7768:
7764:
7739:
7736:
7721:
7716:
7713:
7710:
7707:
7704:
7701:
7698:
7695:
7692:
7689:
7686:
7680:
7677:
7668:
7665:
7662:
7659:
7656:
7652:
7646:
7643:
7640:
7637:
7634:
7630:
7626:
7623:
7620:
7617:
7614:
7611:
7608:
7605:
7602:
7576:
7573:
7572:
7571:
7560:
7557:
7554:
7551:
7548:
7543:
7540:
7535:
7530:
7527:
7523:
7519:
7516:
7513:
7510:
7507:
7504:
7501:
7496:
7493:
7489:
7468:
7465:
7462:
7457:
7454:
7450:
7429:
7426:
7423:
7420:
7417:
7414:
7411:
7408:
7405:
7402:
7399:
7396:
7391:
7388:
7384:
7363:
7341:
7338:
7334:
7309:
7298:
7291:
7279:
7268:
7261:
7245:
7242:
7239:
7234:
7231:
7227:
7223:
7219:
7215:
7212:
7209:
7204:
7201:
7197:
7192:
7171:
7160:
7159:
7158:
7142:
7122:
7119:
7116:
7111:
7106:
7103:
7099:
7095:
7092:
7089:
7086:
7083:
7078:
7075:
7071:
7056:
7044:
7024:
7021:
7018:
7013:
7010:
7006:
7002:
6999:
6996:
6993:
6990:
6985:
6982:
6978:
6951:
6948:
6945:
6942:
6937:
6934:
6930:
6926:
6923:
6920:
6917:
6912:
6909:
6905:
6883:
6880:
6868:
6865:
6859:
6855:
6852:
6849:
6846:
6843:
6840:
6834:
6831:
6828:
6825:
6820:
6817:
6812:
6808:
6800:
6796:
6791:
6787:
6784:
6781:
6778:
6773:
6770:
6766:
6741:
6738:
6732:
6728:
6725:
6722:
6719:
6713:
6710:
6707:
6704:
6701:
6698:
6693:
6690:
6685:
6681:
6673:
6669:
6664:
6660:
6657:
6654:
6651:
6646:
6643:
6639:
6616:
6596:
6593:
6590:
6585:
6581:
6577:
6572:
6568:
6564:
6544:
6524:
6521:
6501:
6481:
6469:
6466:
6436:
6431:
6427:
6424:
6421:
6418:
6415:
6412:
6405:
6402:
6399:
6396:
6391:
6388:
6385:
6380:
6377:
6374:
6370:
6364:
6361:
6354:
6351:
6348:
6344:
6340:
6337:
6335:
6333:
6330:
6327:
6322:
6319:
6315:
6311:
6310:
6307:
6302:
6294:
6290:
6287:
6284:
6281:
6275:
6272:
6269:
6266:
6263:
6260:
6255:
6250:
6246:
6240:
6237:
6230:
6227:
6224:
6220:
6216:
6213:
6211:
6209:
6206:
6203:
6198:
6195:
6191:
6187:
6186:
6157:
6137:
6107:
6103:
6097:
6093:
6090:
6087:
6084:
6081:
6078:
6071:
6068:
6065:
6062:
6058:
6054:
6051:
6048:
6045:
6043:
6041:
6038:
6035:
6030:
6027:
6023:
6019:
6018:
6014:
6008:
6004:
6001:
5998:
5995:
5992:
5989:
5983:
5980:
5977:
5974:
5970:
5966:
5963:
5960:
5957:
5955:
5953:
5950:
5947:
5942:
5939:
5935:
5931:
5930:
5898:
5894:
5891:
5888:
5885:
5882:
5879:
5872:
5869:
5866:
5863:
5858:
5855:
5852:
5848:
5844:
5841:
5838:
5835:
5830:
5827:
5823:
5812:
5799:
5796:
5793:
5790:
5770:
5750:
5738:
5735:
5722:
5702:
5699:
5696:
5693:
5667:
5663:
5660:
5657:
5654:
5628:
5623:
5615:
5611:
5608:
5605:
5602:
5599:
5596:
5590:
5587:
5584:
5581:
5576:
5571:
5568:
5564:
5560:
5557:
5552:
5544:
5540:
5537:
5534:
5531:
5525:
5522:
5519:
5516:
5513:
5510:
5505:
5500:
5497:
5493:
5489:
5486:
5483:
5480:
5475:
5472:
5468:
5457:
5444:
5424:
5421:
5418:
5415:
5391:
5388:
5385:
5380:
5377:
5373:
5352:
5349:
5346:
5343:
5328:
5325:
5312:
5309:
5308:
5307:
5293:
5288:
5283:
5279:
5276:
5273:
5270:
5266:
5262:
5259:
5256:
5253:
5247:
5242:
5237:
5233:
5230:
5224:
5219:
5215:
5211:
5207:
5204:
5201:
5198:
5194:
5190:
5187:
5184:
5180:
5176:
5173:
5170:
5167:
5163:
5159:
5156:
5153:
5150:
5147:
5141:
5136:
5131:
5107:
5102:
5097:
5093:
5090:
5087:
5084:
5080:
5076:
5073:
5070:
5067:
5061:
5056:
5051:
5047:
5044:
5038:
5033:
5029:
5025:
5021:
5018:
5015:
5012:
5008:
5004:
5001:
4998:
4994:
4990:
4987:
4984:
4981:
4977:
4973:
4970:
4967:
4964:
4961:
4955:
4950:
4945:
4929:
4926:
4912:
4907:
4902:
4898:
4888:
4885:
4881:
4877:
4871:
4866:
4861:
4854:
4848:
4824:
4819:
4814:
4810:
4800:
4797:
4793:
4789:
4783:
4778:
4773:
4766:
4760:
4743:
4730:
4727:
4714:
4709:
4705:
4699:
4695:
4691:
4688:
4685:
4665:
4662:
4659:
4656:
4653:
4633:
4630:
4627:
4604:
4599:
4594:
4570:
4564:
4558:
4554:
4550:
4545:
4541:
4537:
4532:
4528:
4523:
4518:
4514:
4483:
4456:
4453:
4447:
4441:
4435:
4431:
4428:
4425:
4419:
4413:
4408:
4403:
4375:
4350:
4344:
4341:
4336:
4332:
4326:
4322:
4318:
4315:
4312:
4309:
4307:
4304:
4302:
4297:
4293:
4287:
4283:
4279:
4276:
4273:
4270:
4268:
4263:
4259:
4253:
4249:
4245:
4242:
4239:
4236:
4235:
4232:
4229:
4226:
4224:
4221:
4219:
4216:
4214:
4211:
4210:
4207:
4204:
4199:
4195:
4189:
4185:
4181:
4178:
4175:
4172:
4170:
4167:
4165:
4160:
4156:
4150:
4146:
4142:
4139:
4136:
4133:
4131:
4126:
4122:
4116:
4112:
4108:
4105:
4102:
4099:
4098:
4095:
4092:
4087:
4083:
4077:
4073:
4069:
4066:
4063:
4060:
4058:
4055:
4053:
4048:
4044:
4038:
4034:
4030:
4027:
4024:
4021:
4019:
4014:
4010:
4004:
4000:
3996:
3993:
3990:
3987:
3986:
3984:
3979:
3973:
3968:
3963:
3937:
3934:
3931:
3904:
3875:
3868:
3862:
3856:
3851:
3847:
3844:
3838:
3832:
3827:
3822:
3811:
3809:is defined by
3799:expected value
3779:
3774:
3768:
3764:
3760:
3757:
3754:
3749:
3745:
3741:
3738:
3734:
3702:
3681:
3678:
3675:
3652:
3647:
3641:
3637:
3633:
3630:
3627:
3622:
3618:
3614:
3611:
3607:
3587:
3584:
3572:
3569:
3564:
3558:
3555:
3552:
3549:
3546:
3543:
3540:
3537:
3534:
3531:
3528:
3525:
3520:
3517:
3513:
3507:
3502:
3499:
3495:
3491:
3488:
3485:
3482:
3477:
3474:
3470:
3448:
3443:
3437:
3434:
3431:
3428:
3425:
3422:
3419:
3416:
3413:
3410:
3407:
3402:
3399:
3395:
3389:
3384:
3381:
3377:
3373:
3370:
3367:
3364:
3361:
3356:
3353:
3349:
3320:
3317:
3312:
3304:
3301:
3298:
3295:
3292:
3289:
3285:
3281:
3278:
3275:
3272:
3267:
3264:
3260:
3254:
3249:
3246:
3242:
3238:
3235:
3232:
3229:
3224:
3221:
3217:
3195:
3190:
3182:
3179:
3176:
3173:
3170:
3166:
3162:
3159:
3156:
3151:
3148:
3144:
3138:
3133:
3130:
3126:
3122:
3119:
3116:
3113:
3110:
3105:
3102:
3098:
3069:
3066:
3062:
3036:
3033:
3029:
3012:
3009:
2996:
2987:for all other
2976:
2956:
2953:
2950:
2930:
2927:
2914:
2908:
2903:
2894:
2890:
2885:
2880:
2875:
2871:
2868:
2864:
2858:
2853:
2844:
2840:
2835:
2830:
2825:
2821:
2818:
2815:
2810:
2805:
2801:
2796:
2792:
2788:
2783:
2779:
2775:
2772:
2767:
2764:
2760:
2755:
2737:
2734:
2721:
2718:
2715:
2712:
2707:
2704:
2700:
2679:
2676:
2673:
2670:
2665:
2662:
2658:
2654:
2650:
2646:
2643:
2640:
2637:
2632:
2629:
2625:
2620:
2607:
2604:
2592:
2587:
2583:
2580:
2577:
2574:
2571:
2566:
2563:
2559:
2552:
2549:
2546:
2543:
2540:
2535:
2532:
2528:
2505:
2501:
2496:
2492:
2488:
2483:
2479:
2475:
2472:
2467:
2464:
2460:
2453:
2450:
2445:
2441:
2437:
2432:
2428:
2424:
2421:
2416:
2413:
2409:
2382:
2379:
2375:
2362:
2359:
2357:
2354:
2330:
2326:
2320:
2314:
2310:
2307:
2304:
2299:
2295:
2291:
2285:
2282:
2279:
2274:
2271:
2268:
2264:
2260:
2256:
2252:
2249:
2243:
2236:
2232:
2227:
2224:
2221:
2218:
2213:
2210:
2206:
2199:
2196:
2193:
2190:
2185:
2182:
2178:
2144:
2141:
2138:
2135:
2132:
2129:
2107:
2104:
2100:
2077:
2067:
2063:
2058:
2050:
2046:
2041:
2034:
2028:
2024:
2017:
2013:
2008:
2004:
1997:
1993:
1988:
1984:
1978:
1971:
1967:
1962:
1958:
1951:
1947:
1942:
1938:
1934:
1930:
1927:
1921:
1911:
1907:
1902:
1894:
1890:
1885:
1879:
1874:
1870:
1866:
1861:
1857:
1853:
1850:
1845:
1842:
1838:
1831:
1828:
1823:
1819:
1815:
1810:
1806:
1802:
1797:
1794:
1790:
1764:
1761:
1749:
1744:
1740:
1736:
1733:
1730:
1727:
1724:
1719:
1716:
1712:
1684:
1681:
1676:
1673:
1669:
1663:
1657:
1654:
1646:
1643:
1640:
1636:
1631:
1627:
1624:
1621:
1617:
1611:
1607:
1604:
1601:
1596:
1592:
1588:
1582:
1579:
1576:
1571:
1568:
1565:
1561:
1557:
1553:
1549:
1546:
1543:
1540:
1537:
1534:
1531:
1526:
1523:
1519:
1508:
1487:
1481:
1475:
1472:
1464:
1461:
1458:
1454:
1449:
1445:
1442:
1439:
1436:
1433:
1430:
1427:
1422:
1419:
1415:
1404:
1386:
1382:
1378:
1373:
1369:
1365:
1362:
1336:
1332:
1309:
1305:
1282:
1278:
1257:
1248:then the mean
1232:
1227:
1223:
1219:
1206:
1203:
1178:
1174:
1167:
1164:
1154:
1150:
1145:
1141:
1137:
1129:
1125:
1118:
1115:
1105:
1101:
1096:
1091:
1087:
1084:
1081:
1077:
1071:
1067:
1060:
1056:
1051:
1047:
1040:
1036:
1031:
1027:
1021:
1014:
1010:
1005:
1001:
994:
990:
985:
981:
977:
973:
970:
967:
964:
959:
955:
951:
946:
942:
938:
935:
930:
927:
923:
912:
897:
893:
870:
866:
856:between times
839:expected value
826:
802:
794:
790:
783:
780:
770:
766:
761:
756:
752:
749:
746:
743:
738:
734:
730:
725:
721:
717:
714:
709:
706:
702:
691:
676:
672:
649:
645:
635:between times
620:
600:
578:
573:
569:
543:
539:
515:
485:
481:
444:
424:
403:
398:
394:
390:
374:random process
365:
362:
340:autocovariance
273:
270:
267:
247:
244:
241:
232:is the reason
188:
187:
185:
184:
177:
170:
162:
159:
158:
155:
154:
149:
144:
139:
133:
128:
127:
124:
123:
120:
119:
114:
109:
104:
98:
93:
92:
89:
88:
85:
84:
79:
74:
69:
63:
58:
57:
54:
53:
45:
44:
38:
37:
26:
9:
6:
4:
3:
2:
13531:
13520:
13517:
13515:
13512:
13510:
13507:
13506:
13504:
13489:
13488:
13479:
13477:
13476:
13467:
13465:
13464:
13459:
13453:
13451:
13450:
13441:
13440:
13437:
13423:
13420:
13418:
13417:Geostatistics
13415:
13413:
13410:
13408:
13405:
13403:
13400:
13399:
13397:
13395:
13391:
13385:
13384:Psychometrics
13382:
13380:
13377:
13375:
13372:
13370:
13367:
13365:
13362:
13360:
13357:
13355:
13352:
13350:
13347:
13345:
13342:
13340:
13337:
13336:
13334:
13332:
13328:
13322:
13319:
13317:
13314:
13312:
13308:
13305:
13303:
13300:
13298:
13295:
13293:
13290:
13289:
13287:
13285:
13281:
13275:
13272:
13270:
13267:
13265:
13261:
13258:
13256:
13253:
13252:
13250:
13248:
13247:Biostatistics
13244:
13240:
13236:
13231:
13227:
13209:
13208:Log-rank test
13206:
13205:
13203:
13199:
13193:
13190:
13189:
13187:
13185:
13181:
13175:
13172:
13170:
13167:
13165:
13162:
13160:
13157:
13156:
13154:
13152:
13148:
13145:
13143:
13139:
13129:
13126:
13124:
13121:
13119:
13116:
13114:
13111:
13109:
13106:
13105:
13103:
13101:
13097:
13091:
13088:
13086:
13083:
13081:
13079:(BoxâJenkins)
13075:
13073:
13070:
13068:
13065:
13061:
13058:
13057:
13056:
13053:
13052:
13050:
13048:
13044:
13038:
13035:
13033:
13032:DurbinâWatson
13030:
13028:
13022:
13020:
13017:
13015:
13014:DickeyâFuller
13012:
13011:
13009:
13005:
12999:
12996:
12994:
12991:
12989:
12988:Cointegration
12986:
12984:
12981:
12979:
12976:
12974:
12971:
12969:
12966:
12964:
12963:Decomposition
12961:
12960:
12958:
12954:
12951:
12949:
12945:
12935:
12932:
12931:
12930:
12927:
12926:
12925:
12922:
12918:
12915:
12914:
12913:
12910:
12908:
12905:
12903:
12900:
12898:
12895:
12893:
12890:
12888:
12885:
12883:
12880:
12878:
12875:
12874:
12872:
12870:
12866:
12860:
12857:
12855:
12852:
12850:
12847:
12845:
12842:
12840:
12837:
12835:
12834:Cohen's kappa
12832:
12831:
12829:
12827:
12823:
12819:
12815:
12811:
12807:
12803:
12798:
12794:
12780:
12777:
12775:
12772:
12770:
12767:
12765:
12762:
12761:
12759:
12757:
12753:
12747:
12743:
12739:
12733:
12731:
12728:
12727:
12725:
12723:
12719:
12713:
12710:
12708:
12705:
12703:
12700:
12698:
12695:
12693:
12690:
12688:
12687:Nonparametric
12685:
12683:
12680:
12679:
12677:
12673:
12667:
12664:
12662:
12659:
12657:
12654:
12652:
12649:
12648:
12646:
12644:
12640:
12634:
12631:
12629:
12626:
12624:
12621:
12619:
12616:
12614:
12611:
12610:
12608:
12606:
12602:
12596:
12593:
12591:
12588:
12586:
12583:
12581:
12578:
12577:
12575:
12573:
12569:
12565:
12558:
12555:
12553:
12550:
12549:
12545:
12541:
12525:
12522:
12521:
12520:
12517:
12515:
12512:
12510:
12507:
12503:
12500:
12498:
12495:
12494:
12493:
12490:
12489:
12487:
12485:
12481:
12471:
12468:
12464:
12458:
12456:
12450:
12448:
12442:
12441:
12440:
12437:
12436:Nonparametric
12434:
12432:
12426:
12422:
12419:
12418:
12417:
12411:
12407:
12406:Sample median
12404:
12403:
12402:
12399:
12398:
12396:
12394:
12390:
12382:
12379:
12377:
12374:
12372:
12369:
12368:
12367:
12364:
12362:
12359:
12357:
12351:
12349:
12346:
12344:
12341:
12339:
12336:
12334:
12331:
12329:
12327:
12323:
12321:
12318:
12317:
12315:
12313:
12309:
12303:
12301:
12297:
12295:
12293:
12288:
12286:
12281:
12277:
12276:
12273:
12270:
12268:
12264:
12254:
12251:
12249:
12246:
12244:
12241:
12240:
12238:
12236:
12232:
12226:
12223:
12219:
12216:
12215:
12214:
12211:
12207:
12204:
12203:
12202:
12199:
12197:
12194:
12193:
12191:
12189:
12185:
12177:
12174:
12172:
12169:
12168:
12167:
12164:
12162:
12159:
12157:
12154:
12152:
12149:
12147:
12144:
12142:
12139:
12138:
12136:
12134:
12130:
12124:
12121:
12117:
12114:
12110:
12107:
12105:
12102:
12101:
12100:
12097:
12096:
12095:
12092:
12088:
12085:
12083:
12080:
12078:
12075:
12073:
12070:
12069:
12068:
12065:
12064:
12062:
12060:
12056:
12053:
12051:
12047:
12041:
12038:
12036:
12033:
12029:
12026:
12025:
12024:
12021:
12019:
12016:
12012:
12011:loss function
12009:
12008:
12007:
12004:
12000:
11997:
11995:
11992:
11990:
11987:
11986:
11985:
11982:
11980:
11977:
11975:
11972:
11968:
11965:
11963:
11960:
11958:
11952:
11949:
11948:
11947:
11944:
11940:
11937:
11935:
11932:
11930:
11927:
11926:
11925:
11922:
11918:
11915:
11913:
11910:
11909:
11908:
11905:
11901:
11898:
11897:
11896:
11893:
11889:
11886:
11885:
11884:
11881:
11879:
11876:
11874:
11871:
11869:
11866:
11865:
11863:
11861:
11857:
11853:
11849:
11844:
11840:
11826:
11823:
11821:
11818:
11816:
11813:
11811:
11808:
11807:
11805:
11803:
11799:
11793:
11790:
11788:
11785:
11783:
11780:
11779:
11777:
11773:
11767:
11764:
11762:
11759:
11757:
11754:
11752:
11749:
11747:
11744:
11742:
11739:
11737:
11734:
11733:
11731:
11729:
11725:
11719:
11716:
11714:
11713:Questionnaire
11711:
11709:
11706:
11702:
11699:
11697:
11694:
11693:
11692:
11689:
11688:
11686:
11684:
11680:
11674:
11671:
11669:
11666:
11664:
11661:
11659:
11656:
11654:
11651:
11649:
11646:
11644:
11641:
11639:
11636:
11635:
11633:
11631:
11627:
11623:
11619:
11614:
11610:
11596:
11593:
11591:
11588:
11586:
11583:
11581:
11578:
11576:
11573:
11571:
11568:
11566:
11563:
11561:
11558:
11556:
11553:
11551:
11548:
11546:
11543:
11541:
11540:Control chart
11538:
11536:
11533:
11531:
11528:
11526:
11523:
11522:
11520:
11518:
11514:
11508:
11505:
11501:
11498:
11496:
11493:
11492:
11491:
11488:
11486:
11483:
11481:
11478:
11477:
11475:
11473:
11469:
11463:
11460:
11458:
11455:
11453:
11450:
11449:
11447:
11443:
11437:
11434:
11433:
11431:
11429:
11425:
11413:
11410:
11408:
11405:
11403:
11400:
11399:
11398:
11395:
11393:
11390:
11389:
11387:
11385:
11381:
11375:
11372:
11370:
11367:
11365:
11362:
11360:
11357:
11355:
11352:
11350:
11347:
11345:
11342:
11341:
11339:
11337:
11333:
11327:
11324:
11322:
11319:
11315:
11312:
11310:
11307:
11305:
11302:
11300:
11297:
11295:
11292:
11290:
11287:
11285:
11282:
11280:
11277:
11275:
11272:
11270:
11267:
11266:
11265:
11262:
11261:
11259:
11257:
11253:
11250:
11248:
11244:
11240:
11236:
11231:
11227:
11221:
11218:
11216:
11213:
11212:
11209:
11205:
11198:
11193:
11191:
11186:
11184:
11179:
11178:
11175:
11166:
11165:
11160:
11157:
11152:
11149:
11148:9780128133477
11145:
11141:
11140:
11135:
11132:
11128:
11124:
11120:
11116:
11112:
11108:
11104:
11100:
11096:
11091:
11087:
11081:
11077:
11076:
11071:
11070:Marno Verbeek
11067:
11063:
11057:
11053:
11048:
11047:
11041:
11037:
11036:
11012:
11005:
10998:
10990:
10986:
10985:
10980:
10973:
10965:
10961:
10957:
10953:
10949:
10945:
10937:
10929:
10923:
10919:
10912:
10904:
10900:
10896:
10892:
10887:
10882:
10878:
10874:
10870:
10866:
10862:
10855:
10847:
10843:
10838:
10833:
10829:
10825:
10821:
10817:
10813:
10809:
10805:
10798:
10790:
10784:
10780:
10773:
10765:
10761:
10755:
10747:
10743:
10739:
10735:
10728:
10720:
10714:
10710:
10705:
10704:
10695:
10687:
10681:
10677:
10670:
10662:
10658:
10654:
10650:
10646:
10642:
10637:
10632:
10628:
10625:
10624:
10616:
10608:
10602:
10598:
10591:
10583:
10577:
10573:
10566:
10558:
10552:
10548:
10541:
10533:
10527:
10523:
10516:
10514:
10506:
10500:
10498:
10496:
10489:
10485:
10479:
10477:
10475:
10473:
10471:
10469:
10460:
10454:
10450:
10443:
10441:
10439:
10437:
10435:
10433:
10431:
10426:
10415:
10412:
10410:
10407:
10405:
10402:
10400:
10397:
10395:
10392:
10389:
10386:
10384:
10381:
10379:
10376:
10374:
10371:
10369:
10366:
10364:
10361:
10359:
10356:
10354:
10351:
10348:
10345:
10343:
10340:
10338:
10335:
10333:
10330:
10328:
10325:
10324:
10317:
10303:
10300:
10297:
10294:
10291:
10266:
10262:
10258:
10253:
10249:
10237:
10220:
10215:
10211:
10207:
10197:
10183:
10175:
10159:
10151:
10147:
10142:
10140:
10136:
10124:
10120:
10117:
10113:
10109:
10106:
10102:
10099:
10095:
10091:
10088:
10084:
10081:
10077:
10074:
10070:
10066:
10062:
10059:
10055:
10051:
10047:
10043:
10040:
10036:
10033:
10029:
10026:
10022:
10018:
10014:
10010:
10006:
10003:
9999:
9995:
9991:
9988:
9984:
9981:
9977:
9973:
9970:
9966:
9963:
9962:doppler shift
9958:
9954:
9950:
9946:
9942:
9938:
9934:
9930:
9926:
9923:
9920:, both using
9919:
9915:
9912:
9908:
9904:
9901:
9897:
9896:
9895:
9893:
9883:
9869:
9866:
9863:
9843:
9840:
9834:
9828:
9808:
9805:
9802:
9799:
9796:
9793:
9790:
9787:
9784:
9764:
9761:
9755:
9749:
9741:
9737:
9732:
9730:
9726:
9721:
9719:
9715:
9700:
9696:
9685:
9681:
9677:
9673:
9669:
9665:
9661:
9657:
9653:
9648:
9646:
9642:
9638:
9634:
9630:
9626:
9622:
9617:
9615:
9611:
9607:
9603:
9599:
9595:
9591:
9581:
9567:
9547:
9518:
9514:
9509:
9506:
9502:
9497:
9494:
9491:
9487:
9482:
9477:
9474:
9471:
9467:
9438:
9435:
9432:
9428:
9423:
9420:
9416:
9411:
9407:
9402:
9397:
9393:
9381:
9378:
9362:
9342:
9339:
9336:
9328:
9324:
9321:
9320:
9301:
9297:
9276:
9268:
9267:
9266:
9264:
9260:
9259:
9240:
9236:
9228:and variance
9215:
9195:
9192:
9189:
9180:
9164:
9161:
9156:
9153:
9150:
9146:
9136:
9133:
9128:
9124:
9115:
9112:
9109:
9104:
9101:
9098:
9094:
9085:
9081:
9074:
9071:
9068:
9061:
9056:
9050:
9038:
9027:
9008:
9004:
8999:
8996:
8992:
8987:
8983:
8978:
8973:
8969:
8958:observations
8945:
8937:
8927:
8923:
8919:
8914:
8908:
8904:
8890:
8888:
8884:
8879:
8856:
8850:
8844:
8841:
8838:
8836:
8828:
8822:
8812:
8804:
8799:
8795:
8788:
8780:
8776:
8772:
8770:
8762:
8756:
8743:
8737:
8731:
8728:
8725:
8723:
8715:
8707:
8703:
8690:
8688:
8682:
8678:
8673:
8667:
8663:
8657:
8653:
8648:
8646:
8630:
8627:
8604:
8601:
8598:
8595:
8592:
8589:
8586:
8583:
8580:
8577:
8574:
8571:
8568:
8565:
8562:
8556:
8551:
8548:
8544:
8535:
8519:
8513:
8510:
8507:
8504:
8501:
8498:
8495:
8492:
8489:
8486:
8483:
8480:
8477:
8474:
8471:
8468:
8465:
8459:
8456:
8435:
8432:
8429:
8426:
8420:
8412:
8409:
8405:
8401:
8395:
8392:
8384:
8381:
8377:
8356:
8353:
8350:
8344:
8336:
8333:
8329:
8325:
8319:
8316:
8308:
8305:
8301:
8281:
8278:
8275:
8269:
8261:
8258:
8254:
8230:
8227:
8224:
8221:
8218:
8215:
8212:
8209:
8206:
8203:
8200:
8194:
8189:
8186:
8182:
8172:
8155:
8152:
8147:
8142:
8137:
8132:
8129:
8121:
8118:
8113:
8108:
8101:
8094:
8091:
8086:
8081:
8072:
8067:
8064:
8059:
8056:
8048:
8045:
8040:
8035:
8030:
8023:
8020:
8015:
8010:
7981:
7978:
7973:
7969:
7948:
7945:
7942:
7937:
7933:
7929:
7926:
7923:
7918:
7914:
7910:
7907:
7904:
7899:
7895:
7871:
7868:
7865:
7862:
7859:
7856:
7850:
7847:
7825:
7822:
7819:
7810:
7801:
7797:
7791:
7787:
7783:
7777:
7769:
7766:
7762:
7753:
7749:
7745:
7735:
7732:
7719:
7714:
7711:
7708:
7705:
7702:
7699:
7696:
7693:
7690:
7687:
7684:
7675:
7666:
7663:
7660:
7657:
7654:
7650:
7644:
7641:
7638:
7635:
7632:
7628:
7624:
7618:
7615:
7612:
7609:
7606:
7600:
7592:
7590:
7586:
7582:
7555:
7538:
7528:
7525:
7521:
7517:
7514:
7508:
7502:
7494:
7491:
7487:
7463:
7455:
7452:
7448:
7424:
7421:
7415:
7412:
7406:
7397:
7389:
7386:
7382:
7361:
7339:
7336:
7332:
7323:
7320:to represent
7307:
7299:
7296:
7292:
7277:
7269:
7266:
7262:
7259:
7240:
7232:
7229:
7225:
7221:
7210:
7202:
7199:
7195:
7169:
7161:
7156:
7140:
7117:
7109:
7104:
7101:
7097:
7093:
7087:
7084:
7076:
7073:
7069:
7061:
7057:
7042:
7019:
7011:
7008:
7004:
7000:
6994:
6991:
6983:
6980:
6976:
6968:
6967:even function
6964:
6963:
6946:
6943:
6935:
6932:
6928:
6924:
6918:
6910:
6907:
6903:
6894:
6893:
6892:
6890:
6879:
6866:
6863:
6850:
6847:
6844:
6838:
6829:
6823:
6818:
6815:
6810:
6806:
6798:
6794:
6789:
6785:
6779:
6771:
6768:
6764:
6755:
6752:
6739:
6736:
6723:
6717:
6708:
6705:
6702:
6696:
6691:
6688:
6683:
6679:
6671:
6667:
6662:
6658:
6652:
6644:
6641:
6637:
6628:
6614:
6591:
6588:
6583:
6579:
6575:
6570:
6566:
6519:
6499:
6479:
6465:
6463:
6459:
6454:
6451:
6434:
6422:
6419:
6416:
6410:
6400:
6394:
6389:
6386:
6383:
6378:
6375:
6372:
6368:
6362:
6359:
6346:
6338:
6336:
6328:
6320:
6317:
6313:
6305:
6285:
6279:
6270:
6267:
6264:
6258:
6253:
6248:
6244:
6238:
6235:
6222:
6214:
6212:
6204:
6196:
6193:
6189:
6176:
6174:
6169:
6155:
6135:
6127:
6122:
6105:
6101:
6088:
6085:
6082:
6076:
6066:
6060:
6056:
6052:
6046:
6044:
6036:
6028:
6025:
6021:
6012:
5999:
5996:
5993:
5987:
5978:
5972:
5968:
5964:
5958:
5956:
5948:
5940:
5937:
5933:
5920:
5918:
5911:
5889:
5886:
5883:
5877:
5867:
5861:
5856:
5853:
5850:
5846:
5842:
5836:
5828:
5825:
5821:
5811:
5794:
5788:
5768:
5748:
5734:
5720:
5697:
5691:
5683:
5658:
5652:
5639:
5626:
5606:
5603:
5600:
5594:
5585:
5579:
5566:
5562:
5558:
5555:
5535:
5529:
5520:
5517:
5514:
5508:
5495:
5491:
5487:
5481:
5473:
5470:
5466:
5456:
5442:
5419:
5413:
5405:
5386:
5378:
5375:
5371:
5347:
5341:
5334:
5324:
5322:
5318:
5274:
5257:
5251:
5231:
5202:
5196:
5171:
5165:
5151:
5145:
5088:
5071:
5065:
5045:
5016:
5010:
4985:
4979:
4965:
4959:
4934:
4930:
4927:
4910:
4900:
4892:for all
4886:
4883:
4875:
4822:
4812:
4804:for all
4798:
4795:
4787:
4748:
4744:
4741:
4737:
4733:
4732:
4726:
4707:
4703:
4697:
4693:
4686:
4676:-th entry is
4660:
4657:
4654:
4644:matrix whose
4631:
4628:
4625:
4562:
4556:
4552:
4548:
4543:
4539:
4535:
4530:
4526:
4521:
4516:
4502:
4500:
4467:
4454:
4426:
4417:
4392:
4390:
4363:
4348:
4334:
4330:
4324:
4320:
4313:
4305:
4295:
4291:
4285:
4281:
4274:
4261:
4257:
4251:
4247:
4240:
4227:
4222:
4217:
4212:
4197:
4193:
4187:
4183:
4176:
4168:
4158:
4154:
4148:
4144:
4137:
4124:
4120:
4114:
4110:
4103:
4085:
4081:
4075:
4071:
4064:
4056:
4046:
4042:
4036:
4032:
4025:
4012:
4008:
4002:
3998:
3991:
3982:
3977:
3952:
3949:
3935:
3932:
3929:
3921:
3887:
3873:
3849:
3845:
3836:
3810:
3808:
3804:
3800:
3796:
3766:
3762:
3758:
3755:
3752:
3747:
3743:
3736:
3724:
3723:random vector
3719:
3717:
3679:
3676:
3673:
3639:
3635:
3631:
3628:
3625:
3620:
3616:
3609:
3597:
3596:random vector
3593:
3583:
3570:
3567:
3553:
3550:
3547:
3544:
3538:
3535:
3529:
3523:
3518:
3515:
3497:
3493:
3489:
3483:
3475:
3472:
3468:
3459:
3446:
3432:
3429:
3426:
3423:
3417:
3414:
3408:
3400:
3397:
3393:
3379:
3375:
3371:
3365:
3359:
3354:
3351:
3338:
3336:
3331:
3318:
3315:
3302:
3299:
3296:
3293:
3290:
3287:
3283:
3276:
3270:
3265:
3262:
3244:
3240:
3236:
3230:
3222:
3219:
3215:
3206:
3193:
3180:
3177:
3174:
3171:
3168:
3164:
3157:
3149:
3146:
3142:
3128:
3124:
3120:
3114:
3108:
3103:
3100:
3087:
3085:
3067:
3064:
3060:
3052:
3034:
3031:
3018:
3008:
2994:
2974:
2954:
2951:
2948:
2940:
2936:
2926:
2912:
2906:
2892:
2888:
2883:
2873:
2869:
2862:
2856:
2842:
2838:
2833:
2823:
2819:
2813:
2808:
2803:
2794:
2790:
2786:
2781:
2777:
2770:
2765:
2762:
2753:
2743:
2733:
2716:
2710:
2705:
2702:
2674:
2668:
2663:
2660:
2652:
2648:
2641:
2635:
2630:
2627:
2618:
2603:
2590:
2578:
2575:
2569:
2564:
2561:
2550:
2544:
2538:
2533:
2530:
2494:
2490:
2486:
2481:
2477:
2470:
2465:
2462:
2451:
2443:
2439:
2435:
2430:
2426:
2419:
2414:
2411:
2398:
2397:even function
2380:
2377:
2353:
2351:
2346:
2328:
2324:
2318:
2305:
2302:
2297:
2293:
2280:
2277:
2272:
2269:
2266:
2262:
2254:
2250:
2241:
2234:
2230:
2222:
2216:
2211:
2208:
2197:
2191:
2183:
2180:
2176:
2167:
2165:
2160:
2158:
2139:
2136:
2133:
2130:
2105:
2102:
2098:
2088:
2075:
2065:
2061:
2056:
2048:
2044:
2039:
2032:
2015:
2011:
2006:
2002:
1995:
1991:
1986:
1969:
1965:
1960:
1956:
1949:
1945:
1940:
1932:
1928:
1919:
1909:
1905:
1900:
1892:
1888:
1883:
1872:
1868:
1864:
1859:
1855:
1848:
1843:
1840:
1829:
1821:
1817:
1813:
1808:
1804:
1795:
1792:
1788:
1779:
1776:
1774:
1770:
1763:Normalization
1760:
1747:
1742:
1738:
1734:
1728:
1722:
1717:
1714:
1701:
1697:
1679:
1674:
1671:
1667:
1661:
1652:
1644:
1641:
1638:
1634:
1629:
1625:
1619:
1615:
1602:
1599:
1594:
1590:
1577:
1574:
1569:
1566:
1563:
1559:
1551:
1547:
1541:
1535:
1529:
1524:
1521:
1507:
1505:
1499:
1485:
1479:
1470:
1462:
1459:
1456:
1452:
1447:
1443:
1437:
1431:
1425:
1420:
1417:
1403:
1402:
1384:
1380:
1376:
1371:
1367:
1363:
1360:
1352:
1351:even function
1334:
1330:
1307:
1303:
1280:
1276:
1255:
1247:
1230:
1225:
1221:
1217:
1202:
1200:
1193:
1176:
1172:
1162:
1152:
1148:
1143:
1139:
1135:
1127:
1123:
1113:
1103:
1099:
1094:
1089:
1085:
1079:
1075:
1058:
1054:
1049:
1045:
1038:
1034:
1029:
1012:
1008:
1003:
999:
992:
988:
983:
975:
971:
965:
957:
953:
949:
944:
940:
933:
928:
925:
911:
895:
891:
868:
864:
855:
850:
848:
844:
840:
814:
800:
792:
788:
778:
768:
764:
759:
754:
750:
744:
736:
732:
728:
723:
719:
712:
707:
704:
690:
674:
670:
647:
643:
634:
618:
598:
576:
571:
567:
559:
541:
537:
529:
513:
505:
501:
483:
479:
470:
466:
463:process or a
462:
461:discrete-time
458:
442:
422:
401:
396:
392:
388:
379:
375:
371:
361:
359:
355:
351:
347:
343:
341:
336:
334:
330:
326:
322:
318:
314:
310:
306:
302:
299:case, is the
298:
297:discrete time
294:
290:
271:
268:
265:
245:
242:
239:
219:
215:
210:
203:
199:
194:
183:
178:
176:
171:
169:
164:
163:
161:
160:
153:
150:
148:
145:
143:
140:
138:
135:
134:
131:
126:
125:
118:
115:
113:
110:
108:
105:
103:
100:
99:
96:
91:
90:
83:
80:
78:
75:
73:
70:
68:
65:
64:
61:
56:
55:
51:
47:
46:
43:
40:
39:
36:
32:
31:
19:
13485:
13473:
13454:
13447:
13359:Econometrics
13309: /
13292:Chemometrics
13269:Epidemiology
13262: /
13235:Applications
13077:ARIMA model
13054:
13024:Q-statistic
12973:Stationarity
12869:Multivariate
12812: /
12808: /
12806:Multivariate
12804: /
12744: /
12740: /
12514:Bayes factor
12413:Signed rank
12325:
12299:
12291:
12279:
11974:Completeness
11810:Cohort study
11708:Opinion poll
11643:Missing data
11630:Study design
11585:Scatter plot
11507:Scatter plot
11500:Spearman's Ï
11462:Grouped data
11162:
11137:
11102:
11098:
11074:
11045:
11018:. Retrieved
10997:
10989:the original
10982:
10972:
10947:
10943:
10936:
10917:
10911:
10868:
10864:
10854:
10811:
10807:
10797:
10778:
10772:
10763:
10754:
10737:
10733:
10727:
10702:
10694:
10675:
10669:
10626:
10621:
10615:
10596:
10590:
10571:
10565:
10546:
10540:
10521:
10504:
10448:
10198:
10143:
10134:
10133:
10065:astrophysics
10050:mass spectra
10021:musical beat
9916:produced by
9889:
9886:Applications
9739:
9733:
9722:
9717:
9679:
9675:
9671:
9663:
9649:
9629:econometrics
9618:
9587:
9539:
9317:
9256:
9181:
9028:
8933:
8921:
8917:
8911:data with a
8906:
8902:
8891:
8880:
8691:
8680:
8676:
8665:
8661:
8655:
8649:
8173:
7741:
7733:
7593:
7578:
6885:
6756:
6753:
6629:
6471:
6458:last forever
6457:
6455:
6452:
6177:
6170:
6123:
5921:
5913:
5813:
5740:
5641:
5458:
5406:integral of
5330:
5320:
5314:
4932:
4503:
4468:
4393:
4364:
3953:
3950:
3918:denotes the
3889:
3812:
3806:
3720:
3718:algorithms.
3591:
3589:
3460:
3339:
3332:
3207:
3088:
3014:
2932:
2739:
2690:Notice that
2609:
2364:
2347:
2168:
2161:
2089:
1780:
1777:
1766:
1702:
1699:
1509:
1503:
1501:
1405:
1400:
1353:of the lag
1208:
1195:
913:
853:
851:
847:well defined
816:
692:
632:
367:
344:
337:
315:obscured by
292:
288:
287:
217:
129:
94:
59:
13487:WikiProject
13402:Cartography
13364:Jurimetrics
13316:Reliability
13047:Time domain
13026:(LjungâBox)
12948:Time-series
12826:Categorical
12810:Time-series
12802:Categorical
12737:(Bernoulli)
12572:Correlation
12552:Correlation
12348:JarqueâBera
12320:Chi-squared
12082:M-estimator
12035:Asymptotics
11979:Sufficiency
11746:Interaction
11658:Replication
11638:Effect size
11595:Violin plot
11575:Radar chart
11555:Forest plot
11545:Correlogram
11495:Kendall's Ï
11105:(5): 2180.
11040:Kmenta, Jan
10865:Soft Matter
10358:Correlogram
10146:time series
10094:geosciences
9944:calculated.
9327:periodogram
8913:logarithmic
8645:Z-transform
7581:dimensional
7322:convolution
3805:exist, the
3793:containing
2935:white noise
611:, for each
500:realization
465:real number
348:processes,
333:time domain
301:correlation
202:correlogram
13503:Categories
13354:Demography
13072:ARMA model
12877:Regression
12454:(Friedman)
12415:(Wilcoxon)
12353:Normality
12343:Lilliefors
12290:Student's
12166:Resampling
12040:Robustness
12028:divergence
12018:Efficiency
11956:(monotone)
11951:Likelihood
11868:Population
11701:Stratified
11653:Population
11472:Dependence
11428:Count data
11359:Percentile
11336:Dispersion
11269:Arithmetic
11204:Statistics
11127:Guang Gong
10950:: 106173.
10421:References
10236:stationary
10098:geophysics
10080:panel data
10017:distortion
9742:, we have
8930:Estimation
6882:Properties
6607:of length
6126:stationary
3920:transposed
2356:Properties
455:may be an
370:statistics
35:Statistics
12735:Logistic
12502:posterior
12428:Rank sum
12176:Jackknife
12171:Bootstrap
11989:Bootstrap
11924:Parameter
11873:Statistic
11668:Statistic
11580:Run chart
11565:Pie chart
11560:Histogram
11550:Fan chart
11525:Bar chart
11407:L-moments
11294:Geometric
11164:MathWorld
11078:. Wiley.
10964:198468676
10895:1744-683X
10636:0912.3824
10301:−
10292:τ
9998:frequency
9994:astronomy
9864:τ
9835:τ
9803:…
9785:τ
9762:≠
9756:τ
9697:χ
9507:…
9436:−
9421:…
9340:−
9298:σ
9277:μ
9237:σ
9216:μ
9165:μ
9162:−
9137:μ
9134:−
9113:−
9095:∑
9082:σ
9072:−
9042:^
8997:…
8845:
8829:τ
8805:∗
8732:
8685:with two
8605:…
8563:…
8514:…
8505:−
8484:−
8466:…
8430:−
8393:−
8317:−
8228:−
8201:−
8153:−
8130:−
8119:−
8092:−
8065:−
8057:−
8046:−
8031:×
8021:−
7946:−
7869:−
7823:−
7814:¯
7788:∑
7715:ℓ
7712:−
7700:−
7688:−
7679:¯
7629:∑
7619:ℓ
7591:would be
7556:τ
7542:¯
7526:−
7518:∗
7503:τ
7464:τ
7422:−
7387:−
7337:−
7308:∗
7278:τ
7222:≤
7211:τ
7170:τ
7118:τ
7110:∗
7088:τ
7085:−
7020:τ
6995:τ
6992:−
6947:τ
6944:−
6919:τ
6858:¯
6851:τ
6848:−
6790:∫
6786:≜
6780:τ
6731:¯
6709:τ
6663:∫
6659:≜
6653:τ
6543:∞
6523:∞
6520:−
6430:¯
6423:ℓ
6420:−
6387:−
6369:∑
6353:∞
6350:→
6329:ℓ
6293:¯
6271:τ
6245:∫
6229:∞
6226:→
6205:τ
6096:¯
6089:ℓ
6086:−
6053:
6037:ℓ
6007:¯
6000:τ
5997:−
5965:
5949:τ
5897:¯
5890:ℓ
5887:−
5854:∈
5847:∑
5837:ℓ
5769:ℓ
5666:¯
5614:¯
5607:τ
5604:−
5575:∞
5570:∞
5567:−
5563:∫
5543:¯
5521:τ
5504:∞
5499:∞
5496:−
5492:∫
5482:τ
5443:τ
5387:τ
5275:
5258:
5252:−
5203:
5197:−
5172:
5166:−
5152:
5089:
5072:
5066:−
5017:
5011:−
4986:
4980:−
4966:
4901:∈
4884:≥
4876:
4813:∈
4796:≥
4788:
4687:
4629:×
4427:
4418:≜
4314:
4306:⋯
4275:
4241:
4228:⋮
4223:⋱
4218:⋮
4213:⋮
4177:
4169:⋯
4138:
4104:
4065:
4057:⋯
4026:
3992:
3933:×
3846:
3837:≜
3756:…
3677:×
3629:…
3568:τ
3554:τ
3548:π
3539:
3530:τ
3524:
3506:∞
3501:∞
3498:−
3494:∫
3433:τ
3427:π
3418:
3388:∞
3383:∞
3380:−
3376:∫
3366:τ
3360:
3316:τ
3303:τ
3297:π
3288:−
3277:τ
3271:
3253:∞
3248:∞
3245:−
3241:∫
3181:τ
3175:π
3137:∞
3132:∞
3129:−
3125:∫
3115:τ
3109:
2995:τ
2949:τ
2870:
2820:
2814:≤
2771:
2711:
2669:
2653:≤
2642:τ
2636:
2586:¯
2579:τ
2576:−
2570:
2545:τ
2539:
2504:¯
2471:
2420:
2325:σ
2313:¯
2306:μ
2303:−
2281:μ
2278:−
2273:τ
2251:
2231:σ
2223:τ
2217:
2192:τ
2177:ρ
2131:−
2099:ρ
2057:σ
2040:σ
2027:¯
2007:μ
2003:−
1961:μ
1957:−
1929:
1901:σ
1884:σ
1849:
1789:ρ
1739:σ
1723:
1683:¯
1680:μ
1675:μ
1672:−
1656:¯
1645:τ
1626:
1610:¯
1603:μ
1600:−
1578:μ
1575:−
1570:τ
1548:
1536:τ
1530:
1474:¯
1463:τ
1444:
1432:τ
1426:
1377:−
1361:τ
1277:σ
1256:μ
1199:power law
1166:¯
1163:μ
1144:μ
1140:−
1117:¯
1086:
1070:¯
1050:μ
1046:−
1004:μ
1000:−
972:
934:
782:¯
751:
713:
568:σ
538:μ
346:Unit root
335:signals.
269:⋆
243:∗
13449:Category
13142:Survival
13019:Johansen
12742:Binomial
12697:Isotonic
12284:(normal)
11929:location
11736:Blocking
11691:Sampling
11570:QâQ plot
11535:Box plot
11517:Graphics
11412:Skewness
11402:Kurtosis
11374:Variance
11304:Heronian
11299:Harmonic
11042:(1986).
11011:Archived
10903:28106203
10846:22208184
10320:See also
10069:galaxies
9937:micelles
9727:and the
9674:, where
9645:t-scores
9600:(AR), a
9263:variance
9258:unbiased
8936:discrete
8246:, where
7744:discrete
5331:Given a
4497:denotes
3803:variance
3082:via the
1502:and the
591:at time
558:variance
325:harmonic
13475:Commons
13422:Kriging
13307:Process
13264:studies
13123:Wavelet
12956:General
12123:Plug-in
11917:L space
11696:Cluster
11397:Moments
11215:Outline
11107:Bibcode
11052:298â334
10873:Bibcode
10837:3244056
10816:Bibcode
10661:7173093
10641:Bibcode
10058:peptide
10046:SEQUEST
10002:pulsars
9682:is the
8689:(FFT):
6173:ergodic
5761:at lag
4749:, i.e.
3049:to the
837:is the
457:integer
376:is the
295:in the
13344:Census
12934:Normal
12882:Manova
12702:Robust
12452:2-way
12444:1-way
12282:-test
11953:
11530:Biplot
11321:Median
11314:Lehmer
11256:Center
11146:
11082:
11058:
11020:28 May
10962:
10924:
10901:
10893:
10844:
10834:
10785:
10715:
10711:â195.
10682:
10659:
10603:
10578:
10553:
10528:
10486:
10455:
9918:lasers
9914:pulses
9856:, for
9821:, and
9777:, for
9592:using
8934:For a
7961:, and
7887:(i.e.
7579:Multi-
5642:where
5333:signal
4421:
3890:where
3840:
3797:whose
3721:For a
3666:is an
2395:is an
2162:For a
817:where
467:for a
459:for a
356:, and
305:signal
216:, and
12968:Trend
12497:prior
12439:anova
12328:-test
12302:-test
12294:-test
12201:Power
12146:Pivot
11939:shape
11934:scale
11384:Shape
11364:Range
11309:Heinz
11284:Cubic
11220:Index
11014:(PDF)
11007:(PDF)
10960:S2CID
10657:S2CID
10631:arXiv
10368:CUSUM
10148:of a
10025:tempo
10009:music
9911:light
9716:with
8652:order
7153:is a
7133:when
7035:when
6148:, or
4618:is a
4469:Here
4387:is a
2941:) at
1244:is a
317:noise
303:of a
13201:Test
12401:Sign
12253:Wald
11326:Mode
11264:Mean
11144:ISBN
11080:ISBN
11056:ISBN
11022:2022
10984:Time
10922:ISBN
10899:PMID
10891:ISSN
10842:PMID
10783:ISBN
10713:ISBN
10680:ISBN
10601:ISBN
10576:ISBN
10551:ISBN
10526:ISBN
10484:ISBN
10453:ISBN
10044:The
9978:and
9967:The
9892:data
9867:>
9637:BLUE
9456:and
9289:and
9193:<
8920:log(
8842:IFFT
8664:log(
8369:and
7750:. A
7324:and
4931:The
3801:and
3015:The
2740:The
1322:and
883:and
662:and
556:and
528:mean
258:and
198:sine
12381:BIC
12376:AIC
11115:doi
10952:doi
10948:132
10881:doi
10832:PMC
10824:doi
10812:101
10742:doi
10709:190
10649:doi
10627:182
10234:is
10144:A
10121:In
10110:In
10103:In
10092:In
10078:In
10063:In
10007:In
10000:of
9992:In
9974:In
9949:GPS
9619:In
9588:In
9269:If
8729:FFT
6535:to
6472:If
6343:lim
6219:lim
5810:is
5684:of
5315:In
4365:If
3536:cos
3415:cos
1209:If
1201:).
689:is
504:run
368:In
13505::
11161:.
11129:.
11113:.
11103:60
11101:.
11097:.
11054:.
10981:.
10958:.
10946:.
10897:.
10889:.
10879:.
10869:13
10867:.
10863:.
10840:.
10830:.
10822:.
10810:.
10806:.
10762:.
10738:47
10736:.
10655:.
10647:.
10639:.
10512:^
10494:^
10467:^
10429:^
10316:.
9882:.
9672:TR
9325:A
8889:.
8587:14
8569:14
8279:14
8216:14
8143:14
7182:,
6891:.
6627::
6168:.
5455:.
4725:.
4501:.
3948:.
3086::
3007:.
2345:.
2159:.
1506::
910::
849:.
352:,
342:.
12326:G
12300:F
12292:t
12280:Z
11999:V
11994:U
11196:e
11189:t
11182:v
11167:.
11150:.
11121:.
11117::
11109::
11088:.
11064:.
11024:.
10966:.
10954::
10930:.
10905:.
10883::
10875::
10848:.
10826::
10818::
10791:.
10748:.
10744::
10721:.
10688:.
10663:.
10651::
10643::
10633::
10609:.
10584:.
10559:.
10534:.
10461:.
10304:t
10298:s
10295:=
10272:)
10267:s
10263:X
10259:,
10254:t
10250:X
10246:(
10221:}
10216:t
10212:X
10208:{
10184:s
10160:t
10075:.
10060:.
10027:.
10004:.
9924:.
9870:q
9844:0
9841:=
9838:)
9832:(
9829:R
9809:q
9806:,
9800:,
9797:1
9794:,
9791:0
9788:=
9765:0
9759:)
9753:(
9750:R
9740:q
9718:k
9701:2
9680:R
9676:T
9664:k
9568:X
9548:k
9524:}
9519:n
9515:X
9510:,
9503:,
9498:2
9495:+
9492:k
9488:X
9483:,
9478:1
9475:+
9472:k
9468:X
9464:{
9444:}
9439:k
9433:n
9429:X
9424:,
9417:,
9412:2
9408:X
9403:,
9398:1
9394:X
9390:{
9379:.
9363:n
9343:k
9337:n
9322:.
9302:2
9241:2
9196:n
9190:k
9168:)
9157:k
9154:+
9151:t
9147:X
9143:(
9140:)
9129:t
9125:X
9121:(
9116:k
9110:n
9105:1
9102:=
9099:t
9086:2
9078:)
9075:k
9069:n
9066:(
9062:1
9057:=
9054:)
9051:k
9048:(
9039:R
9014:}
9009:n
9005:X
9000:,
8993:,
8988:2
8984:X
8979:,
8974:1
8970:X
8966:{
8946:n
8924:)
8922:n
8918:n
8909:)
8907:t
8905:(
8903:X
8898:Ï
8894:Ï
8863:]
8860:)
8857:f
8854:(
8851:S
8848:[
8839:=
8832:)
8826:(
8823:R
8816:)
8813:f
8810:(
8800:R
8796:F
8792:)
8789:f
8786:(
8781:R
8777:F
8773:=
8766:)
8763:f
8760:(
8757:S
8750:]
8747:)
8744:t
8741:(
8738:X
8735:[
8726:=
8719:)
8716:f
8713:(
8708:R
8704:F
8683:)
8681:t
8679:(
8677:X
8668:)
8666:n
8662:n
8656:n
8631:.
8628:x
8608:)
8602:,
8599:1
8596:,
8593:1
8590:,
8584:,
8581:1
8578:,
8575:1
8572:,
8566:,
8560:(
8557:=
8552:x
8549:x
8545:R
8520:,
8517:)
8511:,
8508:1
8502:,
8499:3
8496:,
8493:2
8490:,
8487:1
8481:,
8478:3
8475:,
8472:2
8469:,
8463:(
8460:=
8457:x
8436:,
8433:2
8427:=
8424:)
8421:2
8418:(
8413:x
8410:x
8406:R
8402:=
8399:)
8396:2
8390:(
8385:x
8382:x
8378:R
8357:,
8354:3
8351:=
8348:)
8345:1
8342:(
8337:x
8334:x
8330:R
8326:=
8323:)
8320:1
8314:(
8309:x
8306:x
8302:R
8282:,
8276:=
8273:)
8270:0
8267:(
8262:x
8259:x
8255:R
8234:)
8231:2
8225:,
8222:3
8219:,
8213:,
8210:3
8207:,
8204:2
8198:(
8195:=
8190:x
8187:x
8183:R
8156:2
8148:3
8138:3
8133:2
8122:2
8114:6
8109:4
8102:+
8095:3
8087:9
8082:6
8073:1
8068:3
8060:2
8049:1
8041:3
8036:2
8024:1
8016:3
8011:2
7996:i
7982:0
7979:=
7974:i
7970:x
7949:1
7943:=
7938:2
7934:x
7930:,
7927:3
7924:=
7919:1
7915:x
7911:,
7908:2
7905:=
7900:0
7896:x
7875:)
7872:1
7866:,
7863:3
7860:,
7857:2
7854:(
7851:=
7848:x
7826:j
7820:n
7811:x
7802:n
7798:x
7792:n
7784:=
7781:)
7778:j
7775:(
7770:x
7767:x
7763:R
7720:.
7709:r
7706:,
7703:k
7697:q
7694:,
7691:j
7685:n
7676:x
7667:r
7664:,
7661:q
7658:,
7655:n
7651:x
7645:r
7642:,
7639:q
7636:,
7633:n
7625:=
7622:)
7616:,
7613:k
7610:,
7607:j
7604:(
7601:R
7559:)
7553:(
7550:)
7547:)
7539:f
7534:(
7529:1
7522:g
7515:f
7512:(
7509:=
7506:)
7500:(
7495:f
7492:f
7488:R
7467:)
7461:(
7456:f
7453:f
7449:R
7428:)
7425:t
7419:(
7416:f
7413:=
7410:)
7407:t
7404:(
7401:)
7398:f
7395:(
7390:1
7383:g
7362:f
7340:1
7333:g
7244:)
7241:0
7238:(
7233:f
7230:f
7226:R
7218:|
7214:)
7208:(
7203:f
7200:f
7196:R
7191:|
7157:.
7141:f
7121:)
7115:(
7105:f
7102:f
7098:R
7094:=
7091:)
7082:(
7077:f
7074:f
7070:R
7043:f
7023:)
7017:(
7012:f
7009:f
7005:R
7001:=
6998:)
6989:(
6984:f
6981:f
6977:R
6950:)
6941:(
6936:f
6933:f
6929:R
6925:=
6922:)
6916:(
6911:f
6908:f
6904:R
6867:t
6864:d
6854:)
6845:t
6842:(
6839:f
6833:)
6830:t
6827:(
6824:f
6819:T
6816:+
6811:0
6807:t
6799:0
6795:t
6783:)
6777:(
6772:f
6769:f
6765:R
6740:t
6737:d
6727:)
6724:t
6721:(
6718:f
6712:)
6706:+
6703:t
6700:(
6697:f
6692:T
6689:+
6684:0
6680:t
6672:0
6668:t
6656:)
6650:(
6645:f
6642:f
6638:R
6615:T
6595:]
6592:T
6589:+
6584:0
6580:t
6576:,
6571:0
6567:t
6563:[
6500:T
6480:f
6435:.
6426:)
6417:n
6414:(
6411:y
6404:)
6401:n
6398:(
6395:y
6390:1
6384:N
6379:0
6376:=
6373:n
6363:N
6360:1
6347:N
6339:=
6332:)
6326:(
6321:y
6318:y
6314:R
6306:t
6301:d
6289:)
6286:t
6283:(
6280:f
6274:)
6268:+
6265:t
6262:(
6259:f
6254:T
6249:0
6239:T
6236:1
6223:T
6215:=
6208:)
6202:(
6197:f
6194:f
6190:R
6156:n
6136:t
6106:.
6102:]
6092:)
6083:n
6080:(
6077:y
6070:)
6067:n
6064:(
6061:y
6057:[
6050:E
6047:=
6040:)
6034:(
6029:y
6026:y
6022:R
6013:]
6003:)
5994:t
5991:(
5988:f
5982:)
5979:t
5976:(
5973:f
5969:[
5962:E
5959:=
5952:)
5946:(
5941:f
5938:f
5934:R
5893:)
5884:n
5881:(
5878:y
5871:)
5868:n
5865:(
5862:y
5857:Z
5851:n
5843:=
5840:)
5834:(
5829:y
5826:y
5822:R
5798:)
5795:n
5792:(
5789:y
5749:R
5721:t
5701:)
5698:t
5695:(
5692:f
5662:)
5659:t
5656:(
5653:f
5627:t
5622:d
5610:)
5601:t
5598:(
5595:f
5589:)
5586:t
5583:(
5580:f
5559:=
5556:t
5551:d
5539:)
5536:t
5533:(
5530:f
5524:)
5518:+
5515:t
5512:(
5509:f
5488:=
5485:)
5479:(
5474:f
5471:f
5467:R
5423:)
5420:t
5417:(
5414:f
5390:)
5384:(
5379:f
5376:f
5372:R
5351:)
5348:t
5345:(
5342:f
5292:H
5287:]
5282:Z
5278:[
5272:E
5269:]
5265:Z
5261:[
5255:E
5246:Z
5241:Z
5236:R
5232:=
5229:]
5223:H
5218:)
5214:]
5210:Z
5206:[
5200:E
5193:Z
5189:(
5186:)
5183:]
5179:Z
5175:[
5169:E
5162:Z
5158:(
5155:[
5149:E
5146:=
5140:Z
5135:Z
5130:K
5106:T
5101:]
5096:X
5092:[
5086:E
5083:]
5079:X
5075:[
5069:E
5060:X
5055:X
5050:R
5046:=
5043:]
5037:T
5032:)
5028:]
5024:X
5020:[
5014:E
5007:X
5003:(
5000:)
4997:]
4993:X
4989:[
4983:E
4976:X
4972:(
4969:[
4963:E
4960:=
4954:X
4949:X
4944:K
4911:n
4906:C
4897:a
4887:0
4880:a
4870:Z
4865:Z
4860:R
4853:H
4847:a
4823:n
4818:R
4809:a
4799:0
4792:a
4782:X
4777:X
4772:R
4765:T
4759:a
4713:]
4708:j
4704:X
4698:i
4694:X
4690:[
4684:E
4664:)
4661:j
4658:,
4655:i
4652:(
4632:3
4626:3
4603:X
4598:X
4593:R
4569:T
4563:)
4557:3
4553:X
4549:,
4544:2
4540:X
4536:,
4531:1
4527:X
4522:(
4517:=
4513:X
4482:H
4455:.
4452:]
4446:H
4440:Z
4434:Z
4430:[
4424:E
4412:Z
4407:Z
4402:R
4374:Z
4349:]
4340:]
4335:n
4331:X
4325:n
4321:X
4317:[
4311:E
4301:]
4296:2
4292:X
4286:n
4282:X
4278:[
4272:E
4267:]
4262:1
4258:X
4252:n
4248:X
4244:[
4238:E
4203:]
4198:n
4194:X
4188:2
4184:X
4180:[
4174:E
4164:]
4159:2
4155:X
4149:2
4145:X
4141:[
4135:E
4130:]
4125:1
4121:X
4115:2
4111:X
4107:[
4101:E
4091:]
4086:n
4082:X
4076:1
4072:X
4068:[
4062:E
4052:]
4047:2
4043:X
4037:1
4033:X
4029:[
4023:E
4018:]
4013:1
4009:X
4003:1
3999:X
3995:[
3989:E
3983:[
3978:=
3972:X
3967:X
3962:R
3936:n
3930:n
3903:T
3874:]
3867:T
3861:X
3855:X
3850:[
3843:E
3831:X
3826:X
3821:R
3778:T
3773:)
3767:n
3763:X
3759:,
3753:,
3748:1
3744:X
3740:(
3737:=
3733:X
3701:X
3680:n
3674:n
3651:T
3646:)
3640:n
3636:X
3632:,
3626:,
3621:1
3617:X
3613:(
3610:=
3606:X
3571:.
3563:d
3557:)
3551:f
3545:2
3542:(
3533:)
3527:(
3519:X
3516:X
3512:R
3490:=
3487:)
3484:f
3481:(
3476:X
3473:X
3469:S
3447:f
3442:d
3436:)
3430:f
3424:2
3421:(
3412:)
3409:f
3406:(
3401:X
3398:X
3394:S
3372:=
3369:)
3363:(
3355:X
3352:X
3348:R
3319:.
3311:d
3300:f
3294:2
3291:i
3284:e
3280:)
3274:(
3266:X
3263:X
3259:R
3237:=
3234:)
3231:f
3228:(
3223:X
3220:X
3216:S
3194:f
3189:d
3178:f
3172:2
3169:i
3165:e
3161:)
3158:f
3155:(
3150:X
3147:X
3143:S
3121:=
3118:)
3112:(
3104:X
3101:X
3097:R
3068:X
3065:X
3061:S
3035:X
3032:X
3028:R
2975:0
2955:0
2952:=
2913:]
2907:2
2902:|
2893:2
2889:t
2884:X
2879:|
2874:[
2867:E
2863:]
2857:2
2852:|
2843:1
2839:t
2834:X
2829:|
2824:[
2817:E
2809:2
2804:|
2800:)
2795:2
2791:t
2787:,
2782:1
2778:t
2774:(
2766:X
2763:X
2759:R
2754:|
2720:)
2717:0
2714:(
2706:X
2703:X
2699:R
2678:)
2675:0
2672:(
2664:X
2661:X
2657:R
2649:|
2645:)
2639:(
2631:X
2628:X
2624:R
2619:|
2591:.
2582:)
2573:(
2565:X
2562:X
2558:R
2551:=
2548:)
2542:(
2534:X
2531:X
2527:R
2500:)
2495:1
2491:t
2487:,
2482:2
2478:t
2474:(
2466:X
2463:X
2459:R
2452:=
2449:)
2444:2
2440:t
2436:,
2431:1
2427:t
2423:(
2415:X
2412:X
2408:R
2381:X
2378:X
2374:R
2329:2
2319:]
2309:)
2298:t
2294:X
2290:(
2284:)
2270:+
2267:t
2263:X
2259:(
2255:[
2248:E
2242:=
2235:2
2226:)
2220:(
2212:X
2209:X
2205:K
2198:=
2195:)
2189:(
2184:X
2181:X
2143:]
2140:1
2137:,
2134:1
2128:[
2106:X
2103:X
2076:.
2066:2
2062:t
2049:1
2045:t
2033:]
2023:)
2016:2
2012:t
1996:2
1992:t
1987:X
1983:(
1977:)
1970:1
1966:t
1950:1
1946:t
1941:X
1937:(
1933:[
1926:E
1920:=
1910:2
1906:t
1893:1
1889:t
1878:)
1873:2
1869:t
1865:,
1860:1
1856:t
1852:(
1844:X
1841:X
1837:K
1830:=
1827:)
1822:2
1818:t
1814:,
1809:1
1805:t
1801:(
1796:X
1793:X
1748:.
1743:2
1735:=
1732:)
1729:0
1726:(
1718:X
1715:X
1711:K
1668:]
1662:t
1653:X
1642:+
1639:t
1635:X
1630:[
1623:E
1620:=
1616:]
1606:)
1595:t
1591:X
1587:(
1581:)
1567:+
1564:t
1560:X
1556:(
1552:[
1545:E
1542:=
1539:)
1533:(
1525:X
1522:X
1518:K
1486:]
1480:t
1471:X
1460:+
1457:t
1453:X
1448:[
1441:E
1438:=
1435:)
1429:(
1421:X
1418:X
1414:R
1385:1
1381:t
1372:2
1368:t
1364:=
1335:2
1331:t
1308:1
1304:t
1281:2
1231:}
1226:t
1222:X
1218:{
1177:2
1173:t
1153:1
1149:t
1136:]
1128:2
1124:t
1114:X
1104:1
1100:t
1095:X
1090:[
1083:E
1080:=
1076:]
1066:)
1059:2
1055:t
1039:2
1035:t
1030:X
1026:(
1020:)
1013:1
1009:t
993:1
989:t
984:X
980:(
976:[
969:E
966:=
963:)
958:2
954:t
950:,
945:1
941:t
937:(
929:X
926:X
922:K
896:2
892:t
869:1
865:t
825:E
801:]
793:2
789:t
779:X
769:1
765:t
760:X
755:[
748:E
745:=
742:)
737:2
733:t
729:,
724:1
720:t
716:(
708:X
705:X
701:R
675:2
671:t
648:1
644:t
619:t
599:t
577:2
572:t
542:t
514:t
484:t
480:X
443:t
423:t
402:}
397:t
393:X
389:{
272:g
266:f
246:f
240:g
230:f
226:f
222:f
181:e
174:t
167:v
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
