3171:
3157:
3195:
3183:
803:
and references there; in addition this paper gives an extension of the Wold
Theorem that allows more generality for the moving average (not necessarily stable, causal, or minimum delay) accompanied by a sharper characterization of the innovation (identically and independently distributed, not just
592:
This theorem can be considered as an existence theorem: any stationary process has this seemingly special representation. Not only is the existence of such a simple linear and exact representation remarkable, but even more so is the special nature of the moving average model. Imagine creating a
756:
but not independent sequence, then the linear model exists but it is not the only representation of the dynamic dependence of the series. In this latter case, it is possible that the linear model may not be very useful, and there would be a nonlinear model relating the observed value of
394:
is a "deterministic" time series, in the sense that it is completely determined as a linear combination of its past values (see e.g. Anderson (1971) Ch. 7, Section 7.6.3. pp. 420-421). It may include "deterministic terms" like sine/cosine waves of
184:
628:
that exactly represents this process. How this all works for the case of causality and the minimum delay property is discussed in
Scargle (1981), where an extension of the Wold decomposition is discussed.
488:
750:
692:
258:
392:
325:
587:
508:
782:
723:
661:
618:
547:
289:
219:
77:
788:, it is often the case that only linear predictors are considered, partly on the grounds of simplicity, in which case the Wold decomposition is directly relevant.
2292:
2797:
413:
353:
804:
uncorrelated). This extension allows the possibility of models that are more faithful to physical or astrophysical processes, and in particular can sense âłthe
2947:
2571:
1212:
2345:
2784:
96:
415:, but it is a stochastic process and it is also covariance-stationary, it cannot be an arbitrary deterministic process that violates stationarity.
795:
is an alternative that may have only a few coefficients if the corresponding moving average has many. These two models can be combined into an
1207:
907:
1811:
959:
796:
2594:
2486:
850:
3199:
2772:
2646:
3221:
2830:
2491:
2236:
1607:
1197:
1821:
2881:
2093:
1900:
1789:
1747:
261:
986:
3124:
2083:
879:
791:
The Wold representation depends on an infinite number of parameters, although in practice they usually decay rapidly. The
2133:
2675:
2624:
2609:
2599:
2468:
2340:
2307:
2088:
1918:
2744:
2045:
39:
3019:
2820:
1799:
1468:
932:
428:
2904:
2871:
2876:
2619:
2378:
2284:
2264:
2172:
1883:
1701:
1184:
1056:
2050:
1816:
1674:
2636:
2404:
2125:
1979:
1908:
1828:
1686:
1667:
1375:
1096:
2749:
3119:
2886:
2434:
2399:
2363:
2148:
1590:
1499:
1458:
1370:
1061:
900:
818:
695:
19:
This article is about the theorem as used in time series analysis. For an abstract mathematical statement, see
2156:
2140:
3028:
2641:
2581:
2518:
1878:
1740:
1730:
1580:
1494:
2789:
2726:
3066:
2996:
2481:
2368:
1365:
1262:
1169:
1048:
947:
3187:
2065:
593:
process that is a moving average but not satisfying these properties 1â4. For example, the coefficients
3091:
3033:
2976:
2802:
2695:
2604:
2330:
2214:
2073:
1955:
1947:
1762:
1658:
1636:
1595:
1560:
1527:
1473:
1448:
1403:
1342:
1302:
1104:
927:
3170:
2060:
728:
670:
236:
3226:
3014:
2589:
2538:
2514:
2476:
2394:
2373:
2325:
2204:
2182:
2151:
1937:
1888:
1806:
1779:
1735:
1691:
1453:
1229:
1109:
860:
799:, or an autoregressive-integrated-moving average (ARIMA) model if non-stationarity is involved. See
792:
785:
3161:
3086:
3009:
2690:
2454:
2447:
2409:
2317:
2297:
2269:
2002:
1868:
1863:
1853:
1845:
1663:
1624:
1514:
1504:
1413:
1192:
1148:
1066:
991:
893:
2736:
3175:
2986:
2840:
2685:
2561:
2458:
2442:
2419:
2196:
1930:
1913:
1873:
1784:
1679:
1641:
1612:
1572:
1532:
1478:
1395:
1081:
1076:
47:
20:
878:, Second revised edition, with an Appendix on "Recent Developments in Time Series Analysis" by
842:
835:
370:
297:
3081:
3051:
3043:
2863:
2854:
2779:
2710:
2566:
2551:
2526:
2414:
2355:
2221:
2209:
1835:
1752:
1696:
1619:
1463:
1385:
1164:
1038:
865:
Studies in astronomical time series analysis. I â Modeling random processes in the time domain
846:
559:
493:
3106:
3061:
2825:
2812:
2705:
2680:
2614:
2546:
2424:
2032:
1925:
1858:
1771:
1718:
1537:
1408:
1202:
1001:
968:
633:
760:
701:
698:, then the linear model is the only possible representation relating the observed value of
639:
596:
525:
267:
197:
55:
3023:
2767:
2629:
2556:
2231:
2105:
2078:
2055:
2024:
1651:
1646:
1600:
1330:
981:
2972:
2967:
1430:
1360:
1006:
398:
338:
3215:
3129:
3096:
2959:
2920:
2731:
2700:
2164:
2118:
1723:
1425:
1252:
1016:
1011:
805:
292:
1282:
3071:
3004:
2981:
2896:
2226:
1522:
1420:
1355:
1297:
1219:
1174:
830:
753:
664:
38:(not to be confused with the Wold theorem that is the discrete-time analog of the
3114:
3076:
2759:
2660:
2522:
2335:
2302:
1794:
1711:
1706:
1350:
1307:
1287:
1267:
1257:
1026:
871:
222:
50:
43:
1960:
1440:
1140:
1071:
1021:
996:
916:
27:
179:{\displaystyle Y_{t}=\sum _{j=0}^{\infty }b_{j}\varepsilon _{t-j}+\eta _{t},}
2113:
1965:
1585:
1380:
1292:
1277:
1272:
1237:
1629:
1247:
1124:
1119:
1114:
1086:
3134:
2835:
867:. Astrophysical Journal Supplement Series. Vol. 45. pp. 1â71.
359:
infinite vector of moving average weights (coefficients or parameters)
3056:
2037:
2011:
1991:
1242:
1033:
624:
model. Nevertheless the theorem assures the existence of a causal
976:
2945:
2512:
2259:
1558:
1328:
945:
889:
885:
632:
The usefulness of the Wold
Theorem is that it allows the
841:(Revised ed.). San Diego: Academic Press. pp.
421:
The moving average coefficients have these properties:
291:â that is, a white noise process that is input to the
763:
731:
704:
673:
642:
599:
562:
528:
496:
431:
401:
373:
341:
300:
270:
239:
200:
99:
58:
2798:
Autoregressive conditional heteroskedasticity (ARCH)
3105:
3042:
2995:
2958:
2913:
2895:
2862:
2853:
2811:
2758:
2719:
2668:
2659:
2580:
2537:
2467:
2433:
2387:
2354:
2316:
2283:
2195:
2104:
2023:
1978:
1946:
1899:
1844:
1770:
1761:
1571:
1513:
1487:
1439:
1394:
1341:
1228:
1183:
1157:
1139:
1095:
1047:
967:
958:
834:
776:
744:
717:
686:
655:
612:
581:
541:
502:
482:
407:
386:
347:
319:
283:
252:
213:
178:
79:can be written as the sum of two time series, one
71:
876:A Study in the Analysis of Stationary Time Series
483:{\displaystyle \sum _{j=1}^{\infty }|b_{j}|^{2}}
2346:Multivariate adaptive regression splines (MARS)
833:; Grether, David M.; Carvalho, José L. (1995).
901:
784:to its past evolution. However, in practical
8:
314:
301:
2955:
2942:
2859:
2665:
2534:
2509:
2280:
2256:
1984:
1767:
1568:
1555:
1338:
1325:
964:
955:
942:
908:
894:
886:
797:autoregressive-moving average (ARMA) model
882:. Almqvist and Wiksell Book Co., Uppsala.
768:
762:
736:
730:
709:
703:
678:
672:
647:
641:
604:
598:
567:
561:
533:
527:
495:
474:
469:
462:
453:
447:
436:
430:
400:
378:
372:
340:
308:
299:
275:
269:
260:is an uncorrelated sequence which is the
244:
238:
205:
199:
167:
148:
138:
128:
117:
104:
98:
63:
57:
823:The Statistical Analysis of Time Series
800:
2872:KaplanâMeier estimator (product limit)
725:to its past evolution. However, when
512:Causal (i.e. there are no terms with
7:
3182:
2882:Accelerated failure time (AFT) model
3194:
2477:Analysis of variance (ANOVA, anova)
2572:CochranâMantelâHaenszel statistics
1198:Pearson product-moment correlation
497:
448:
129:
14:
425:Stable, that is, square summable
3193:
3181:
3169:
3156:
3155:
837:Analysis of Economic Time Series
745:{\displaystyle \varepsilon _{t}}
687:{\displaystyle \varepsilon _{t}}
253:{\displaystyle \varepsilon _{t}}
2831:Least-squares spectral analysis
16:Theorem of stationary processes
1812:Mean-unbiased minimum-variance
470:
454:
1:
3125:Geographic information system
2341:Simultaneous equations models
556:It is conventional to define
2308:Coefficient of determination
1919:Uniformly most powerful test
626:minimum delay moving average
620:could define an acausal and
2877:Proportional hazards models
2821:Spectral density estimation
2803:Vector autoregression (VAR)
2237:Maximum posterior estimator
1469:Randomized controlled trial
36:Wold representation theorem
3243:
2637:Multivariate distributions
1057:Average absolute deviation
18:
3151:
2954:
2941:
2625:Structural equation model
2533:
2508:
2279:
2255:
1987:
1961:Score/Lagrange multiplier
1567:
1554:
1376:Sample size determination
1337:
1324:
954:
941:
923:
387:{\displaystyle \eta _{t}}
320:{\displaystyle \{b_{j}\}}
3120:Environmental statistics
2642:Elliptical distributions
2435:Generalized linear model
2364:Simple linear regression
2134:HodgesâLehmann estimator
1591:Probability distribution
1500:Stochastic approximation
1062:Coefficient of variation
663:to be approximated by a
636:evolution of a variable
2780:Cross-correlation (XCF)
2388:Non-standard predictors
1822:LehmannâScheffĂ© theorem
1495:Adaptive clinical trial
582:{\displaystyle b_{0}=1}
503:{\displaystyle \infty }
40:WienerâKhinchin theorem
3222:Theorems in statistics
3176:Mathematics portal
2997:Engineering statistics
2905:NelsonâAalen estimator
2482:Analysis of covariance
2369:Ordinary least squares
2293:Pearson product-moment
1697:Statistical functional
1608:Empirical distribution
1441:Controlled experiments
1170:Frequency distribution
948:Descriptive statistics
778:
746:
719:
688:
657:
614:
583:
543:
504:
484:
452:
409:
388:
349:
321:
285:
254:
215:
180:
133:
73:
3092:Population statistics
3034:System identification
2768:Autocorrelation (ACF)
2696:Exponential smoothing
2610:Discriminant analysis
2605:Canonical correlation
2469:Partition of variance
2331:Regression validation
2175:(JonckheereâTerpstra)
2074:Likelihood-ratio test
1763:Frequentist inference
1675:Locationâscale family
1596:Sampling distribution
1561:Statistical inference
1528:Cross-sectional study
1515:Observational studies
1474:Randomized experiment
1303:Stem-and-leaf display
1105:Central limit theorem
779:
777:{\displaystyle Y_{t}}
747:
720:
718:{\displaystyle Y_{t}}
689:
667:. If the innovations
658:
656:{\displaystyle Y_{t}}
615:
613:{\displaystyle b_{j}}
584:
544:
542:{\displaystyle b_{j}}
505:
485:
432:
410:
389:
350:
322:
286:
284:{\displaystyle Y_{t}}
255:
216:
214:{\displaystyle Y_{t}}
181:
113:
74:
72:{\displaystyle Y_{t}}
48:covariance-stationary
3015:Probabilistic design
2600:Principal components
2443:Exponential families
2395:Nonlinear regression
2374:General linear model
2336:Mixed effects models
2326:Errors and residuals
2303:Confounding variable
2205:Bayesian probability
2183:Van der Waerden test
2173:Ordered alternative
1938:Multiple comparisons
1817:RaoâBlackwellization
1780:Estimating equations
1736:Statistical distance
1454:Factorial experiment
987:Arithmetic-Geometric
793:autoregressive model
786:time series analysis
761:
729:
702:
671:
640:
597:
560:
526:
494:
429:
399:
371:
339:
298:
268:
237:
198:
97:
56:
32:Wold's decomposition
3087:Official statistics
3010:Methods engineering
2691:Seasonal adjustment
2459:Poisson regressions
2379:Bayesian regression
2318:Regression analysis
2298:Partial correlation
2270:Regression analysis
1869:Prediction interval
1864:Likelihood interval
1854:Confidence interval
1846:Interval estimation
1807:Unbiased estimators
1625:Model specification
1505:Up-and-down designs
1193:Partial correlation
1149:Index of dispersion
1067:Interquartile range
3107:Spatial statistics
2987:Medical statistics
2887:First hitting time
2841:Whittle likelihood
2492:Degrees of freedom
2487:Multivariate ANOVA
2420:Heteroscedasticity
2232:Bayesian estimator
2197:Bayesian inference
2046:KolmogorovâSmirnov
1931:Randomization test
1901:Testing hypotheses
1874:Tolerance interval
1785:Maximum likelihood
1680:Exponential family
1613:Density estimation
1573:Statistical theory
1533:Natural experiment
1479:Scientific control
1396:Survey methodology
1082:Standard deviation
774:
742:
715:
684:
653:
610:
579:
539:
500:
480:
405:
384:
345:
317:
281:
262:innovation process
250:
211:
176:
69:
46:, says that every
21:Wold decomposition
3209:
3208:
3147:
3146:
3143:
3142:
3082:National accounts
3052:Actuarial science
3044:Social statistics
2937:
2936:
2933:
2932:
2929:
2928:
2864:Survival function
2849:
2848:
2711:Granger causality
2552:Contingency table
2527:Survival analysis
2504:
2503:
2500:
2499:
2356:Linear regression
2251:
2250:
2247:
2246:
2222:Credible interval
2191:
2190:
1974:
1973:
1790:Method of moments
1659:Parametric family
1620:Statistical model
1550:
1549:
1546:
1545:
1464:Random assignment
1386:Statistical power
1320:
1319:
1316:
1315:
1165:Contingency table
1135:
1134:
1002:Generalized/power
622:non-minimum delay
408:{\displaystyle t}
348:{\displaystyle b}
225:being considered,
3234:
3197:
3196:
3185:
3184:
3174:
3173:
3159:
3158:
3062:Crime statistics
2956:
2943:
2860:
2826:Fourier analysis
2813:Frequency domain
2793:
2740:
2706:Structural break
2666:
2615:Cluster analysis
2562:Log-linear model
2535:
2510:
2451:
2425:Homoscedasticity
2281:
2257:
2176:
2168:
2160:
2159:(KruskalâWallis)
2144:
2129:
2084:Cross validation
2069:
2051:AndersonâDarling
1998:
1985:
1956:Likelihood-ratio
1948:Parametric tests
1926:Permutation test
1909:1- & 2-tails
1800:Minimum distance
1772:Point estimation
1768:
1719:Optimal decision
1670:
1569:
1556:
1538:Quasi-experiment
1488:Adaptive designs
1339:
1326:
1203:Rank correlation
965:
956:
943:
910:
903:
896:
887:
868:
856:
840:
826:
783:
781:
780:
775:
773:
772:
751:
749:
748:
743:
741:
740:
724:
722:
721:
716:
714:
713:
693:
691:
690:
685:
683:
682:
662:
660:
659:
654:
652:
651:
627:
623:
619:
617:
616:
611:
609:
608:
588:
586:
585:
580:
572:
571:
548:
546:
545:
540:
538:
537:
509:
507:
506:
501:
489:
487:
486:
481:
479:
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473:
467:
466:
457:
451:
446:
414:
412:
411:
406:
393:
391:
390:
385:
383:
382:
354:
352:
351:
346:
326:
324:
323:
318:
313:
312:
290:
288:
287:
282:
280:
279:
259:
257:
256:
251:
249:
248:
220:
218:
217:
212:
210:
209:
185:
183:
182:
177:
172:
171:
159:
158:
143:
142:
132:
127:
109:
108:
78:
76:
75:
70:
68:
67:
42:), named after
3242:
3241:
3237:
3236:
3235:
3233:
3232:
3231:
3212:
3211:
3210:
3205:
3168:
3139:
3101:
3038:
3024:quality control
2991:
2973:Clinical trials
2950:
2925:
2909:
2897:Hazard function
2891:
2845:
2807:
2791:
2754:
2750:BreuschâGodfrey
2738:
2715:
2655:
2630:Factor analysis
2576:
2557:Graphical model
2529:
2496:
2463:
2449:
2429:
2383:
2350:
2312:
2275:
2274:
2243:
2187:
2174:
2166:
2158:
2142:
2127:
2106:Rank statistics
2100:
2079:Model selection
2067:
2025:Goodness of fit
2019:
1996:
1970:
1942:
1895:
1840:
1829:Median unbiased
1757:
1668:
1601:Order statistic
1563:
1542:
1509:
1483:
1435:
1390:
1333:
1331:Data collection
1312:
1224:
1179:
1153:
1131:
1091:
1043:
960:Continuous data
950:
937:
919:
914:
859:
853:
829:
819:Anderson, T. W.
817:
814:
764:
759:
758:
732:
727:
726:
705:
700:
699:
674:
669:
668:
643:
638:
637:
625:
621:
600:
595:
594:
563:
558:
557:
549:independent of
529:
524:
523:
492:
491:
468:
458:
427:
426:
397:
396:
374:
369:
368:
337:
336:
304:
296:
295:
271:
266:
265:
264:to the process
240:
235:
234:
201:
196:
195:
163:
144:
134:
100:
95:
94:
59:
54:
53:
24:
17:
12:
11:
5:
3240:
3238:
3230:
3229:
3224:
3214:
3213:
3207:
3206:
3204:
3203:
3191:
3179:
3165:
3152:
3149:
3148:
3145:
3144:
3141:
3140:
3138:
3137:
3132:
3127:
3122:
3117:
3111:
3109:
3103:
3102:
3100:
3099:
3094:
3089:
3084:
3079:
3074:
3069:
3064:
3059:
3054:
3048:
3046:
3040:
3039:
3037:
3036:
3031:
3026:
3017:
3012:
3007:
3001:
2999:
2993:
2992:
2990:
2989:
2984:
2979:
2970:
2968:Bioinformatics
2964:
2962:
2952:
2951:
2946:
2939:
2938:
2935:
2934:
2931:
2930:
2927:
2926:
2924:
2923:
2917:
2915:
2911:
2910:
2908:
2907:
2901:
2899:
2893:
2892:
2890:
2889:
2884:
2879:
2874:
2868:
2866:
2857:
2851:
2850:
2847:
2846:
2844:
2843:
2838:
2833:
2828:
2823:
2817:
2815:
2809:
2808:
2806:
2805:
2800:
2795:
2787:
2782:
2777:
2776:
2775:
2773:partial (PACF)
2764:
2762:
2756:
2755:
2753:
2752:
2747:
2742:
2734:
2729:
2723:
2721:
2720:Specific tests
2717:
2716:
2714:
2713:
2708:
2703:
2698:
2693:
2688:
2683:
2678:
2672:
2670:
2663:
2657:
2656:
2654:
2653:
2652:
2651:
2650:
2649:
2634:
2633:
2632:
2622:
2620:Classification
2617:
2612:
2607:
2602:
2597:
2592:
2586:
2584:
2578:
2577:
2575:
2574:
2569:
2567:McNemar's test
2564:
2559:
2554:
2549:
2543:
2541:
2531:
2530:
2513:
2506:
2505:
2502:
2501:
2498:
2497:
2495:
2494:
2489:
2484:
2479:
2473:
2471:
2465:
2464:
2462:
2461:
2445:
2439:
2437:
2431:
2430:
2428:
2427:
2422:
2417:
2412:
2407:
2405:Semiparametric
2402:
2397:
2391:
2389:
2385:
2384:
2382:
2381:
2376:
2371:
2366:
2360:
2358:
2352:
2351:
2349:
2348:
2343:
2338:
2333:
2328:
2322:
2320:
2314:
2313:
2311:
2310:
2305:
2300:
2295:
2289:
2287:
2277:
2276:
2273:
2272:
2267:
2261:
2260:
2253:
2252:
2249:
2248:
2245:
2244:
2242:
2241:
2240:
2239:
2229:
2224:
2219:
2218:
2217:
2212:
2201:
2199:
2193:
2192:
2189:
2188:
2186:
2185:
2180:
2179:
2178:
2170:
2162:
2146:
2143:(MannâWhitney)
2138:
2137:
2136:
2123:
2122:
2121:
2110:
2108:
2102:
2101:
2099:
2098:
2097:
2096:
2091:
2086:
2076:
2071:
2068:(ShapiroâWilk)
2063:
2058:
2053:
2048:
2043:
2035:
2029:
2027:
2021:
2020:
2018:
2017:
2009:
2000:
1988:
1982:
1980:Specific tests
1976:
1975:
1972:
1971:
1969:
1968:
1963:
1958:
1952:
1950:
1944:
1943:
1941:
1940:
1935:
1934:
1933:
1923:
1922:
1921:
1911:
1905:
1903:
1897:
1896:
1894:
1893:
1892:
1891:
1886:
1876:
1871:
1866:
1861:
1856:
1850:
1848:
1842:
1841:
1839:
1838:
1833:
1832:
1831:
1826:
1825:
1824:
1819:
1804:
1803:
1802:
1797:
1792:
1787:
1776:
1774:
1765:
1759:
1758:
1756:
1755:
1750:
1745:
1744:
1743:
1733:
1728:
1727:
1726:
1716:
1715:
1714:
1709:
1704:
1694:
1689:
1684:
1683:
1682:
1677:
1672:
1656:
1655:
1654:
1649:
1644:
1634:
1633:
1632:
1627:
1617:
1616:
1615:
1605:
1604:
1603:
1593:
1588:
1583:
1577:
1575:
1565:
1564:
1559:
1552:
1551:
1548:
1547:
1544:
1543:
1541:
1540:
1535:
1530:
1525:
1519:
1517:
1511:
1510:
1508:
1507:
1502:
1497:
1491:
1489:
1485:
1484:
1482:
1481:
1476:
1471:
1466:
1461:
1456:
1451:
1445:
1443:
1437:
1436:
1434:
1433:
1431:Standard error
1428:
1423:
1418:
1417:
1416:
1411:
1400:
1398:
1392:
1391:
1389:
1388:
1383:
1378:
1373:
1368:
1363:
1361:Optimal design
1358:
1353:
1347:
1345:
1335:
1334:
1329:
1322:
1321:
1318:
1317:
1314:
1313:
1311:
1310:
1305:
1300:
1295:
1290:
1285:
1280:
1275:
1270:
1265:
1260:
1255:
1250:
1245:
1240:
1234:
1232:
1226:
1225:
1223:
1222:
1217:
1216:
1215:
1210:
1200:
1195:
1189:
1187:
1181:
1180:
1178:
1177:
1172:
1167:
1161:
1159:
1158:Summary tables
1155:
1154:
1152:
1151:
1145:
1143:
1137:
1136:
1133:
1132:
1130:
1129:
1128:
1127:
1122:
1117:
1107:
1101:
1099:
1093:
1092:
1090:
1089:
1084:
1079:
1074:
1069:
1064:
1059:
1053:
1051:
1045:
1044:
1042:
1041:
1036:
1031:
1030:
1029:
1024:
1019:
1014:
1009:
1004:
999:
994:
992:Contraharmonic
989:
984:
973:
971:
962:
952:
951:
946:
939:
938:
936:
935:
930:
924:
921:
920:
915:
913:
912:
905:
898:
890:
884:
883:
869:
861:Scargle, J. D.
857:
851:
827:
813:
810:
801:Scargle (1981)
771:
767:
739:
735:
712:
708:
681:
677:
650:
646:
607:
603:
590:
589:
578:
575:
570:
566:
554:
536:
532:
520:
517:
510:
499:
477:
472:
465:
461:
456:
450:
445:
442:
439:
435:
419:
418:
417:
416:
404:
381:
377:
363:
362:
361:
360:
344:
331:
330:
329:
328:
316:
311:
307:
303:
278:
274:
247:
243:
229:
228:
227:
226:
208:
204:
187:
186:
175:
170:
166:
162:
157:
154:
151:
147:
141:
137:
131:
126:
123:
120:
116:
112:
107:
103:
66:
62:
15:
13:
10:
9:
6:
4:
3:
2:
3239:
3228:
3225:
3223:
3220:
3219:
3217:
3202:
3201:
3192:
3190:
3189:
3180:
3178:
3177:
3172:
3166:
3164:
3163:
3154:
3153:
3150:
3136:
3133:
3131:
3130:Geostatistics
3128:
3126:
3123:
3121:
3118:
3116:
3113:
3112:
3110:
3108:
3104:
3098:
3097:Psychometrics
3095:
3093:
3090:
3088:
3085:
3083:
3080:
3078:
3075:
3073:
3070:
3068:
3065:
3063:
3060:
3058:
3055:
3053:
3050:
3049:
3047:
3045:
3041:
3035:
3032:
3030:
3027:
3025:
3021:
3018:
3016:
3013:
3011:
3008:
3006:
3003:
3002:
3000:
2998:
2994:
2988:
2985:
2983:
2980:
2978:
2974:
2971:
2969:
2966:
2965:
2963:
2961:
2960:Biostatistics
2957:
2953:
2949:
2944:
2940:
2922:
2921:Log-rank test
2919:
2918:
2916:
2912:
2906:
2903:
2902:
2900:
2898:
2894:
2888:
2885:
2883:
2880:
2878:
2875:
2873:
2870:
2869:
2867:
2865:
2861:
2858:
2856:
2852:
2842:
2839:
2837:
2834:
2832:
2829:
2827:
2824:
2822:
2819:
2818:
2816:
2814:
2810:
2804:
2801:
2799:
2796:
2794:
2792:(BoxâJenkins)
2788:
2786:
2783:
2781:
2778:
2774:
2771:
2770:
2769:
2766:
2765:
2763:
2761:
2757:
2751:
2748:
2746:
2745:DurbinâWatson
2743:
2741:
2735:
2733:
2730:
2728:
2727:DickeyâFuller
2725:
2724:
2722:
2718:
2712:
2709:
2707:
2704:
2702:
2701:Cointegration
2699:
2697:
2694:
2692:
2689:
2687:
2684:
2682:
2679:
2677:
2676:Decomposition
2674:
2673:
2671:
2667:
2664:
2662:
2658:
2648:
2645:
2644:
2643:
2640:
2639:
2638:
2635:
2631:
2628:
2627:
2626:
2623:
2621:
2618:
2616:
2613:
2611:
2608:
2606:
2603:
2601:
2598:
2596:
2593:
2591:
2588:
2587:
2585:
2583:
2579:
2573:
2570:
2568:
2565:
2563:
2560:
2558:
2555:
2553:
2550:
2548:
2547:Cohen's kappa
2545:
2544:
2542:
2540:
2536:
2532:
2528:
2524:
2520:
2516:
2511:
2507:
2493:
2490:
2488:
2485:
2483:
2480:
2478:
2475:
2474:
2472:
2470:
2466:
2460:
2456:
2452:
2446:
2444:
2441:
2440:
2438:
2436:
2432:
2426:
2423:
2421:
2418:
2416:
2413:
2411:
2408:
2406:
2403:
2401:
2400:Nonparametric
2398:
2396:
2393:
2392:
2390:
2386:
2380:
2377:
2375:
2372:
2370:
2367:
2365:
2362:
2361:
2359:
2357:
2353:
2347:
2344:
2342:
2339:
2337:
2334:
2332:
2329:
2327:
2324:
2323:
2321:
2319:
2315:
2309:
2306:
2304:
2301:
2299:
2296:
2294:
2291:
2290:
2288:
2286:
2282:
2278:
2271:
2268:
2266:
2263:
2262:
2258:
2254:
2238:
2235:
2234:
2233:
2230:
2228:
2225:
2223:
2220:
2216:
2213:
2211:
2208:
2207:
2206:
2203:
2202:
2200:
2198:
2194:
2184:
2181:
2177:
2171:
2169:
2163:
2161:
2155:
2154:
2153:
2150:
2149:Nonparametric
2147:
2145:
2139:
2135:
2132:
2131:
2130:
2124:
2120:
2119:Sample median
2117:
2116:
2115:
2112:
2111:
2109:
2107:
2103:
2095:
2092:
2090:
2087:
2085:
2082:
2081:
2080:
2077:
2075:
2072:
2070:
2064:
2062:
2059:
2057:
2054:
2052:
2049:
2047:
2044:
2042:
2040:
2036:
2034:
2031:
2030:
2028:
2026:
2022:
2016:
2014:
2010:
2008:
2006:
2001:
1999:
1994:
1990:
1989:
1986:
1983:
1981:
1977:
1967:
1964:
1962:
1959:
1957:
1954:
1953:
1951:
1949:
1945:
1939:
1936:
1932:
1929:
1928:
1927:
1924:
1920:
1917:
1916:
1915:
1912:
1910:
1907:
1906:
1904:
1902:
1898:
1890:
1887:
1885:
1882:
1881:
1880:
1877:
1875:
1872:
1870:
1867:
1865:
1862:
1860:
1857:
1855:
1852:
1851:
1849:
1847:
1843:
1837:
1834:
1830:
1827:
1823:
1820:
1818:
1815:
1814:
1813:
1810:
1809:
1808:
1805:
1801:
1798:
1796:
1793:
1791:
1788:
1786:
1783:
1782:
1781:
1778:
1777:
1775:
1773:
1769:
1766:
1764:
1760:
1754:
1751:
1749:
1746:
1742:
1739:
1738:
1737:
1734:
1732:
1729:
1725:
1724:loss function
1722:
1721:
1720:
1717:
1713:
1710:
1708:
1705:
1703:
1700:
1699:
1698:
1695:
1693:
1690:
1688:
1685:
1681:
1678:
1676:
1673:
1671:
1665:
1662:
1661:
1660:
1657:
1653:
1650:
1648:
1645:
1643:
1640:
1639:
1638:
1635:
1631:
1628:
1626:
1623:
1622:
1621:
1618:
1614:
1611:
1610:
1609:
1606:
1602:
1599:
1598:
1597:
1594:
1592:
1589:
1587:
1584:
1582:
1579:
1578:
1576:
1574:
1570:
1566:
1562:
1557:
1553:
1539:
1536:
1534:
1531:
1529:
1526:
1524:
1521:
1520:
1518:
1516:
1512:
1506:
1503:
1501:
1498:
1496:
1493:
1492:
1490:
1486:
1480:
1477:
1475:
1472:
1470:
1467:
1465:
1462:
1460:
1457:
1455:
1452:
1450:
1447:
1446:
1444:
1442:
1438:
1432:
1429:
1427:
1426:Questionnaire
1424:
1422:
1419:
1415:
1412:
1410:
1407:
1406:
1405:
1402:
1401:
1399:
1397:
1393:
1387:
1384:
1382:
1379:
1377:
1374:
1372:
1369:
1367:
1364:
1362:
1359:
1357:
1354:
1352:
1349:
1348:
1346:
1344:
1340:
1336:
1332:
1327:
1323:
1309:
1306:
1304:
1301:
1299:
1296:
1294:
1291:
1289:
1286:
1284:
1281:
1279:
1276:
1274:
1271:
1269:
1266:
1264:
1261:
1259:
1256:
1254:
1253:Control chart
1251:
1249:
1246:
1244:
1241:
1239:
1236:
1235:
1233:
1231:
1227:
1221:
1218:
1214:
1211:
1209:
1206:
1205:
1204:
1201:
1199:
1196:
1194:
1191:
1190:
1188:
1186:
1182:
1176:
1173:
1171:
1168:
1166:
1163:
1162:
1160:
1156:
1150:
1147:
1146:
1144:
1142:
1138:
1126:
1123:
1121:
1118:
1116:
1113:
1112:
1111:
1108:
1106:
1103:
1102:
1100:
1098:
1094:
1088:
1085:
1083:
1080:
1078:
1075:
1073:
1070:
1068:
1065:
1063:
1060:
1058:
1055:
1054:
1052:
1050:
1046:
1040:
1037:
1035:
1032:
1028:
1025:
1023:
1020:
1018:
1015:
1013:
1010:
1008:
1005:
1003:
1000:
998:
995:
993:
990:
988:
985:
983:
980:
979:
978:
975:
974:
972:
970:
966:
963:
961:
957:
953:
949:
944:
940:
934:
931:
929:
926:
925:
922:
918:
911:
906:
904:
899:
897:
892:
891:
888:
881:
880:Peter Whittle
877:
873:
870:
866:
862:
858:
854:
852:0-12-515751-7
848:
844:
839:
838:
832:
828:
824:
820:
816:
815:
811:
809:
807:
806:arrow of time
802:
798:
794:
789:
787:
769:
765:
755:
752:is merely an
737:
733:
710:
706:
697:
679:
675:
666:
648:
644:
635:
630:
605:
601:
576:
573:
568:
564:
555:
552:
534:
530:
521:
519:Minimum delay
518:
515:
511:
475:
463:
459:
443:
440:
437:
433:
424:
423:
422:
402:
379:
375:
367:
366:
365:
364:
358:
342:
335:
334:
333:
332:
309:
305:
294:
293:linear filter
276:
272:
263:
245:
241:
233:
232:
231:
230:
224:
206:
202:
194:
193:
192:
191:
190:
173:
168:
164:
160:
155:
152:
149:
145:
139:
135:
124:
121:
118:
114:
110:
105:
101:
93:
92:
91:
88:
86:
82:
81:deterministic
64:
60:
52:
49:
45:
41:
37:
33:
29:
22:
3198:
3186:
3167:
3160:
3072:Econometrics
3022: /
3005:Chemometrics
2982:Epidemiology
2975: /
2948:Applications
2790:ARIMA model
2737:Q-statistic
2686:Stationarity
2582:Multivariate
2525: /
2521: /
2519:Multivariate
2517: /
2457: /
2453: /
2227:Bayes factor
2126:Signed rank
2038:
2012:
2004:
1992:
1687:Completeness
1523:Cohort study
1421:Opinion poll
1356:Missing data
1343:Study design
1298:Scatter plot
1220:Scatter plot
1213:Spearman's Ï
1175:Grouped data
875:
864:
836:
822:
790:
754:uncorrelated
665:linear model
631:
591:
550:
513:
420:
356:
188:
89:
84:
80:
35:
31:
25:
3227:Time series
3200:WikiProject
3115:Cartography
3077:Jurimetrics
3029:Reliability
2760:Time domain
2739:(LjungâBox)
2661:Time-series
2539:Categorical
2523:Time-series
2515:Categorical
2450:(Bernoulli)
2285:Correlation
2265:Correlation
2061:JarqueâBera
2033:Chi-squared
1795:M-estimator
1748:Asymptotics
1692:Sufficiency
1459:Interaction
1371:Replication
1351:Effect size
1308:Violin plot
1288:Radar chart
1268:Forest plot
1258:Correlogram
1208:Kendall's Ï
831:Nerlove, M.
696:independent
223:time series
51:time series
44:Herman Wold
3216:Categories
3067:Demography
2785:ARMA model
2590:Regression
2167:(Friedman)
2128:(Wilcoxon)
2066:Normality
2056:Lilliefors
2003:Student's
1879:Resampling
1753:Robustness
1741:divergence
1731:Efficiency
1669:(monotone)
1664:Likelihood
1581:Population
1414:Stratified
1366:Population
1185:Dependence
1141:Count data
1072:Percentile
1049:Dispersion
982:Arithmetic
917:Statistics
812:References
522:Constant (
85:stochastic
28:statistics
2448:Logistic
2215:posterior
2141:Rank sum
1889:Jackknife
1884:Bootstrap
1702:Bootstrap
1637:Parameter
1586:Statistic
1381:Statistic
1293:Run chart
1278:Pie chart
1273:Histogram
1263:Fan chart
1238:Bar chart
1120:L-moments
1007:Geometric
734:ε
676:ε
498:∞
449:∞
434:∑
376:η
242:ε
165:η
153:−
146:ε
130:∞
115:∑
90:Formally
3162:Category
2855:Survival
2732:Johansen
2455:Binomial
2410:Isotonic
1997:(normal)
1642:location
1449:Blocking
1404:Sampling
1283:QâQ plot
1248:Box plot
1230:Graphics
1125:Skewness
1115:Kurtosis
1087:Variance
1017:Heronian
1012:Harmonic
872:Wold, H.
863:(1981).
825:. Wiley.
821:(1971).
357:possibly
83:and one
3188:Commons
3135:Kriging
3020:Process
2977:studies
2836:Wavelet
2669:General
1836:Plug-in
1630:L space
1409:Cluster
1110:Moments
928:Outline
874:(1954)
634:dynamic
516:< 0)
355:is the
221:is the
189:where:
34:or the
3057:Census
2647:Normal
2595:Manova
2415:Robust
2165:2-way
2157:1-way
1995:-test
1666:
1243:Biplot
1034:Median
1027:Lehmer
969:Center
849:
2681:Trend
2210:prior
2152:anova
2041:-test
2015:-test
2007:-test
1914:Power
1859:Pivot
1652:shape
1647:scale
1097:Shape
1077:Range
1022:Heinz
997:Cubic
933:Index
843:30â36
490:<
2914:Test
2114:Sign
1966:Wald
1039:Mode
977:Mean
847:ISBN
694:are
2094:BIC
2089:AIC
808:.âł
26:In
3218::
845:.
87:.
30:,
2039:G
2013:F
2005:t
1993:Z
1712:V
1707:U
909:e
902:t
895:v
855:.
770:t
766:Y
738:t
711:t
707:Y
680:t
649:t
645:Y
606:j
602:b
577:1
574:=
569:0
565:b
553:)
551:t
535:j
531:b
514:j
476:2
471:|
464:j
460:b
455:|
444:1
441:=
438:j
403:t
380:t
343:b
327:.
315:}
310:j
306:b
302:{
277:t
273:Y
246:t
207:t
203:Y
174:,
169:t
161:+
156:j
150:t
140:j
136:b
125:0
122:=
119:j
111:=
106:t
102:Y
65:t
61:Y
23:.
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