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Decomposition of time series

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Sometimes the trend and cyclical components are grouped into one, called the trend-cycle component. The trend-cycle component can just be referred to as the "trend" component, even though it may contain cyclical behavior. For example, a seasonal decomposition of time series by Loess (STL) plot
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In policy analysis, forecasting future production of biofuels is key data for making better decisions, and statistical time series models have recently been developed to forecast renewable energy sources, and a multiplicative decomposition method was designed to forecast future production of
160:. It seeks to construct, from an observed time series, a number of component series (that could be used to reconstruct the original by additions or multiplications) where each of these has a certain characteristic or type of behavior. For example, time series are usually decomposed into: 559:. The R statistical software also includes many packages for time series decomposition, such as seasonal, stl, stlplus, and bfast. Bayesian methods are also available; one example is the BEAST method in a package Rbeast in R, Matlab, and Python. 490:
An additive model would be used when the variations around the trend do not vary with the level of the time series whereas a multiplicative model would be appropriate if the trend is proportional to the level of the time series.
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decomposes a time series into seasonal, trend and irregular components using loess and plots the components separately, whereby the cyclical component (if present in the data) is included in the "trend" component plot.
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Kendall shows an example of a decomposition into smooth, seasonal and irregular factors for a set of data containing values of the monthly aircraft miles flown by
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into several components, each representing one of the underlying categories of patterns. There are two principal types of decomposition, which are outlined below.
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makes use of the idea of decomposing a times series into deterministic and non-deterministic components (or predictable and unpredictable components). See
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An example of using multiplicative decomposition in biohydrogen production forecast.
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An example of statistical software for this type of decomposition is the program
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Statistical task that deconstructs a time series into several components
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Asadi, Nooshin; Karimi Alavijeh, Masih; Zilouei, Hamid (2016).
29: 858: 198:, which reflects the long-term progression of the series ( 813:
Li, Yang; Zhao, Kaiguang; Hu, Tongxi; Zhang, Xuesong.
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Autoregressive conditional heteroskedasticity (ARCH)
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"Models with Trend". 672: 670: 613: 611: 609: 785:"seasonal: R Interface to X-13-ARIMA-SEATS" 3207: 3193: 3185: 2928: 2915: 2832: 2638: 2507: 2482: 2253: 2229: 1957: 1740: 1541: 1528: 1311: 1298: 937: 928: 915: 881: 867: 859: 649:The Oxford Dictionary of Statistical Terms 476: 467: 454: 441: 428: 415: 409: 379: 366: 353: 340: 327: 321: 285: 279: 248: 242: 215: 209: 174: 168: 120:Learn how and when to remove this message 734:International Journal of Hydrogen Energy 401:whereas a multiplicative model would be 640: 638: 605: 2845:Kaplan–Meier estimator (product limit) 148:Decomposition based on rates of change 678:"6.1 Time series components | OTexts" 653:. New York: Oxford University Press. 619:"6.1 Time series components | OTexts" 499:Decomposition based on predictability 7: 3155: 2855:Accelerated failure time (AFT) model 723: 721: 58:adding citations to reliable sources 3167: 2450:Analysis of variance (ANOVA, anova) 2545:Cochran–Mantel–Haenszel statistics 1171:Pearson product-moment correlation 25: 264:, the seasonal component at time 231:, the cyclical component at time 3166: 3154: 3142: 3129: 3128: 702:"6.5 STL decomposition | OTexts" 34: 3260:Associative (causal) forecasts 2804:Least-squares spectral analysis 836:Applied Econometric Time Series 584:Least-squares spectral analysis 45:needs additional citations for 1785:Mean-unbiased minimum-variance 742:10.1016/j.ijhydene.2016.10.021 69:"Decomposition of time series" 1: 3098:Geographic information system 2314:Simultaneous equations models 309:Hence a time series using an 3245:Decomposition of time series 2281:Coefficient of determination 1892:Uniformly most powerful test 134:decomposition of time series 2850:Proportional hazards models 2794:Spectral density estimation 2776:Vector autoregression (VAR) 2210:Maximum posterior estimator 1442:Randomized controlled trial 3314: 3226:Historical data forecasts 2610:Multivariate distributions 1030:Average absolute deviation 18:Decomposing of time series 3258: 3224: 3124: 2927: 2914: 2598:Structural equation model 2506: 2481: 2252: 2228: 1960: 1934:Score/Lagrange multiplier 1540: 1527: 1349:Sample size determination 1310: 1297: 927: 914: 896: 140:task that deconstructs a 3268:Simple linear regression 3093:Environmental statistics 2615:Elliptical distributions 2408:Generalized linear model 2337:Simple linear regression 2107:Hodges–Lehmann estimator 1564:Probability distribution 1473:Stochastic approximation 1035:Coefficient of variation 2753:Cross-correlation (XCF) 2361:Non-standard predictors 1795:Lehmann–ScheffĂ© theorem 1468:Adaptive clinical trial 574:Hilbert–Huang transform 3149:Mathematics portal 2970:Engineering statistics 2878:Nelson–Aalen estimator 2455:Analysis of covariance 2342:Ordinary least squares 2266:Pearson product-moment 1670:Statistical functional 1581:Empirical distribution 1414:Controlled experiments 1143:Frequency distribution 921:Descriptive statistics 528: 481: 392: 295: 258: 225: 184: 3235:Exponential smoothing 3065:Population statistics 3007:System identification 2741:Autocorrelation (ACF) 2669:Exponential smoothing 2583:Discriminant analysis 2578:Canonical correlation 2442:Partition of variance 2304:Regression validation 2148:(Jonckheere–Terpstra) 2047:Likelihood-ratio test 1736:Frequentist inference 1648:Location–scale family 1569:Sampling distribution 1534:Statistical inference 1501:Cross-sectional study 1488:Observational studies 1447:Randomized experiment 1276:Stem-and-leaf display 1078:Central limit theorem 555:that is based on the 526: 482: 393: 313:can be thought of as 296: 294:{\displaystyle I_{t}} 259: 257:{\displaystyle S_{t}} 226: 224:{\displaystyle C_{t}} 185: 183:{\displaystyle T_{t}} 2988:Probabilistic design 2573:Principal components 2416:Exponential families 2368:Nonlinear regression 2347:General linear model 2309:Mixed effects models 2299:Errors and residuals 2276:Confounding variable 2178:Bayesian probability 2156:Van der Waerden test 2146:Ordered alternative 1911:Multiple comparisons 1790:Rao–Blackwellization 1753:Estimating equations 1709:Statistical distance 1427:Factorial experiment 960:Arithmetic-Geometric 505:time series analysis 408: 320: 278: 241: 208: 167: 154:time series analysis 54:improve this article 3273:Regression analysis 3060:Official statistics 2983:Methods engineering 2664:Seasonal adjustment 2432:Poisson regressions 2352:Bayesian regression 2291:Regression analysis 2271:Partial correlation 2243:Regression analysis 1842:Prediction interval 1837:Likelihood interval 1827:Confidence interval 1819:Interval estimation 1780:Unbiased estimators 1598:Model specification 1478:Up-and-down designs 1166:Partial correlation 1122:Index of dispersion 1040:Interquartile range 158:seasonal adjustment 3080:Spatial statistics 2960:Medical statistics 2860:First hitting time 2814:Whittle likelihood 2465:Degrees of freedom 2460:Multivariate ANOVA 2393:Heteroscedasticity 2205:Bayesian estimator 2170:Bayesian inference 2019:Kolmogorov–Smirnov 1904:Randomization test 1874:Testing hypotheses 1847:Tolerance interval 1758:Maximum likelihood 1653:Exponential family 1586:Density estimation 1546:Statistical theory 1506:Natural experiment 1452:Scientific control 1369:Survey methodology 1055:Standard deviation 645:Dodge, Y. (2003). 569:Frequency spectrum 529: 513:Wold decomposition 477: 388: 291: 254: 221: 180: 3285: 3284: 3278:Econometric model 3182: 3181: 3120: 3119: 3116: 3115: 3055:National accounts 3025:Actuarial science 3017:Social statistics 2910: 2909: 2906: 2905: 2902: 2901: 2837:Survival function 2822: 2821: 2684:Granger causality 2525:Contingency table 2500:Survival analysis 2477: 2476: 2473: 2472: 2329:Linear regression 2224: 2223: 2220: 2219: 2195:Credible interval 2164: 2163: 1947: 1946: 1763:Method of moments 1632:Parametric family 1593:Statistical model 1523: 1522: 1519: 1518: 1437:Random assignment 1359:Statistical power 1293: 1292: 1289: 1288: 1138:Contingency table 1108: 1107: 975:Generalized/power 200:secular variation 156:, especially for 130: 129: 122: 104: 16:(Redirected from 3305: 3209: 3202: 3195: 3186: 3170: 3169: 3158: 3157: 3147: 3146: 3132: 3131: 3035:Crime statistics 2929: 2916: 2833: 2799:Fourier analysis 2786:Frequency domain 2766: 2713: 2679:Structural break 2639: 2588:Cluster analysis 2535:Log-linear model 2508: 2483: 2424: 2398:Homoscedasticity 2254: 2230: 2149: 2141: 2133: 2132:(Kruskal–Wallis) 2117: 2102: 2057:Cross validation 2042: 2024:Anderson–Darling 1971: 1958: 1929:Likelihood-ratio 1921:Parametric tests 1899:Permutation test 1882:1- & 2-tails 1773:Minimum distance 1745:Point estimation 1741: 1692:Optimal decision 1643: 1542: 1529: 1511:Quasi-experiment 1461:Adaptive designs 1312: 1299: 1176:Rank correlation 938: 929: 916: 883: 876: 869: 860: 855: 839: 819: 818: 810: 804: 803: 795: 789: 788: 783:Sax, Christoph. 780: 774: 773: 752: 746: 745: 725: 716: 715: 713: 712: 698: 692: 691: 689: 688: 674: 665: 664: 652: 642: 633: 632: 630: 629: 615: 589:Stochastic drift 557:Berlin procedure 486: 484: 483: 478: 472: 471: 459: 458: 446: 445: 433: 432: 420: 419: 397: 395: 394: 389: 384: 383: 371: 370: 358: 357: 345: 344: 332: 331: 300: 298: 297: 292: 290: 289: 263: 261: 260: 255: 253: 252: 230: 228: 227: 222: 220: 219: 189: 187: 186: 181: 179: 178: 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616: 607: 602: 594:Trend filtering 565: 549: 521: 501: 463: 450: 437: 424: 411: 406: 405: 375: 362: 349: 336: 323: 318: 317: 281: 276: 275: 244: 239: 238: 211: 206: 205: 192:trend component 170: 165: 164: 150: 126: 115: 109: 106: 63: 61: 51: 39: 28: 23: 22: 15: 12: 11: 5: 3311: 3309: 3301: 3300: 3290: 3289: 3283: 3282: 3280: 3275: 3270: 3265: 3263:Moving average 3259: 3256: 3255: 3253: 3252: 3250:NaĂŻve approach 3247: 3242: 3240:Trend analysis 3237: 3232: 3230:Moving average 3225: 3222: 3221: 3214: 3212: 3211: 3204: 3197: 3189: 3180: 3179: 3177: 3176: 3164: 3152: 3138: 3125: 3122: 3121: 3118: 3117: 3114: 3113: 3111: 3110: 3105: 3100: 3095: 3090: 3084: 3082: 3076: 3075: 3073: 3072: 3067: 3062: 3057: 3052: 3047: 3042: 3037: 3032: 3027: 3021: 3019: 3013: 3012: 3010: 3009: 3004: 2999: 2990: 2985: 2980: 2974: 2972: 2966: 2965: 2963: 2962: 2957: 2952: 2943: 2941:Bioinformatics 2937: 2935: 2925: 2924: 2919: 2912: 2911: 2908: 2907: 2904: 2903: 2900: 2899: 2897: 2896: 2890: 2888: 2884: 2883: 2881: 2880: 2874: 2872: 2866: 2865: 2863: 2862: 2857: 2852: 2847: 2841: 2839: 2830: 2824: 2823: 2820: 2819: 2817: 2816: 2811: 2806: 2801: 2796: 2790: 2788: 2782: 2781: 2779: 2778: 2773: 2768: 2760: 2755: 2750: 2749: 2748: 2746:partial (PACF) 2737: 2735: 2729: 2728: 2726: 2725: 2720: 2715: 2707: 2702: 2696: 2694: 2693:Specific tests 2690: 2689: 2687: 2686: 2681: 2676: 2671: 2666: 2661: 2656: 2651: 2645: 2643: 2636: 2630: 2629: 2627: 2626: 2625: 2624: 2623: 2622: 2607: 2606: 2605: 2595: 2593:Classification 2590: 2585: 2580: 2575: 2570: 2565: 2559: 2557: 2551: 2550: 2548: 2547: 2542: 2540:McNemar's test 2537: 2532: 2527: 2522: 2516: 2514: 2504: 2503: 2486: 2479: 2478: 2475: 2474: 2471: 2470: 2468: 2467: 2462: 2457: 2452: 2446: 2444: 2438: 2437: 2435: 2434: 2418: 2412: 2410: 2404: 2403: 2401: 2400: 2395: 2390: 2385: 2380: 2378:Semiparametric 2375: 2370: 2364: 2362: 2358: 2357: 2355: 2354: 2349: 2344: 2339: 2333: 2331: 2325: 2324: 2322: 2321: 2316: 2311: 2306: 2301: 2295: 2293: 2287: 2286: 2284: 2283: 2278: 2273: 2268: 2262: 2260: 2250: 2249: 2246: 2245: 2240: 2234: 2233: 2226: 2225: 2222: 2221: 2218: 2217: 2215: 2214: 2213: 2212: 2202: 2197: 2192: 2191: 2190: 2185: 2174: 2172: 2166: 2165: 2162: 2161: 2159: 2158: 2153: 2152: 2151: 2143: 2135: 2119: 2116:(Mann–Whitney) 2111: 2110: 2109: 2096: 2095: 2094: 2083: 2081: 2075: 2074: 2072: 2071: 2070: 2069: 2064: 2059: 2049: 2044: 2041:(Shapiro–Wilk) 2036: 2031: 2026: 2021: 2016: 2008: 2002: 2000: 1994: 1993: 1991: 1990: 1982: 1973: 1961: 1955: 1953:Specific tests 1949: 1948: 1945: 1944: 1942: 1941: 1936: 1931: 1925: 1923: 1917: 1916: 1914: 1913: 1908: 1907: 1906: 1896: 1895: 1894: 1884: 1878: 1876: 1870: 1869: 1867: 1866: 1865: 1864: 1859: 1849: 1844: 1839: 1834: 1829: 1823: 1821: 1815: 1814: 1812: 1811: 1806: 1805: 1804: 1799: 1798: 1797: 1792: 1777: 1776: 1775: 1770: 1765: 1760: 1749: 1747: 1738: 1732: 1731: 1729: 1728: 1723: 1718: 1717: 1716: 1706: 1701: 1700: 1699: 1689: 1688: 1687: 1682: 1677: 1667: 1662: 1657: 1656: 1655: 1650: 1645: 1629: 1628: 1627: 1622: 1617: 1607: 1606: 1605: 1600: 1590: 1589: 1588: 1578: 1577: 1576: 1566: 1561: 1556: 1550: 1548: 1538: 1537: 1532: 1525: 1524: 1521: 1520: 1517: 1516: 1514: 1513: 1508: 1503: 1498: 1492: 1490: 1484: 1483: 1481: 1480: 1475: 1470: 1464: 1462: 1458: 1457: 1455: 1454: 1449: 1444: 1439: 1434: 1429: 1424: 1418: 1416: 1410: 1409: 1407: 1406: 1404:Standard error 1401: 1396: 1391: 1390: 1389: 1384: 1373: 1371: 1365: 1364: 1362: 1361: 1356: 1351: 1346: 1341: 1336: 1334:Optimal design 1331: 1326: 1320: 1318: 1308: 1307: 1302: 1295: 1294: 1291: 1290: 1287: 1286: 1284: 1283: 1278: 1273: 1268: 1263: 1258: 1253: 1248: 1243: 1238: 1233: 1228: 1223: 1218: 1213: 1207: 1205: 1199: 1198: 1196: 1195: 1190: 1189: 1188: 1183: 1173: 1168: 1162: 1160: 1154: 1153: 1151: 1150: 1145: 1140: 1134: 1132: 1131:Summary tables 1128: 1127: 1125: 1124: 1118: 1116: 1110: 1109: 1106: 1105: 1103: 1102: 1101: 1100: 1095: 1090: 1080: 1074: 1072: 1066: 1065: 1063: 1062: 1057: 1052: 1047: 1042: 1037: 1032: 1026: 1024: 1018: 1017: 1015: 1014: 1009: 1004: 1003: 1002: 997: 992: 987: 982: 977: 972: 967: 965:Contraharmonic 962: 957: 946: 944: 935: 925: 924: 919: 912: 911: 909: 908: 903: 897: 894: 893: 888: 886: 885: 878: 871: 863: 857: 856: 850: 827: 824: 821: 820: 805: 790: 775: 768: 756:Kendall, M. G. 747: 717: 706:www.otexts.org 693: 682:www.otexts.org 666: 659: 634: 623:www.otexts.org 604: 603: 601: 598: 597: 596: 591: 586: 581: 576: 571: 564: 561: 548: 545: 520: 517: 509:Wold's theorem 503:The theory of 500: 497: 488: 487: 475: 470: 466: 462: 457: 453: 449: 444: 440: 436: 431: 427: 423: 418: 414: 399: 398: 387: 382: 378: 374: 369: 365: 361: 356: 352: 348: 343: 339: 335: 330: 326: 311:additive model 307: 306: 288: 284: 273: 251: 247: 236: 218: 214: 203: 177: 173: 149: 146: 128: 127: 42: 40: 33: 26: 24: 14: 13: 10: 9: 6: 4: 3: 2: 3310: 3299: 3296: 3295: 3293: 3279: 3276: 3274: 3271: 3269: 3266: 3264: 3261: 3257: 3251: 3248: 3246: 3243: 3241: 3238: 3236: 3233: 3231: 3228: 3227: 3223: 3218: 3215:Quantitative 3210: 3205: 3203: 3198: 3196: 3191: 3190: 3187: 3175: 3174: 3165: 3163: 3162: 3153: 3151: 3150: 3145: 3139: 3137: 3136: 3127: 3126: 3123: 3109: 3106: 3104: 3103:Geostatistics 3101: 3099: 3096: 3094: 3091: 3089: 3086: 3085: 3083: 3081: 3077: 3071: 3070:Psychometrics 3068: 3066: 3063: 3061: 3058: 3056: 3053: 3051: 3048: 3046: 3043: 3041: 3038: 3036: 3033: 3031: 3028: 3026: 3023: 3022: 3020: 3018: 3014: 3008: 3005: 3003: 3000: 2998: 2994: 2991: 2989: 2986: 2984: 2981: 2979: 2976: 2975: 2973: 2971: 2967: 2961: 2958: 2956: 2953: 2951: 2947: 2944: 2942: 2939: 2938: 2936: 2934: 2933:Biostatistics 2930: 2926: 2922: 2917: 2913: 2895: 2894:Log-rank test 2892: 2891: 2889: 2885: 2879: 2876: 2875: 2873: 2871: 2867: 2861: 2858: 2856: 2853: 2851: 2848: 2846: 2843: 2842: 2840: 2838: 2834: 2831: 2829: 2825: 2815: 2812: 2810: 2807: 2805: 2802: 2800: 2797: 2795: 2792: 2791: 2789: 2787: 2783: 2777: 2774: 2772: 2769: 2767: 2765:(Box–Jenkins) 2761: 2759: 2756: 2754: 2751: 2747: 2744: 2743: 2742: 2739: 2738: 2736: 2734: 2730: 2724: 2721: 2719: 2718:Durbin–Watson 2716: 2714: 2708: 2706: 2703: 2701: 2700:Dickey–Fuller 2698: 2697: 2695: 2691: 2685: 2682: 2680: 2677: 2675: 2674:Cointegration 2672: 2670: 2667: 2665: 2662: 2660: 2657: 2655: 2652: 2650: 2649:Decomposition 2647: 2646: 2644: 2640: 2637: 2635: 2631: 2621: 2618: 2617: 2616: 2613: 2612: 2611: 2608: 2604: 2601: 2600: 2599: 2596: 2594: 2591: 2589: 2586: 2584: 2581: 2579: 2576: 2574: 2571: 2569: 2566: 2564: 2561: 2560: 2558: 2556: 2552: 2546: 2543: 2541: 2538: 2536: 2533: 2531: 2528: 2526: 2523: 2521: 2520:Cohen's kappa 2518: 2517: 2515: 2513: 2509: 2505: 2501: 2497: 2493: 2489: 2484: 2480: 2466: 2463: 2461: 2458: 2456: 2453: 2451: 2448: 2447: 2445: 2443: 2439: 2433: 2429: 2425: 2419: 2417: 2414: 2413: 2411: 2409: 2405: 2399: 2396: 2394: 2391: 2389: 2386: 2384: 2381: 2379: 2376: 2374: 2373:Nonparametric 2371: 2369: 2366: 2365: 2363: 2359: 2353: 2350: 2348: 2345: 2343: 2340: 2338: 2335: 2334: 2332: 2330: 2326: 2320: 2317: 2315: 2312: 2310: 2307: 2305: 2302: 2300: 2297: 2296: 2294: 2292: 2288: 2282: 2279: 2277: 2274: 2272: 2269: 2267: 2264: 2263: 2261: 2259: 2255: 2251: 2244: 2241: 2239: 2236: 2235: 2231: 2227: 2211: 2208: 2207: 2206: 2203: 2201: 2198: 2196: 2193: 2189: 2186: 2184: 2181: 2180: 2179: 2176: 2175: 2173: 2171: 2167: 2157: 2154: 2150: 2144: 2142: 2136: 2134: 2128: 2127: 2126: 2123: 2122:Nonparametric 2120: 2118: 2112: 2108: 2105: 2104: 2103: 2097: 2093: 2092:Sample median 2090: 2089: 2088: 2085: 2084: 2082: 2080: 2076: 2068: 2065: 2063: 2060: 2058: 2055: 2054: 2053: 2050: 2048: 2045: 2043: 2037: 2035: 2032: 2030: 2027: 2025: 2022: 2020: 2017: 2015: 2013: 2009: 2007: 2004: 2003: 2001: 1999: 1995: 1989: 1987: 1983: 1981: 1979: 1974: 1972: 1967: 1963: 1962: 1959: 1956: 1954: 1950: 1940: 1937: 1935: 1932: 1930: 1927: 1926: 1924: 1922: 1918: 1912: 1909: 1905: 1902: 1901: 1900: 1897: 1893: 1890: 1889: 1888: 1885: 1883: 1880: 1879: 1877: 1875: 1871: 1863: 1860: 1858: 1855: 1854: 1853: 1850: 1848: 1845: 1843: 1840: 1838: 1835: 1833: 1830: 1828: 1825: 1824: 1822: 1820: 1816: 1810: 1807: 1803: 1800: 1796: 1793: 1791: 1788: 1787: 1786: 1783: 1782: 1781: 1778: 1774: 1771: 1769: 1766: 1764: 1761: 1759: 1756: 1755: 1754: 1751: 1750: 1748: 1746: 1742: 1739: 1737: 1733: 1727: 1724: 1722: 1719: 1715: 1712: 1711: 1710: 1707: 1705: 1702: 1698: 1697:loss function 1695: 1694: 1693: 1690: 1686: 1683: 1681: 1678: 1676: 1673: 1672: 1671: 1668: 1666: 1663: 1661: 1658: 1654: 1651: 1649: 1646: 1644: 1638: 1635: 1634: 1633: 1630: 1626: 1623: 1621: 1618: 1616: 1613: 1612: 1611: 1608: 1604: 1601: 1599: 1596: 1595: 1594: 1591: 1587: 1584: 1583: 1582: 1579: 1575: 1572: 1571: 1570: 1567: 1565: 1562: 1560: 1557: 1555: 1552: 1551: 1549: 1547: 1543: 1539: 1535: 1530: 1526: 1512: 1509: 1507: 1504: 1502: 1499: 1497: 1494: 1493: 1491: 1489: 1485: 1479: 1476: 1474: 1471: 1469: 1466: 1465: 1463: 1459: 1453: 1450: 1448: 1445: 1443: 1440: 1438: 1435: 1433: 1430: 1428: 1425: 1423: 1420: 1419: 1417: 1415: 1411: 1405: 1402: 1400: 1399:Questionnaire 1397: 1395: 1392: 1388: 1385: 1383: 1380: 1379: 1378: 1375: 1374: 1372: 1370: 1366: 1360: 1357: 1355: 1352: 1350: 1347: 1345: 1342: 1340: 1337: 1335: 1332: 1330: 1327: 1325: 1322: 1321: 1319: 1317: 1313: 1309: 1305: 1300: 1296: 1282: 1279: 1277: 1274: 1272: 1269: 1267: 1264: 1262: 1259: 1257: 1254: 1252: 1249: 1247: 1244: 1242: 1239: 1237: 1234: 1232: 1229: 1227: 1226:Control chart 1224: 1222: 1219: 1217: 1214: 1212: 1209: 1208: 1206: 1204: 1200: 1194: 1191: 1187: 1184: 1182: 1179: 1178: 1177: 1174: 1172: 1169: 1167: 1164: 1163: 1161: 1159: 1155: 1149: 1146: 1144: 1141: 1139: 1136: 1135: 1133: 1129: 1123: 1120: 1119: 1117: 1115: 1111: 1099: 1096: 1094: 1091: 1089: 1086: 1085: 1084: 1081: 1079: 1076: 1075: 1073: 1071: 1067: 1061: 1058: 1056: 1053: 1051: 1048: 1046: 1043: 1041: 1038: 1036: 1033: 1031: 1028: 1027: 1025: 1023: 1019: 1013: 1010: 1008: 1005: 1001: 998: 996: 993: 991: 988: 986: 983: 981: 978: 976: 973: 971: 968: 966: 963: 961: 958: 956: 953: 952: 951: 948: 947: 945: 943: 939: 936: 934: 930: 926: 922: 917: 913: 907: 904: 902: 899: 898: 895: 891: 884: 879: 877: 872: 870: 865: 864: 861: 853: 851:0-471-23065-0 847: 843: 838: 837: 830: 829: 825: 816: 809: 806: 801: 798:Hafen, Ryan. 794: 791: 786: 779: 776: 771: 769:0-85264-241-5 765: 761: 757: 751: 748: 743: 739: 735: 731: 724: 722: 718: 707: 703: 697: 694: 683: 679: 673: 671: 667: 662: 660:0-19-920613-9 656: 651: 650: 641: 639: 635: 624: 620: 614: 612: 610: 606: 599: 595: 592: 590: 587: 585: 582: 580: 579:Least squares 577: 575: 572: 570: 567: 566: 562: 560: 558: 554: 546: 544: 542: 536: 534: 525: 518: 516: 514: 510: 506: 498: 496: 492: 473: 468: 464: 460: 455: 451: 447: 442: 438: 434: 429: 425: 421: 416: 412: 404: 403: 402: 385: 380: 376: 372: 367: 363: 359: 354: 350: 346: 341: 337: 333: 328: 324: 316: 315: 314: 312: 304: 286: 282: 274: 271: 268:, reflecting 267: 249: 245: 237: 234: 216: 212: 204: 201: 197: 193: 175: 171: 163: 162: 161: 159: 155: 147: 145: 143: 139: 135: 124: 121: 113: 102: 99: 95: 92: 88: 85: 81: 78: 74: 71: â€“  70: 66: 65:Find sources: 59: 55: 49: 48: 43:This article 41: 37: 32: 31: 19: 3244: 3171: 3159: 3140: 3133: 3045:Econometrics 2995: / 2978:Chemometrics 2955:Epidemiology 2948: / 2921:Applications 2763:ARIMA model 2710:Q-statistic 2659:Stationarity 2648: 2555:Multivariate 2498: / 2494: / 2492:Multivariate 2490: / 2430: / 2426: / 2200:Bayes factor 2099:Signed rank 2011: 1985: 1977: 1965: 1660:Completeness 1496:Cohort study 1394:Opinion poll 1329:Missing data 1316:Study design 1271:Scatter plot 1193:Scatter plot 1186:Spearman's ρ 1148:Grouped data 835: 808: 793: 778: 759: 750: 733: 709:. Retrieved 705: 696: 685:. Retrieved 681: 648: 626:. Retrieved 622: 550: 537: 530: 502: 493: 489: 400: 308: 302: 265: 232: 195: 151: 133: 131: 116: 110:October 2015 107: 97: 90: 83: 76: 64: 52:Please help 47:verification 44: 3298:Time series 3217:forecasting 3173:WikiProject 3088:Cartography 3050:Jurimetrics 3002:Reliability 2733:Time domain 2712:(Ljung–Box) 2634:Time-series 2512:Categorical 2496:Time-series 2488:Categorical 2423:(Bernoulli) 2258:Correlation 2238:Correlation 2034:Jarque–Bera 2006:Chi-squared 1768:M-estimator 1721:Asymptotics 1665:Sufficiency 1432:Interaction 1344:Replication 1324:Effect size 1281:Violin plot 1261:Radar chart 1241:Forest plot 1231:Correlogram 1181:Kendall's τ 760:Time-Series 541:biohydrogen 533:UK airlines 270:seasonality 142:time series 138:statistical 3040:Demography 2758:ARMA model 2563:Regression 2140:(Friedman) 2101:(Wilcoxon) 2039:Normality 2029:Lilliefors 1976:Student's 1852:Resampling 1726:Robustness 1714:divergence 1704:Efficiency 1642:(monotone) 1637:Likelihood 1554:Population 1387:Stratified 1339:Population 1158:Dependence 1114:Count data 1045:Percentile 1022:Dispersion 955:Arithmetic 890:Statistics 711:2016-05-18 687:2016-05-18 628:2016-05-14 600:References 80:newspapers 2421:Logistic 2188:posterior 2114:Rank sum 1862:Jackknife 1857:Bootstrap 1675:Bootstrap 1610:Parameter 1559:Statistic 1354:Statistic 1266:Run chart 1251:Pie chart 1246:Histogram 1236:Fan chart 1211:Bar chart 1093:L-moments 980:Geometric 461:× 448:× 435:× 3292:Category 3135:Category 2828:Survival 2705:Johansen 2428:Binomial 2383:Isotonic 1970:(normal) 1615:location 1422:Blocking 1377:Sampling 1256:Q–Q plot 1221:Box plot 1203:Graphics 1098:Skewness 1088:Kurtosis 1060:Variance 990:Heronian 985:Harmonic 758:(1976). 563:See also 547:Software 519:Examples 194:at time 3219:methods 3161:Commons 3108:Kriging 2993:Process 2950:studies 2809:Wavelet 2642:General 1809:Plug-in 1603:L space 1382:Cluster 1083:Moments 901:Outline 842:156–238 94:scholar 3030:Census 2620:Normal 2568:Manova 2388:Robust 2138:2-way 2130:1-way 1968:-test 1639:  1216:Biplot 1007:Median 1000:Lehmer 942:Center 848:  766:  657:  190:, the 96:  89:  82:  75:  67:  2654:Trend 2183:prior 2125:anova 2014:-test 1988:-test 1980:-test 1887:Power 1832:Pivot 1625:shape 1620:scale 1070:Shape 1050:Range 995:Heinz 970:Cubic 906:Index 553:BV4.1 136:is a 101:JSTOR 87:books 2887:Test 2087:Sign 1939:Wald 1012:Mode 950:Mean 846:ISBN 764:ISBN 655:ISBN 511:and 132:The 73:news 2067:BIC 2062:AIC 738:doi 56:by 3294:: 844:. 736:. 732:. 720:^ 704:. 680:. 669:^ 637:^ 621:. 608:^ 535:. 515:. 3208:e 3201:t 3194:v 2012:G 1986:F 1978:t 1966:Z 1685:V 1680:U 882:e 875:t 868:v 854:. 817:. 802:. 787:. 772:. 744:. 740:: 714:. 690:. 663:. 631:. 474:. 469:t 465:I 456:t 452:S 443:t 439:C 430:t 426:T 422:= 417:t 413:y 386:, 381:t 377:I 373:+ 368:t 364:S 360:+ 355:t 351:C 347:+ 342:t 338:T 334:= 329:t 325:y 303:t 287:t 283:I 266:t 250:t 246:S 233:t 217:t 213:C 196:t 176:t 172:T 123:) 117:( 112:) 108:( 98:· 91:· 84:· 77:· 50:. 20:)

Index

Decomposing of time series

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"Decomposition of time series"
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statistical
time series
time series analysis
seasonal adjustment
trend component
secular variation
seasonality
additive model
time series analysis
Wold's theorem
Wold decomposition

UK airlines
biohydrogen
BV4.1
Berlin procedure
Frequency spectrum
Hilbert–Huang transform

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