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Author*The author of this computation has been verified*
R Software Modulerwasp_structuraltimeseries.wasp
Title produced by softwareStructural Time Series Models
Date of computationMon, 19 Dec 2016 19:05:09 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/19/t1482170745dozg5msjkzlk47z.htm/, Retrieved Sat, 18 May 2024 01:37:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301434, Retrieved Sat, 18 May 2024 01:37:11 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact64
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Structural Time Series Models] [] [2016-12-19 18:05:09] [9412b5b3b31fe4708efb1e5c8c74b28f] [Current]
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Dataseries X:
40548
40331
39814
39360
38915
38583
38191
37477
37110
36670
36330
36108
35341
34764
34253
33743
33296
32875
32622
32346
31780
31003
28467
28153
27682
27217
26780
26490
26020
25227
25343
24453
23958
23475
23102
22393
21557
20893
20376
19704
19016
18274
18020
17317
16919
16372
16069
15478
15018
14561
14047
13506
13035
12471
11815
11172
10594
9914
9319
8939
8073
7431
7022




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time3 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301434&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]3 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=301434&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301434&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R ServerBig Analytics Cloud Computing Center







Structural Time Series Model -- Interpolation
tObservedLevelSlopeSeasonalStand. Residuals
14054840548000
24033140343.872981168-16.0274163565821-10.9983213346529-0.402503261691992
33981439837.4276536622-76.8072907301685-11.8891722534022-1.52009476208072
43936039380.55554206-139.409532452819-12.0504511079955-1.1474730000025
53891538933.7898021445-198.516401872031-12.1471162465382-0.911551177035637
63858338598.0793511387-227.306437360489-12.181045418802-0.402170489332392
73819138206.6311547369-263.517124203081-12.2126180902122-0.477666617799305
83747737498.4594573331-364.479725281216-12.2785960730661-1.28825186331735
93711037122.5153872574-367.126581356074-12.2799018232963-0.0331264073291893
103667036683.7531010767-383.826239190956-12.2861464627721-0.206667304709793
113633036341.4349069634-374.095545475144-12.28338184753640.119638815299667
123610836117.2153403732-338.845891338831-12.2757623557920.431752844418979
133534135380.8620275443-428.798667639945-32.056705180394-1.33390411901406
143476434767.8730668606-470.512621680634-1.27198988159832-0.444780875988015
153425334255.1142027663-480.489538670381-1.2530893853103-0.12155952508737
163374333744.8360256478-487.527079558091-1.22929725999568-0.085666123030466
173329633296.456043316-478.279956290026-1.253600749364970.11260468500245
183287532875.1201792669-464.829666399115-1.280567267563660.163826413082607
193262232619.1002507261-415.508730911801-1.355947252608460.600818487486315
203234632344.5221490672-382.220293525734-1.394729038238750.405545963889099
213178031784.9723107218-424.107385338829-1.35753127828186-0.510325229608578
223100331011.425228477-506.650897524303-1.30165627618195-1.00568387338422
232846728508.7504335061-978.156766692751-1.05837015616994-5.74476740384792
242815328141.6572653991-833.806707115739-1.115143100468131.75875873449884
252768227604.5607949653-764.79918036703471.50438694462060.924838731227214
262721727211.9568996337-679.303583587835-1.043146316581890.964430484368245
272678026776.1592807904-621.752364807346-1.122036875666130.700658914440278
282649026484.5757997065-543.719768770981-1.302000178438720.949717659221013
292602026019.7282144767-525.083918648305-1.335384026638830.22691400025666
302522725233.5718771657-586.761628970657-1.25110074208652-0.751205320497364
312534325330.4840780022-425.255000064065-1.419344562407871.967386248762
322445324463.3441143893-529.64085176016-1.33645446389147-1.27168905321526
332395823958.8278610069-523.705712267415-1.340046954580820.0723091861215278
342347523475.520853694-514.162328246053-1.34445013045160.116272885582993
352310223100.5189026025-481.288138133613-1.356011647600960.400533606584441
362239322398.8354293565-533.353216036293-1.34205436709639-0.634358818122275
372155721584.6388223851-599.031371078195-21.9840603556284-0.853200806569723
382089320893.5999316292-620.3219534654141.00157035208362-0.245641282875444
392037620372.990064027-596.7580181086770.9775390758590670.286937080909497
401970419704.4559482806-613.7199696176421.00659075270063-0.206498073971135
411901619016.4833432707-631.2637202334031.02992852607044-0.213651913035246
421827418275.1864663995-657.2587796746131.05630632209948-0.316638150357977
431802018011.0028720058-564.3998739235740.9844775970536171.13122045948945
441731717318.6069939364-594.636798221481.00230628714954-0.368375797564949
451691916914.140932655-549.7121797134350.9821148603772940.547337470654057
461637216370.886746504-548.186579865580.9815921989330120.0185875211229651
471606916063.1313754439-491.3880357095310.9667597732931910.692028347366188
481547815478.9213440228-513.3161213320130.971124626480057-0.267171908808119
491501815022.0499721808-500.081365527708-5.190161129043450.169239879734692
501456114559.5284435737-491.3523508149670.7945984603472720.101958922204939
511404714046.6402523342-496.4413732173520.798734068637743-0.0619763208973207
521350613506.0860566467-506.8653676625940.812919873282895-0.126925012068848
531303513033.4970221384-498.7670311546950.8043604889363510.0986332619772589
541247112471.4730230887-513.7113251821350.816408738063792-0.182042574083942
551181511817.0320015405-546.957175097470.836840588970485-0.405019316084368
561117211173.1288192027-569.8593256782930.847569379347783-0.27902185957887
571059410593.3537484577-572.2017809083010.848405838688092-0.0285395428993663
5899149915.30281030845-597.207260846340.855212042235512-0.30466242715297
5993199318.14380645529-597.1958606928730.8552096769966870.000138898975618493
6089398933.81277856859-546.9087017249080.8472569696257640.612700369697859
6180738109.42578675734-612.070256319363-30.8099954504764-0.825348770542103
6274317429.92198049182-627.786448431822.32075495206215-0.185005197598781
6370227015.36643617231-577.4010666956372.286878497187550.613664021419229

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Interpolation \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 40548 & 40548 & 0 & 0 & 0 \tabularnewline
2 & 40331 & 40343.872981168 & -16.0274163565821 & -10.9983213346529 & -0.402503261691992 \tabularnewline
3 & 39814 & 39837.4276536622 & -76.8072907301685 & -11.8891722534022 & -1.52009476208072 \tabularnewline
4 & 39360 & 39380.55554206 & -139.409532452819 & -12.0504511079955 & -1.1474730000025 \tabularnewline
5 & 38915 & 38933.7898021445 & -198.516401872031 & -12.1471162465382 & -0.911551177035637 \tabularnewline
6 & 38583 & 38598.0793511387 & -227.306437360489 & -12.181045418802 & -0.402170489332392 \tabularnewline
7 & 38191 & 38206.6311547369 & -263.517124203081 & -12.2126180902122 & -0.477666617799305 \tabularnewline
8 & 37477 & 37498.4594573331 & -364.479725281216 & -12.2785960730661 & -1.28825186331735 \tabularnewline
9 & 37110 & 37122.5153872574 & -367.126581356074 & -12.2799018232963 & -0.0331264073291893 \tabularnewline
10 & 36670 & 36683.7531010767 & -383.826239190956 & -12.2861464627721 & -0.206667304709793 \tabularnewline
11 & 36330 & 36341.4349069634 & -374.095545475144 & -12.2833818475364 & 0.119638815299667 \tabularnewline
12 & 36108 & 36117.2153403732 & -338.845891338831 & -12.275762355792 & 0.431752844418979 \tabularnewline
13 & 35341 & 35380.8620275443 & -428.798667639945 & -32.056705180394 & -1.33390411901406 \tabularnewline
14 & 34764 & 34767.8730668606 & -470.512621680634 & -1.27198988159832 & -0.444780875988015 \tabularnewline
15 & 34253 & 34255.1142027663 & -480.489538670381 & -1.2530893853103 & -0.12155952508737 \tabularnewline
16 & 33743 & 33744.8360256478 & -487.527079558091 & -1.22929725999568 & -0.085666123030466 \tabularnewline
17 & 33296 & 33296.456043316 & -478.279956290026 & -1.25360074936497 & 0.11260468500245 \tabularnewline
18 & 32875 & 32875.1201792669 & -464.829666399115 & -1.28056726756366 & 0.163826413082607 \tabularnewline
19 & 32622 & 32619.1002507261 & -415.508730911801 & -1.35594725260846 & 0.600818487486315 \tabularnewline
20 & 32346 & 32344.5221490672 & -382.220293525734 & -1.39472903823875 & 0.405545963889099 \tabularnewline
21 & 31780 & 31784.9723107218 & -424.107385338829 & -1.35753127828186 & -0.510325229608578 \tabularnewline
22 & 31003 & 31011.425228477 & -506.650897524303 & -1.30165627618195 & -1.00568387338422 \tabularnewline
23 & 28467 & 28508.7504335061 & -978.156766692751 & -1.05837015616994 & -5.74476740384792 \tabularnewline
24 & 28153 & 28141.6572653991 & -833.806707115739 & -1.11514310046813 & 1.75875873449884 \tabularnewline
25 & 27682 & 27604.5607949653 & -764.799180367034 & 71.5043869446206 & 0.924838731227214 \tabularnewline
26 & 27217 & 27211.9568996337 & -679.303583587835 & -1.04314631658189 & 0.964430484368245 \tabularnewline
27 & 26780 & 26776.1592807904 & -621.752364807346 & -1.12203687566613 & 0.700658914440278 \tabularnewline
28 & 26490 & 26484.5757997065 & -543.719768770981 & -1.30200017843872 & 0.949717659221013 \tabularnewline
29 & 26020 & 26019.7282144767 & -525.083918648305 & -1.33538402663883 & 0.22691400025666 \tabularnewline
30 & 25227 & 25233.5718771657 & -586.761628970657 & -1.25110074208652 & -0.751205320497364 \tabularnewline
31 & 25343 & 25330.4840780022 & -425.255000064065 & -1.41934456240787 & 1.967386248762 \tabularnewline
32 & 24453 & 24463.3441143893 & -529.64085176016 & -1.33645446389147 & -1.27168905321526 \tabularnewline
33 & 23958 & 23958.8278610069 & -523.705712267415 & -1.34004695458082 & 0.0723091861215278 \tabularnewline
34 & 23475 & 23475.520853694 & -514.162328246053 & -1.3444501304516 & 0.116272885582993 \tabularnewline
35 & 23102 & 23100.5189026025 & -481.288138133613 & -1.35601164760096 & 0.400533606584441 \tabularnewline
36 & 22393 & 22398.8354293565 & -533.353216036293 & -1.34205436709639 & -0.634358818122275 \tabularnewline
37 & 21557 & 21584.6388223851 & -599.031371078195 & -21.9840603556284 & -0.853200806569723 \tabularnewline
38 & 20893 & 20893.5999316292 & -620.321953465414 & 1.00157035208362 & -0.245641282875444 \tabularnewline
39 & 20376 & 20372.990064027 & -596.758018108677 & 0.977539075859067 & 0.286937080909497 \tabularnewline
40 & 19704 & 19704.4559482806 & -613.719969617642 & 1.00659075270063 & -0.206498073971135 \tabularnewline
41 & 19016 & 19016.4833432707 & -631.263720233403 & 1.02992852607044 & -0.213651913035246 \tabularnewline
42 & 18274 & 18275.1864663995 & -657.258779674613 & 1.05630632209948 & -0.316638150357977 \tabularnewline
43 & 18020 & 18011.0028720058 & -564.399873923574 & 0.984477597053617 & 1.13122045948945 \tabularnewline
44 & 17317 & 17318.6069939364 & -594.63679822148 & 1.00230628714954 & -0.368375797564949 \tabularnewline
45 & 16919 & 16914.140932655 & -549.712179713435 & 0.982114860377294 & 0.547337470654057 \tabularnewline
46 & 16372 & 16370.886746504 & -548.18657986558 & 0.981592198933012 & 0.0185875211229651 \tabularnewline
47 & 16069 & 16063.1313754439 & -491.388035709531 & 0.966759773293191 & 0.692028347366188 \tabularnewline
48 & 15478 & 15478.9213440228 & -513.316121332013 & 0.971124626480057 & -0.267171908808119 \tabularnewline
49 & 15018 & 15022.0499721808 & -500.081365527708 & -5.19016112904345 & 0.169239879734692 \tabularnewline
50 & 14561 & 14559.5284435737 & -491.352350814967 & 0.794598460347272 & 0.101958922204939 \tabularnewline
51 & 14047 & 14046.6402523342 & -496.441373217352 & 0.798734068637743 & -0.0619763208973207 \tabularnewline
52 & 13506 & 13506.0860566467 & -506.865367662594 & 0.812919873282895 & -0.126925012068848 \tabularnewline
53 & 13035 & 13033.4970221384 & -498.767031154695 & 0.804360488936351 & 0.0986332619772589 \tabularnewline
54 & 12471 & 12471.4730230887 & -513.711325182135 & 0.816408738063792 & -0.182042574083942 \tabularnewline
55 & 11815 & 11817.0320015405 & -546.95717509747 & 0.836840588970485 & -0.405019316084368 \tabularnewline
56 & 11172 & 11173.1288192027 & -569.859325678293 & 0.847569379347783 & -0.27902185957887 \tabularnewline
57 & 10594 & 10593.3537484577 & -572.201780908301 & 0.848405838688092 & -0.0285395428993663 \tabularnewline
58 & 9914 & 9915.30281030845 & -597.20726084634 & 0.855212042235512 & -0.30466242715297 \tabularnewline
59 & 9319 & 9318.14380645529 & -597.195860692873 & 0.855209676996687 & 0.000138898975618493 \tabularnewline
60 & 8939 & 8933.81277856859 & -546.908701724908 & 0.847256969625764 & 0.612700369697859 \tabularnewline
61 & 8073 & 8109.42578675734 & -612.070256319363 & -30.8099954504764 & -0.825348770542103 \tabularnewline
62 & 7431 & 7429.92198049182 & -627.78644843182 & 2.32075495206215 & -0.185005197598781 \tabularnewline
63 & 7022 & 7015.36643617231 & -577.401066695637 & 2.28687849718755 & 0.613664021419229 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301434&T=1

[TABLE]
[ROW][C]Structural Time Series Model -- Interpolation[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Level[/C][C]Slope[/C][C]Seasonal[/C][C]Stand. Residuals[/C][/ROW]
[ROW][C]1[/C][C]40548[/C][C]40548[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]40331[/C][C]40343.872981168[/C][C]-16.0274163565821[/C][C]-10.9983213346529[/C][C]-0.402503261691992[/C][/ROW]
[ROW][C]3[/C][C]39814[/C][C]39837.4276536622[/C][C]-76.8072907301685[/C][C]-11.8891722534022[/C][C]-1.52009476208072[/C][/ROW]
[ROW][C]4[/C][C]39360[/C][C]39380.55554206[/C][C]-139.409532452819[/C][C]-12.0504511079955[/C][C]-1.1474730000025[/C][/ROW]
[ROW][C]5[/C][C]38915[/C][C]38933.7898021445[/C][C]-198.516401872031[/C][C]-12.1471162465382[/C][C]-0.911551177035637[/C][/ROW]
[ROW][C]6[/C][C]38583[/C][C]38598.0793511387[/C][C]-227.306437360489[/C][C]-12.181045418802[/C][C]-0.402170489332392[/C][/ROW]
[ROW][C]7[/C][C]38191[/C][C]38206.6311547369[/C][C]-263.517124203081[/C][C]-12.2126180902122[/C][C]-0.477666617799305[/C][/ROW]
[ROW][C]8[/C][C]37477[/C][C]37498.4594573331[/C][C]-364.479725281216[/C][C]-12.2785960730661[/C][C]-1.28825186331735[/C][/ROW]
[ROW][C]9[/C][C]37110[/C][C]37122.5153872574[/C][C]-367.126581356074[/C][C]-12.2799018232963[/C][C]-0.0331264073291893[/C][/ROW]
[ROW][C]10[/C][C]36670[/C][C]36683.7531010767[/C][C]-383.826239190956[/C][C]-12.2861464627721[/C][C]-0.206667304709793[/C][/ROW]
[ROW][C]11[/C][C]36330[/C][C]36341.4349069634[/C][C]-374.095545475144[/C][C]-12.2833818475364[/C][C]0.119638815299667[/C][/ROW]
[ROW][C]12[/C][C]36108[/C][C]36117.2153403732[/C][C]-338.845891338831[/C][C]-12.275762355792[/C][C]0.431752844418979[/C][/ROW]
[ROW][C]13[/C][C]35341[/C][C]35380.8620275443[/C][C]-428.798667639945[/C][C]-32.056705180394[/C][C]-1.33390411901406[/C][/ROW]
[ROW][C]14[/C][C]34764[/C][C]34767.8730668606[/C][C]-470.512621680634[/C][C]-1.27198988159832[/C][C]-0.444780875988015[/C][/ROW]
[ROW][C]15[/C][C]34253[/C][C]34255.1142027663[/C][C]-480.489538670381[/C][C]-1.2530893853103[/C][C]-0.12155952508737[/C][/ROW]
[ROW][C]16[/C][C]33743[/C][C]33744.8360256478[/C][C]-487.527079558091[/C][C]-1.22929725999568[/C][C]-0.085666123030466[/C][/ROW]
[ROW][C]17[/C][C]33296[/C][C]33296.456043316[/C][C]-478.279956290026[/C][C]-1.25360074936497[/C][C]0.11260468500245[/C][/ROW]
[ROW][C]18[/C][C]32875[/C][C]32875.1201792669[/C][C]-464.829666399115[/C][C]-1.28056726756366[/C][C]0.163826413082607[/C][/ROW]
[ROW][C]19[/C][C]32622[/C][C]32619.1002507261[/C][C]-415.508730911801[/C][C]-1.35594725260846[/C][C]0.600818487486315[/C][/ROW]
[ROW][C]20[/C][C]32346[/C][C]32344.5221490672[/C][C]-382.220293525734[/C][C]-1.39472903823875[/C][C]0.405545963889099[/C][/ROW]
[ROW][C]21[/C][C]31780[/C][C]31784.9723107218[/C][C]-424.107385338829[/C][C]-1.35753127828186[/C][C]-0.510325229608578[/C][/ROW]
[ROW][C]22[/C][C]31003[/C][C]31011.425228477[/C][C]-506.650897524303[/C][C]-1.30165627618195[/C][C]-1.00568387338422[/C][/ROW]
[ROW][C]23[/C][C]28467[/C][C]28508.7504335061[/C][C]-978.156766692751[/C][C]-1.05837015616994[/C][C]-5.74476740384792[/C][/ROW]
[ROW][C]24[/C][C]28153[/C][C]28141.6572653991[/C][C]-833.806707115739[/C][C]-1.11514310046813[/C][C]1.75875873449884[/C][/ROW]
[ROW][C]25[/C][C]27682[/C][C]27604.5607949653[/C][C]-764.799180367034[/C][C]71.5043869446206[/C][C]0.924838731227214[/C][/ROW]
[ROW][C]26[/C][C]27217[/C][C]27211.9568996337[/C][C]-679.303583587835[/C][C]-1.04314631658189[/C][C]0.964430484368245[/C][/ROW]
[ROW][C]27[/C][C]26780[/C][C]26776.1592807904[/C][C]-621.752364807346[/C][C]-1.12203687566613[/C][C]0.700658914440278[/C][/ROW]
[ROW][C]28[/C][C]26490[/C][C]26484.5757997065[/C][C]-543.719768770981[/C][C]-1.30200017843872[/C][C]0.949717659221013[/C][/ROW]
[ROW][C]29[/C][C]26020[/C][C]26019.7282144767[/C][C]-525.083918648305[/C][C]-1.33538402663883[/C][C]0.22691400025666[/C][/ROW]
[ROW][C]30[/C][C]25227[/C][C]25233.5718771657[/C][C]-586.761628970657[/C][C]-1.25110074208652[/C][C]-0.751205320497364[/C][/ROW]
[ROW][C]31[/C][C]25343[/C][C]25330.4840780022[/C][C]-425.255000064065[/C][C]-1.41934456240787[/C][C]1.967386248762[/C][/ROW]
[ROW][C]32[/C][C]24453[/C][C]24463.3441143893[/C][C]-529.64085176016[/C][C]-1.33645446389147[/C][C]-1.27168905321526[/C][/ROW]
[ROW][C]33[/C][C]23958[/C][C]23958.8278610069[/C][C]-523.705712267415[/C][C]-1.34004695458082[/C][C]0.0723091861215278[/C][/ROW]
[ROW][C]34[/C][C]23475[/C][C]23475.520853694[/C][C]-514.162328246053[/C][C]-1.3444501304516[/C][C]0.116272885582993[/C][/ROW]
[ROW][C]35[/C][C]23102[/C][C]23100.5189026025[/C][C]-481.288138133613[/C][C]-1.35601164760096[/C][C]0.400533606584441[/C][/ROW]
[ROW][C]36[/C][C]22393[/C][C]22398.8354293565[/C][C]-533.353216036293[/C][C]-1.34205436709639[/C][C]-0.634358818122275[/C][/ROW]
[ROW][C]37[/C][C]21557[/C][C]21584.6388223851[/C][C]-599.031371078195[/C][C]-21.9840603556284[/C][C]-0.853200806569723[/C][/ROW]
[ROW][C]38[/C][C]20893[/C][C]20893.5999316292[/C][C]-620.321953465414[/C][C]1.00157035208362[/C][C]-0.245641282875444[/C][/ROW]
[ROW][C]39[/C][C]20376[/C][C]20372.990064027[/C][C]-596.758018108677[/C][C]0.977539075859067[/C][C]0.286937080909497[/C][/ROW]
[ROW][C]40[/C][C]19704[/C][C]19704.4559482806[/C][C]-613.719969617642[/C][C]1.00659075270063[/C][C]-0.206498073971135[/C][/ROW]
[ROW][C]41[/C][C]19016[/C][C]19016.4833432707[/C][C]-631.263720233403[/C][C]1.02992852607044[/C][C]-0.213651913035246[/C][/ROW]
[ROW][C]42[/C][C]18274[/C][C]18275.1864663995[/C][C]-657.258779674613[/C][C]1.05630632209948[/C][C]-0.316638150357977[/C][/ROW]
[ROW][C]43[/C][C]18020[/C][C]18011.0028720058[/C][C]-564.399873923574[/C][C]0.984477597053617[/C][C]1.13122045948945[/C][/ROW]
[ROW][C]44[/C][C]17317[/C][C]17318.6069939364[/C][C]-594.63679822148[/C][C]1.00230628714954[/C][C]-0.368375797564949[/C][/ROW]
[ROW][C]45[/C][C]16919[/C][C]16914.140932655[/C][C]-549.712179713435[/C][C]0.982114860377294[/C][C]0.547337470654057[/C][/ROW]
[ROW][C]46[/C][C]16372[/C][C]16370.886746504[/C][C]-548.18657986558[/C][C]0.981592198933012[/C][C]0.0185875211229651[/C][/ROW]
[ROW][C]47[/C][C]16069[/C][C]16063.1313754439[/C][C]-491.388035709531[/C][C]0.966759773293191[/C][C]0.692028347366188[/C][/ROW]
[ROW][C]48[/C][C]15478[/C][C]15478.9213440228[/C][C]-513.316121332013[/C][C]0.971124626480057[/C][C]-0.267171908808119[/C][/ROW]
[ROW][C]49[/C][C]15018[/C][C]15022.0499721808[/C][C]-500.081365527708[/C][C]-5.19016112904345[/C][C]0.169239879734692[/C][/ROW]
[ROW][C]50[/C][C]14561[/C][C]14559.5284435737[/C][C]-491.352350814967[/C][C]0.794598460347272[/C][C]0.101958922204939[/C][/ROW]
[ROW][C]51[/C][C]14047[/C][C]14046.6402523342[/C][C]-496.441373217352[/C][C]0.798734068637743[/C][C]-0.0619763208973207[/C][/ROW]
[ROW][C]52[/C][C]13506[/C][C]13506.0860566467[/C][C]-506.865367662594[/C][C]0.812919873282895[/C][C]-0.126925012068848[/C][/ROW]
[ROW][C]53[/C][C]13035[/C][C]13033.4970221384[/C][C]-498.767031154695[/C][C]0.804360488936351[/C][C]0.0986332619772589[/C][/ROW]
[ROW][C]54[/C][C]12471[/C][C]12471.4730230887[/C][C]-513.711325182135[/C][C]0.816408738063792[/C][C]-0.182042574083942[/C][/ROW]
[ROW][C]55[/C][C]11815[/C][C]11817.0320015405[/C][C]-546.95717509747[/C][C]0.836840588970485[/C][C]-0.405019316084368[/C][/ROW]
[ROW][C]56[/C][C]11172[/C][C]11173.1288192027[/C][C]-569.859325678293[/C][C]0.847569379347783[/C][C]-0.27902185957887[/C][/ROW]
[ROW][C]57[/C][C]10594[/C][C]10593.3537484577[/C][C]-572.201780908301[/C][C]0.848405838688092[/C][C]-0.0285395428993663[/C][/ROW]
[ROW][C]58[/C][C]9914[/C][C]9915.30281030845[/C][C]-597.20726084634[/C][C]0.855212042235512[/C][C]-0.30466242715297[/C][/ROW]
[ROW][C]59[/C][C]9319[/C][C]9318.14380645529[/C][C]-597.195860692873[/C][C]0.855209676996687[/C][C]0.000138898975618493[/C][/ROW]
[ROW][C]60[/C][C]8939[/C][C]8933.81277856859[/C][C]-546.908701724908[/C][C]0.847256969625764[/C][C]0.612700369697859[/C][/ROW]
[ROW][C]61[/C][C]8073[/C][C]8109.42578675734[/C][C]-612.070256319363[/C][C]-30.8099954504764[/C][C]-0.825348770542103[/C][/ROW]
[ROW][C]62[/C][C]7431[/C][C]7429.92198049182[/C][C]-627.78644843182[/C][C]2.32075495206215[/C][C]-0.185005197598781[/C][/ROW]
[ROW][C]63[/C][C]7022[/C][C]7015.36643617231[/C][C]-577.401066695637[/C][C]2.28687849718755[/C][C]0.613664021419229[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301434&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301434&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Structural Time Series Model -- Interpolation
tObservedLevelSlopeSeasonalStand. Residuals
14054840548000
24033140343.872981168-16.0274163565821-10.9983213346529-0.402503261691992
33981439837.4276536622-76.8072907301685-11.8891722534022-1.52009476208072
43936039380.55554206-139.409532452819-12.0504511079955-1.1474730000025
53891538933.7898021445-198.516401872031-12.1471162465382-0.911551177035637
63858338598.0793511387-227.306437360489-12.181045418802-0.402170489332392
73819138206.6311547369-263.517124203081-12.2126180902122-0.477666617799305
83747737498.4594573331-364.479725281216-12.2785960730661-1.28825186331735
93711037122.5153872574-367.126581356074-12.2799018232963-0.0331264073291893
103667036683.7531010767-383.826239190956-12.2861464627721-0.206667304709793
113633036341.4349069634-374.095545475144-12.28338184753640.119638815299667
123610836117.2153403732-338.845891338831-12.2757623557920.431752844418979
133534135380.8620275443-428.798667639945-32.056705180394-1.33390411901406
143476434767.8730668606-470.512621680634-1.27198988159832-0.444780875988015
153425334255.1142027663-480.489538670381-1.2530893853103-0.12155952508737
163374333744.8360256478-487.527079558091-1.22929725999568-0.085666123030466
173329633296.456043316-478.279956290026-1.253600749364970.11260468500245
183287532875.1201792669-464.829666399115-1.280567267563660.163826413082607
193262232619.1002507261-415.508730911801-1.355947252608460.600818487486315
203234632344.5221490672-382.220293525734-1.394729038238750.405545963889099
213178031784.9723107218-424.107385338829-1.35753127828186-0.510325229608578
223100331011.425228477-506.650897524303-1.30165627618195-1.00568387338422
232846728508.7504335061-978.156766692751-1.05837015616994-5.74476740384792
242815328141.6572653991-833.806707115739-1.115143100468131.75875873449884
252768227604.5607949653-764.79918036703471.50438694462060.924838731227214
262721727211.9568996337-679.303583587835-1.043146316581890.964430484368245
272678026776.1592807904-621.752364807346-1.122036875666130.700658914440278
282649026484.5757997065-543.719768770981-1.302000178438720.949717659221013
292602026019.7282144767-525.083918648305-1.335384026638830.22691400025666
302522725233.5718771657-586.761628970657-1.25110074208652-0.751205320497364
312534325330.4840780022-425.255000064065-1.419344562407871.967386248762
322445324463.3441143893-529.64085176016-1.33645446389147-1.27168905321526
332395823958.8278610069-523.705712267415-1.340046954580820.0723091861215278
342347523475.520853694-514.162328246053-1.34445013045160.116272885582993
352310223100.5189026025-481.288138133613-1.356011647600960.400533606584441
362239322398.8354293565-533.353216036293-1.34205436709639-0.634358818122275
372155721584.6388223851-599.031371078195-21.9840603556284-0.853200806569723
382089320893.5999316292-620.3219534654141.00157035208362-0.245641282875444
392037620372.990064027-596.7580181086770.9775390758590670.286937080909497
401970419704.4559482806-613.7199696176421.00659075270063-0.206498073971135
411901619016.4833432707-631.2637202334031.02992852607044-0.213651913035246
421827418275.1864663995-657.2587796746131.05630632209948-0.316638150357977
431802018011.0028720058-564.3998739235740.9844775970536171.13122045948945
441731717318.6069939364-594.636798221481.00230628714954-0.368375797564949
451691916914.140932655-549.7121797134350.9821148603772940.547337470654057
461637216370.886746504-548.186579865580.9815921989330120.0185875211229651
471606916063.1313754439-491.3880357095310.9667597732931910.692028347366188
481547815478.9213440228-513.3161213320130.971124626480057-0.267171908808119
491501815022.0499721808-500.081365527708-5.190161129043450.169239879734692
501456114559.5284435737-491.3523508149670.7945984603472720.101958922204939
511404714046.6402523342-496.4413732173520.798734068637743-0.0619763208973207
521350613506.0860566467-506.8653676625940.812919873282895-0.126925012068848
531303513033.4970221384-498.7670311546950.8043604889363510.0986332619772589
541247112471.4730230887-513.7113251821350.816408738063792-0.182042574083942
551181511817.0320015405-546.957175097470.836840588970485-0.405019316084368
561117211173.1288192027-569.8593256782930.847569379347783-0.27902185957887
571059410593.3537484577-572.2017809083010.848405838688092-0.0285395428993663
5899149915.30281030845-597.207260846340.855212042235512-0.30466242715297
5993199318.14380645529-597.1958606928730.8552096769966870.000138898975618493
6089398933.81277856859-546.9087017249080.8472569696257640.612700369697859
6180738109.42578675734-612.070256319363-30.8099954504764-0.825348770542103
6274317429.92198049182-627.786448431822.32075495206215-0.185005197598781
6370227015.36643617231-577.4010666956372.286878497187550.613664021419229







Structural Time Series Model -- Extrapolation
tObservedLevelSeasonal
16455.691627430936497.08397007473-41.3923426438022
25911.000974177345920.65192218243-9.6509480050964
35302.611065203265344.21987429014-41.6088090868758
44979.321870056964767.78782639784211.534043659126
54301.13350660464191.35577850554109.777728099058
63789.845900282663614.92373061324174.922169669419
73176.459077505963038.49168272094137.96739478502
82321.573023218282462.05963482865-140.48661161037
91855.387593331151885.62758693635-30.2399936051963
101145.621930898341309.19553904405-163.573608145714
11601.961319704317732.763491151753-130.802171447436
1279.8845915913238156.331443259456-76.4468516681319

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Extrapolation \tabularnewline
t & Observed & Level & Seasonal \tabularnewline
1 & 6455.69162743093 & 6497.08397007473 & -41.3923426438022 \tabularnewline
2 & 5911.00097417734 & 5920.65192218243 & -9.6509480050964 \tabularnewline
3 & 5302.61106520326 & 5344.21987429014 & -41.6088090868758 \tabularnewline
4 & 4979.32187005696 & 4767.78782639784 & 211.534043659126 \tabularnewline
5 & 4301.1335066046 & 4191.35577850554 & 109.777728099058 \tabularnewline
6 & 3789.84590028266 & 3614.92373061324 & 174.922169669419 \tabularnewline
7 & 3176.45907750596 & 3038.49168272094 & 137.96739478502 \tabularnewline
8 & 2321.57302321828 & 2462.05963482865 & -140.48661161037 \tabularnewline
9 & 1855.38759333115 & 1885.62758693635 & -30.2399936051963 \tabularnewline
10 & 1145.62193089834 & 1309.19553904405 & -163.573608145714 \tabularnewline
11 & 601.961319704317 & 732.763491151753 & -130.802171447436 \tabularnewline
12 & 79.8845915913238 & 156.331443259456 & -76.4468516681319 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301434&T=2

[TABLE]
[ROW][C]Structural Time Series Model -- Extrapolation[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Level[/C][C]Seasonal[/C][/ROW]
[ROW][C]1[/C][C]6455.69162743093[/C][C]6497.08397007473[/C][C]-41.3923426438022[/C][/ROW]
[ROW][C]2[/C][C]5911.00097417734[/C][C]5920.65192218243[/C][C]-9.6509480050964[/C][/ROW]
[ROW][C]3[/C][C]5302.61106520326[/C][C]5344.21987429014[/C][C]-41.6088090868758[/C][/ROW]
[ROW][C]4[/C][C]4979.32187005696[/C][C]4767.78782639784[/C][C]211.534043659126[/C][/ROW]
[ROW][C]5[/C][C]4301.1335066046[/C][C]4191.35577850554[/C][C]109.777728099058[/C][/ROW]
[ROW][C]6[/C][C]3789.84590028266[/C][C]3614.92373061324[/C][C]174.922169669419[/C][/ROW]
[ROW][C]7[/C][C]3176.45907750596[/C][C]3038.49168272094[/C][C]137.96739478502[/C][/ROW]
[ROW][C]8[/C][C]2321.57302321828[/C][C]2462.05963482865[/C][C]-140.48661161037[/C][/ROW]
[ROW][C]9[/C][C]1855.38759333115[/C][C]1885.62758693635[/C][C]-30.2399936051963[/C][/ROW]
[ROW][C]10[/C][C]1145.62193089834[/C][C]1309.19553904405[/C][C]-163.573608145714[/C][/ROW]
[ROW][C]11[/C][C]601.961319704317[/C][C]732.763491151753[/C][C]-130.802171447436[/C][/ROW]
[ROW][C]12[/C][C]79.8845915913238[/C][C]156.331443259456[/C][C]-76.4468516681319[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301434&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301434&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Structural Time Series Model -- Extrapolation
tObservedLevelSeasonal
16455.691627430936497.08397007473-41.3923426438022
25911.000974177345920.65192218243-9.6509480050964
35302.611065203265344.21987429014-41.6088090868758
44979.321870056964767.78782639784211.534043659126
54301.13350660464191.35577850554109.777728099058
63789.845900282663614.92373061324174.922169669419
73176.459077505963038.49168272094137.96739478502
82321.573023218282462.05963482865-140.48661161037
91855.387593331151885.62758693635-30.2399936051963
101145.621930898341309.19553904405-163.573608145714
11601.961319704317732.763491151753-130.802171447436
1279.8845915913238156.331443259456-76.4468516681319



Parameters (Session):
par1 = 12 ; par2 = 12 ; par3 = BFGS ;
Parameters (R input):
par1 = 12 ; par2 = 12 ; par3 = BFGS ;
R code (references can be found in the software module):
require('stsm')
require('stsm.class')
require('KFKSDS')
par1 <- as.numeric(par1)
par2 <- as.numeric(par2)
nx <- length(x)
x <- ts(x,frequency=par1)
m <- StructTS(x,type='BSM')
print(m$coef)
print(m$fitted)
print(m$resid)
mylevel <- as.numeric(m$fitted[,'level'])
myslope <- as.numeric(m$fitted[,'slope'])
myseas <- as.numeric(m$fitted[,'sea'])
myresid <- as.numeric(m$resid)
myfit <- mylevel+myseas
mm <- stsm.model(model = 'BSM', y = x, transPars = 'StructTS')
fit2 <- stsmFit(mm, stsm.method = 'maxlik.td.optim', method = par3, KF.args = list(P0cov = TRUE))
(fit2.comps <- tsSmooth(fit2, P0cov = FALSE)$states)
m2 <- set.pars(mm, pmax(fit2$par, .Machine$double.eps))
(ss <- char2numeric(m2))
(pred <- predict(ss, x, n.ahead = par2))
mylagmax <- nx/2
bitmap(file='test2.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(x),lag.max = mylagmax,main='Observed')
acf(mylevel,na.action=na.pass,lag.max = mylagmax,main='Level')
acf(myseas,na.action=na.pass,lag.max = mylagmax,main='Seasonal')
acf(myresid,na.action=na.pass,lag.max = mylagmax,main='Standardized Residals')
par(op)
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
spectrum(as.numeric(x),main='Observed')
spectrum(mylevel,main='Level')
spectrum(myseas,main='Seasonal')
spectrum(myresid,main='Standardized Residals')
par(op)
dev.off()
bitmap(file='test4.png')
op <- par(mfrow = c(2,2))
cpgram(as.numeric(x),main='Observed')
cpgram(mylevel,main='Level')
cpgram(myseas,main='Seasonal')
cpgram(myresid,main='Standardized Residals')
par(op)
dev.off()
bitmap(file='test1.png')
plot(as.numeric(m$resid),main='Standardized Residuals',ylab='Residuals',xlab='time',type='b')
grid()
dev.off()
bitmap(file='test5.png')
op <- par(mfrow = c(2,2))
hist(m$resid,main='Residual Histogram')
plot(density(m$resid),main='Residual Kernel Density')
qqnorm(m$resid,main='Residual Normal QQ Plot')
qqline(m$resid)
plot(m$resid^2, myfit^2,main='Sq.Resid vs. Sq.Fit',xlab='Squared residuals',ylab='Squared Fit')
par(op)
dev.off()
bitmap(file='test6.png')
par(mfrow = c(3,1), mar = c(3,3,3,3))
plot(cbind(x, pred$pred), type = 'n', plot.type = 'single', ylab = '')
lines(x)
polygon(c(time(pred$pred), rev(time(pred$pred))), c(pred$pred + 2 * pred$se, rev(pred$pred)), col = 'gray85', border = NA)
polygon(c(time(pred$pred), rev(time(pred$pred))), c(pred$pred - 2 * pred$se, rev(pred$pred)), col = ' gray85', border = NA)
lines(pred$pred, col = 'blue', lwd = 1.5)
mtext(text = 'forecasts of the observed series', side = 3, adj = 0)
plot(cbind(x, pred$a[,1]), type = 'n', plot.type = 'single', ylab = '')
lines(x)
polygon(c(time(pred$a[,1]), rev(time(pred$a[,1]))), c(pred$a[,1] + 2 * sqrt(pred$P[,1]), rev(pred$a[,1])), col = 'gray85', border = NA)
polygon(c(time(pred$a[,1]), rev(time(pred$a[,1]))), c(pred$a[,1] - 2 * sqrt(pred$P[,1]), rev(pred$a[,1])), col = ' gray85', border = NA)
lines(pred$a[,1], col = 'blue', lwd = 1.5)
mtext(text = 'forecasts of the level component', side = 3, adj = 0)
plot(cbind(fit2.comps[,3], pred$a[,3]), type = 'n', plot.type = 'single', ylab = '')
lines(fit2.comps[,3])
polygon(c(time(pred$a[,3]), rev(time(pred$a[,3]))), c(pred$a[,3] + 2 * sqrt(pred$P[,3]), rev(pred$a[,3])), col = 'gray85', border = NA)
polygon(c(time(pred$a[,3]), rev(time(pred$a[,3]))), c(pred$a[,3] - 2 * sqrt(pred$P[,3]), rev(pred$a[,3])), col = ' gray85', border = NA)
lines(pred$a[,3], col = 'blue', lwd = 1.5)
mtext(text = 'forecasts of the seasonal component', side = 3, adj = 0)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Structural Time Series Model -- Interpolation',6,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Level',header=TRUE)
a<-table.element(a,'Slope',header=TRUE)
a<-table.element(a,'Seasonal',header=TRUE)
a<-table.element(a,'Stand. Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nx) {
a<-table.row.start(a)
a<-table.element(a,i,header=TRUE)
a<-table.element(a,x[i])
a<-table.element(a,mylevel[i])
a<-table.element(a,myslope[i])
a<-table.element(a,myseas[i])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Structural Time Series Model -- Extrapolation',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Level',header=TRUE)
a<-table.element(a,'Seasonal',header=TRUE)
a<-table.row.end(a)
for (i in 1:par2) {
a<-table.row.start(a)
a<-table.element(a,i,header=TRUE)
a<-table.element(a,pred$pred[i])
a<-table.element(a,pred$a[i,1])
a<-table.element(a,pred$a[i,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')