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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_structuraltimeseries.wasp
Title produced by softwareStructural Time Series Models
Date of computationTue, 13 Dec 2016 16:09:03 +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/13/t1481641758y4e3zlo0xuswrst.htm/, Retrieved Fri, 01 Nov 2024 03:32:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299140, Retrieved Fri, 01 Nov 2024 03:32:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact89
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Structural Time Series Models] [] [2016-12-13 15:09:03] [9b171b8beffcb53bb49a1e7c02b89c12] [Current]
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Dataseries X:
2669.94
2778.72
2648.44
2631.32
3057.32
2730.66
2730.62
2738.7
2616.36
2773.54
2872.76
2999.42
2730.62
2907.22
2778.04
2833.94
2914.44
2788.86
2742.8
2726.52
2746.44
2927.42
2879.56
3262.02
2883.14
2903.2
2877.7
2874.3
3026.66
2979.42
3109.68
2966.76
2961.04
3103.84
3359.12
3976.24
3049.42
3089.14
3166.26
3459.04
3457.32
3292.66
3432.86
3388.4
3312.9
3390.04
3757.44
4612.38
3613.34
3525.14
3473.06
3662.22
3717.4
3466.9
3443.4
3383.16
3843.64
3692.4
3558.38
3811.02
3470.54
3354.68
3499.96
3537.36
3414.98
3649
3549.72
3680.78
3484.64
3451.92
3831.14
3906.02
3499.54
3620.62
3473.64
3494.32
3799.66
3476.4
3446.86
3441.94
3514.68
3464.96
3579.48
3944.24
3702.42
3716.28
3538.36
3482.58
3665.5
3484.5
3425.08
3421.44
3602.34
3593.44
3478.5
4365.26
3445.2
3473.48
3472.32
3403.82
3575.4
3512.96
3433.04
3495.2
3478.96
3559.28
3887.1
4083.16
3659.52
3693.48
3779.52
3891.62
3895.86
3745.04
3884.46
3862.98




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=299140&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=299140&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299140&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
12669.942669.94000
22778.722704.369755484243.2982394130520223.74827280603190.647820173413504
32648.442689.69404660171.51751759680943-22.5771216644125-0.265169460081158
42631.322668.28352557744-0.322518484738259-11.1492346693359-0.361124139476437
53057.322794.884495279687.91243701354016107.320751972552.12817798296401
62730.662789.977903028667.21607452121146-42.8131250927816-0.223651446999778
72730.622772.437918716276.04633794314354-8.90314680892791-0.442645465409495
82738.72761.425465445425.322510786269480.419478685840408-0.309778616775546
92616.362716.370322363763.35613830280771-30.7515260554086-0.924102936172828
102773.542729.791885742913.7238421639341929.78642472778140.18589404217281
112872.762776.518048847425.2119100863398236.21870412796970.797983604482272
122999.422852.046910537997.5360316705053148.77005957418131.30941575965909
132730.622854.510754753077.92201203732867-115.111530261332-0.126087097027341
142907.222866.480591225068.0105339566301635.68094037422650.0716968091687369
152778.042849.585884287837.0229941804-43.7030134573384-0.408107150829358
162833.942862.640278382177.25661856843064-35.70607929511480.102522400366516
172914.442850.174889941536.5863503467501288.3810642127776-0.349682934890082
182788.862843.674264010376.20041712480794-38.2360433560792-0.238669365734011
192742.82816.687788547885.33399573214404-30.9367425323706-0.615544272712959
202726.522784.024455713634.43188116284639-7.69476281870835-0.711863096985823
212746.442781.182652944264.27117657245048-25.1329354528218-0.137102367421469
222927.422821.852543030725.0285027157613557.22780246653780.688811115298779
232879.562844.774699232115.3699066062403310.90177661163220.339765278050792
243262.022954.364456194456.76134451744516166.7937227251621.99474300548986
252883.142982.367990244046.38787563913507-130.2017457279770.444306846825402
262903.22955.494467120156.0384249978359-8.93822590265787-0.625153904066007
272877.72945.700362980115.66307001672155-48.8709490139709-0.280863427009957
282874.32933.508858851725.19522465624047-37.6619955968902-0.317936117754429
293026.662932.563660383565.04378828996718101.681471995668-0.11163647374267
302979.422952.571166455285.375564066859417.946548293647130.277136224260959
313109.683004.655648652346.3047029030762145.07335773137530.87626220136397
322966.763007.190917361776.23646838311134-35.5422065360707-0.0713009148787499
332961.043012.280607902626.21732145401595-49.743148943594-0.0218066220004299
343103.843032.524647036566.432054210404852.90661604377960.267698205739095
353359.123141.404465571627.7733445760637782.51742209505021.96201865587221
363976.243345.997312643849.35025306617607367.6353563323853.79877090079792
373049.423333.828979613339.41635074311275-254.811952770193-0.42839595827487
383089.143274.282117321868.87191796126904-94.7862342079443-1.31367895491492
393166.263252.299597415198.36722591568769-47.4313605568745-0.566983280128905
403459.043321.80745396689.5510013311109361.48840933201321.11792828696314
413457.323347.997016364439.8718401562846988.50526198841180.30726624736154
423292.663345.348383434259.64661211330184-36.8009249015344-0.234055786252355
433432.863361.284984370269.7500256225669463.49722537976020.118755881007052
443388.43387.549789546039.9977242338773-20.54616407284370.314007130489364
453312.93398.6290084503210.0125003794953-87.13903475133670.0206624871125288
463390.043412.610545118510.0608402866013-27.77090057969080.0760920263736206
473757.443518.9940874788211.026558899239111.5969770350911.85262643464074
484612.383730.1413360945212.3221035406035616.6569593165323.87072950803034
493613.343795.5144557668712.4327919809691-253.3996957997911.03705655862781
503525.143767.5334455435112.1440773398968-189.444060226266-0.773145851303354
513473.063714.5963403574911.3323364778593-158.620480757004-1.21785474333287
523662.223684.4709715450210.705651052916830.0252885775976-0.770848446525712
533717.43668.7377116558210.292184081860382.1188978804096-0.493797660007479
543466.93627.760865193119.52118289187554-95.4126011915877-0.965205482235862
553443.43562.702672378518.47765132282181-23.2454270251754-1.41467673421793
563383.163518.482618875637.80190016035197-66.9503421824742-1.00552365178622
573843.643637.207057226019.0878197943738761.7034817813952.12559013669234
583692.43704.450099909089.67985974912019-88.27388897260091.11791621538671
593558.383681.854418241359.41022721412378-80.9895099516086-0.622155649275723
603811.023558.255234028738.6109568839427428.722819519866-2.57309912669851
613470.543579.854893795388.66487885041606-126.5639287819110.252042779400757
623354.683562.589921328458.4885374799148-173.948317492253-0.497133514402728
633499.963581.612018641348.59606330799252-95.20895109290340.19917161580204
643537.363560.123737983458.2256055229131415.6259390180648-0.56563569839928
653414.983488.646131435817.1879241330517728.109918047532-1.5012363944095
6636493542.606992033117.7865941696020946.34206349024890.885565287731873
673549.723560.008895822637.90285642092666-22.71489564930280.183081461574685
683680.783635.772891236528.65964816548334-43.21280669475961.29835754906848
693484.643598.023402860548.19220699968695-52.7572965430772-0.891204670442932
703451.923572.31297559967.89290764327012-75.9293535680058-0.652832278125242
713831.143645.630843331228.3750393100414199.40700638639291.26268417930231
723906.023614.722576269868.1461785956706343.157191324263-0.759760537089086
733499.543614.662677302268.10518527276361-104.281285562277-0.158756858182438
743620.623666.72847121758.39228355552831-103.6897777206450.844181672666972
753473.643644.337120949878.12250420669459-130.829441047706-0.585863795185463
763494.323592.730889240697.50283219872434-21.5641309662383-1.13164374551659
773799.663647.615757665818.0275515098340491.11333932634040.898185120120902
783476.43603.246187683917.44853283695644-59.2393397077459-0.996623638548705
793446.863573.608211657767.05657075138614-78.6667787865612-0.708379124944555
803441.943542.576732235966.68247449527648-51.0227500871561-0.730323959868199
813514.683546.590403441176.65870082447615-28.4197934268916-0.0513320840651294
823464.963556.715770372256.68595561879857-96.30511272484570.0668350084834451
833579.483535.373764614426.4974242915999380.9879709353984-0.541330730484405
843944.243553.796542771876.56531967112899374.7208189144270.230602833312652
853702.423631.19822104276.94096203555184-22.13263793892651.36888410940752
863716.283688.759785174567.25801261903792-38.81338269947240.973443694139236
873538.363687.898394154857.19496768183315-138.978754613273-0.155206571294685
883482.583646.174026094166.75586398724442-100.28516438868-0.931925698260496
893665.53615.507169121216.3968009148942798.3796021251941-0.712879209220765
903484.53588.432535188276.07335279760328-60.5640911921858-0.639032790099266
913425.083559.734745662995.74882210049311-89.4445499587059-0.665918891768819
923421.443535.313016197035.48500917282066-74.4982092270346-0.579580538821365
933602.343560.982907313385.6462779252888314.92589004714460.388748228730408
943593.443600.105626958335.8850845297298-50.62323389116390.64600301700112
953478.53560.12557544985.59801675264418-21.2721286127429-0.886311773268556
964365.263686.26148867996.267007757141520.1949357369192.33086547556881
973445.23651.951529285976.04967309041848-153.333567926421-0.783948739176382
983473.483609.476335068525.75899429019933-72.3665839604834-0.934337752871104
993472.323597.789357523715.63645418064414-102.711031066213-0.334545501387434
1003403.823565.824759663245.33831306507101-113.133095330339-0.719196476985106
1013575.43533.763291006415.0224223027469890.2002307421626-0.715153790208139
1023512.963537.3179049235.00987151900283-22.4494588112716-0.028108863552876
1033433.043533.654068133894.93768561862153-89.3076021563027-0.166487830107432
1043495.23550.277353090675.02953352306291-70.35437198520920.224839676094544
1053478.963536.577689078024.89380056926872-33.0655750220341-0.361117407027946
1063559.283555.457646594354.98551807814426-14.55373167404670.270103891676816
1073887.13669.405667592355.6268104528804274.2933902722372.10660171049546
1084083.163649.182566348855.48758507916516468.022999684324-0.499945644425356
1093659.523685.73352663695.65168127923871-67.09323151487610.600260908314419
1103693.483710.182050143855.75914767001235-41.36946300911510.362352534492515
1113779.523756.140808747116.01817089513207-29.18388934325270.772717729883143
1123891.623827.481611780066.4832048156523-21.04331356783721.25323839770523
1133895.863834.546168150136.4875870526117560.55640062229390.0111497449496931
1143745.043821.495580108246.33814331225989-50.9785354137769-0.375096756142522
1153884.463867.06026798126.63190973613377-33.8466395271860.754372893009938
1163862.983894.710279453936.78170619836819-59.25121414331540.404964906425558

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Interpolation \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 2669.94 & 2669.94 & 0 & 0 & 0 \tabularnewline
2 & 2778.72 & 2704.36975548424 & 3.29823941305202 & 23.7482728060319 & 0.647820173413504 \tabularnewline
3 & 2648.44 & 2689.6940466017 & 1.51751759680943 & -22.5771216644125 & -0.265169460081158 \tabularnewline
4 & 2631.32 & 2668.28352557744 & -0.322518484738259 & -11.1492346693359 & -0.361124139476437 \tabularnewline
5 & 3057.32 & 2794.88449527968 & 7.91243701354016 & 107.32075197255 & 2.12817798296401 \tabularnewline
6 & 2730.66 & 2789.97790302866 & 7.21607452121146 & -42.8131250927816 & -0.223651446999778 \tabularnewline
7 & 2730.62 & 2772.43791871627 & 6.04633794314354 & -8.90314680892791 & -0.442645465409495 \tabularnewline
8 & 2738.7 & 2761.42546544542 & 5.32251078626948 & 0.419478685840408 & -0.309778616775546 \tabularnewline
9 & 2616.36 & 2716.37032236376 & 3.35613830280771 & -30.7515260554086 & -0.924102936172828 \tabularnewline
10 & 2773.54 & 2729.79188574291 & 3.72384216393419 & 29.7864247277814 & 0.18589404217281 \tabularnewline
11 & 2872.76 & 2776.51804884742 & 5.21191008633982 & 36.2187041279697 & 0.797983604482272 \tabularnewline
12 & 2999.42 & 2852.04691053799 & 7.53603167050531 & 48.7700595741813 & 1.30941575965909 \tabularnewline
13 & 2730.62 & 2854.51075475307 & 7.92201203732867 & -115.111530261332 & -0.126087097027341 \tabularnewline
14 & 2907.22 & 2866.48059122506 & 8.01053395663016 & 35.6809403742265 & 0.0716968091687369 \tabularnewline
15 & 2778.04 & 2849.58588428783 & 7.0229941804 & -43.7030134573384 & -0.408107150829358 \tabularnewline
16 & 2833.94 & 2862.64027838217 & 7.25661856843064 & -35.7060792951148 & 0.102522400366516 \tabularnewline
17 & 2914.44 & 2850.17488994153 & 6.58635034675012 & 88.3810642127776 & -0.349682934890082 \tabularnewline
18 & 2788.86 & 2843.67426401037 & 6.20041712480794 & -38.2360433560792 & -0.238669365734011 \tabularnewline
19 & 2742.8 & 2816.68778854788 & 5.33399573214404 & -30.9367425323706 & -0.615544272712959 \tabularnewline
20 & 2726.52 & 2784.02445571363 & 4.43188116284639 & -7.69476281870835 & -0.711863096985823 \tabularnewline
21 & 2746.44 & 2781.18265294426 & 4.27117657245048 & -25.1329354528218 & -0.137102367421469 \tabularnewline
22 & 2927.42 & 2821.85254303072 & 5.02850271576135 & 57.2278024665378 & 0.688811115298779 \tabularnewline
23 & 2879.56 & 2844.77469923211 & 5.36990660624033 & 10.9017766116322 & 0.339765278050792 \tabularnewline
24 & 3262.02 & 2954.36445619445 & 6.76134451744516 & 166.793722725162 & 1.99474300548986 \tabularnewline
25 & 2883.14 & 2982.36799024404 & 6.38787563913507 & -130.201745727977 & 0.444306846825402 \tabularnewline
26 & 2903.2 & 2955.49446712015 & 6.0384249978359 & -8.93822590265787 & -0.625153904066007 \tabularnewline
27 & 2877.7 & 2945.70036298011 & 5.66307001672155 & -48.8709490139709 & -0.280863427009957 \tabularnewline
28 & 2874.3 & 2933.50885885172 & 5.19522465624047 & -37.6619955968902 & -0.317936117754429 \tabularnewline
29 & 3026.66 & 2932.56366038356 & 5.04378828996718 & 101.681471995668 & -0.11163647374267 \tabularnewline
30 & 2979.42 & 2952.57116645528 & 5.37556406685941 & 7.94654829364713 & 0.277136224260959 \tabularnewline
31 & 3109.68 & 3004.65564865234 & 6.30470290307621 & 45.0733577313753 & 0.87626220136397 \tabularnewline
32 & 2966.76 & 3007.19091736177 & 6.23646838311134 & -35.5422065360707 & -0.0713009148787499 \tabularnewline
33 & 2961.04 & 3012.28060790262 & 6.21732145401595 & -49.743148943594 & -0.0218066220004299 \tabularnewline
34 & 3103.84 & 3032.52464703656 & 6.4320542104048 & 52.9066160437796 & 0.267698205739095 \tabularnewline
35 & 3359.12 & 3141.40446557162 & 7.77334457606377 & 82.5174220950502 & 1.96201865587221 \tabularnewline
36 & 3976.24 & 3345.99731264384 & 9.35025306617607 & 367.635356332385 & 3.79877090079792 \tabularnewline
37 & 3049.42 & 3333.82897961333 & 9.41635074311275 & -254.811952770193 & -0.42839595827487 \tabularnewline
38 & 3089.14 & 3274.28211732186 & 8.87191796126904 & -94.7862342079443 & -1.31367895491492 \tabularnewline
39 & 3166.26 & 3252.29959741519 & 8.36722591568769 & -47.4313605568745 & -0.566983280128905 \tabularnewline
40 & 3459.04 & 3321.8074539668 & 9.55100133111093 & 61.4884093320132 & 1.11792828696314 \tabularnewline
41 & 3457.32 & 3347.99701636443 & 9.87184015628469 & 88.5052619884118 & 0.30726624736154 \tabularnewline
42 & 3292.66 & 3345.34838343425 & 9.64661211330184 & -36.8009249015344 & -0.234055786252355 \tabularnewline
43 & 3432.86 & 3361.28498437026 & 9.75002562256694 & 63.4972253797602 & 0.118755881007052 \tabularnewline
44 & 3388.4 & 3387.54978954603 & 9.9977242338773 & -20.5461640728437 & 0.314007130489364 \tabularnewline
45 & 3312.9 & 3398.62900845032 & 10.0125003794953 & -87.1390347513367 & 0.0206624871125288 \tabularnewline
46 & 3390.04 & 3412.6105451185 & 10.0608402866013 & -27.7709005796908 & 0.0760920263736206 \tabularnewline
47 & 3757.44 & 3518.99408747882 & 11.026558899239 & 111.596977035091 & 1.85262643464074 \tabularnewline
48 & 4612.38 & 3730.14133609452 & 12.3221035406035 & 616.656959316532 & 3.87072950803034 \tabularnewline
49 & 3613.34 & 3795.51445576687 & 12.4327919809691 & -253.399695799791 & 1.03705655862781 \tabularnewline
50 & 3525.14 & 3767.53344554351 & 12.1440773398968 & -189.444060226266 & -0.773145851303354 \tabularnewline
51 & 3473.06 & 3714.59634035749 & 11.3323364778593 & -158.620480757004 & -1.21785474333287 \tabularnewline
52 & 3662.22 & 3684.47097154502 & 10.7056510529168 & 30.0252885775976 & -0.770848446525712 \tabularnewline
53 & 3717.4 & 3668.73771165582 & 10.2921840818603 & 82.1188978804096 & -0.493797660007479 \tabularnewline
54 & 3466.9 & 3627.76086519311 & 9.52118289187554 & -95.4126011915877 & -0.965205482235862 \tabularnewline
55 & 3443.4 & 3562.70267237851 & 8.47765132282181 & -23.2454270251754 & -1.41467673421793 \tabularnewline
56 & 3383.16 & 3518.48261887563 & 7.80190016035197 & -66.9503421824742 & -1.00552365178622 \tabularnewline
57 & 3843.64 & 3637.20705722601 & 9.08781979437387 & 61.703481781395 & 2.12559013669234 \tabularnewline
58 & 3692.4 & 3704.45009990908 & 9.67985974912019 & -88.2738889726009 & 1.11791621538671 \tabularnewline
59 & 3558.38 & 3681.85441824135 & 9.41022721412378 & -80.9895099516086 & -0.622155649275723 \tabularnewline
60 & 3811.02 & 3558.25523402873 & 8.6109568839427 & 428.722819519866 & -2.57309912669851 \tabularnewline
61 & 3470.54 & 3579.85489379538 & 8.66487885041606 & -126.563928781911 & 0.252042779400757 \tabularnewline
62 & 3354.68 & 3562.58992132845 & 8.4885374799148 & -173.948317492253 & -0.497133514402728 \tabularnewline
63 & 3499.96 & 3581.61201864134 & 8.59606330799252 & -95.2089510929034 & 0.19917161580204 \tabularnewline
64 & 3537.36 & 3560.12373798345 & 8.22560552291314 & 15.6259390180648 & -0.56563569839928 \tabularnewline
65 & 3414.98 & 3488.64613143581 & 7.18792413305177 & 28.109918047532 & -1.5012363944095 \tabularnewline
66 & 3649 & 3542.60699203311 & 7.78659416960209 & 46.3420634902489 & 0.885565287731873 \tabularnewline
67 & 3549.72 & 3560.00889582263 & 7.90285642092666 & -22.7148956493028 & 0.183081461574685 \tabularnewline
68 & 3680.78 & 3635.77289123652 & 8.65964816548334 & -43.2128066947596 & 1.29835754906848 \tabularnewline
69 & 3484.64 & 3598.02340286054 & 8.19220699968695 & -52.7572965430772 & -0.891204670442932 \tabularnewline
70 & 3451.92 & 3572.3129755996 & 7.89290764327012 & -75.9293535680058 & -0.652832278125242 \tabularnewline
71 & 3831.14 & 3645.63084333122 & 8.37503931004141 & 99.4070063863929 & 1.26268417930231 \tabularnewline
72 & 3906.02 & 3614.72257626986 & 8.1461785956706 & 343.157191324263 & -0.759760537089086 \tabularnewline
73 & 3499.54 & 3614.66267730226 & 8.10518527276361 & -104.281285562277 & -0.158756858182438 \tabularnewline
74 & 3620.62 & 3666.7284712175 & 8.39228355552831 & -103.689777720645 & 0.844181672666972 \tabularnewline
75 & 3473.64 & 3644.33712094987 & 8.12250420669459 & -130.829441047706 & -0.585863795185463 \tabularnewline
76 & 3494.32 & 3592.73088924069 & 7.50283219872434 & -21.5641309662383 & -1.13164374551659 \tabularnewline
77 & 3799.66 & 3647.61575766581 & 8.02755150983404 & 91.1133393263404 & 0.898185120120902 \tabularnewline
78 & 3476.4 & 3603.24618768391 & 7.44853283695644 & -59.2393397077459 & -0.996623638548705 \tabularnewline
79 & 3446.86 & 3573.60821165776 & 7.05657075138614 & -78.6667787865612 & -0.708379124944555 \tabularnewline
80 & 3441.94 & 3542.57673223596 & 6.68247449527648 & -51.0227500871561 & -0.730323959868199 \tabularnewline
81 & 3514.68 & 3546.59040344117 & 6.65870082447615 & -28.4197934268916 & -0.0513320840651294 \tabularnewline
82 & 3464.96 & 3556.71577037225 & 6.68595561879857 & -96.3051127248457 & 0.0668350084834451 \tabularnewline
83 & 3579.48 & 3535.37376461442 & 6.49742429159993 & 80.9879709353984 & -0.541330730484405 \tabularnewline
84 & 3944.24 & 3553.79654277187 & 6.56531967112899 & 374.720818914427 & 0.230602833312652 \tabularnewline
85 & 3702.42 & 3631.1982210427 & 6.94096203555184 & -22.1326379389265 & 1.36888410940752 \tabularnewline
86 & 3716.28 & 3688.75978517456 & 7.25801261903792 & -38.8133826994724 & 0.973443694139236 \tabularnewline
87 & 3538.36 & 3687.89839415485 & 7.19496768183315 & -138.978754613273 & -0.155206571294685 \tabularnewline
88 & 3482.58 & 3646.17402609416 & 6.75586398724442 & -100.28516438868 & -0.931925698260496 \tabularnewline
89 & 3665.5 & 3615.50716912121 & 6.39680091489427 & 98.3796021251941 & -0.712879209220765 \tabularnewline
90 & 3484.5 & 3588.43253518827 & 6.07335279760328 & -60.5640911921858 & -0.639032790099266 \tabularnewline
91 & 3425.08 & 3559.73474566299 & 5.74882210049311 & -89.4445499587059 & -0.665918891768819 \tabularnewline
92 & 3421.44 & 3535.31301619703 & 5.48500917282066 & -74.4982092270346 & -0.579580538821365 \tabularnewline
93 & 3602.34 & 3560.98290731338 & 5.64627792528883 & 14.9258900471446 & 0.388748228730408 \tabularnewline
94 & 3593.44 & 3600.10562695833 & 5.8850845297298 & -50.6232338911639 & 0.64600301700112 \tabularnewline
95 & 3478.5 & 3560.1255754498 & 5.59801675264418 & -21.2721286127429 & -0.886311773268556 \tabularnewline
96 & 4365.26 & 3686.2614886799 & 6.267007757141 & 520.194935736919 & 2.33086547556881 \tabularnewline
97 & 3445.2 & 3651.95152928597 & 6.04967309041848 & -153.333567926421 & -0.783948739176382 \tabularnewline
98 & 3473.48 & 3609.47633506852 & 5.75899429019933 & -72.3665839604834 & -0.934337752871104 \tabularnewline
99 & 3472.32 & 3597.78935752371 & 5.63645418064414 & -102.711031066213 & -0.334545501387434 \tabularnewline
100 & 3403.82 & 3565.82475966324 & 5.33831306507101 & -113.133095330339 & -0.719196476985106 \tabularnewline
101 & 3575.4 & 3533.76329100641 & 5.02242230274698 & 90.2002307421626 & -0.715153790208139 \tabularnewline
102 & 3512.96 & 3537.317904923 & 5.00987151900283 & -22.4494588112716 & -0.028108863552876 \tabularnewline
103 & 3433.04 & 3533.65406813389 & 4.93768561862153 & -89.3076021563027 & -0.166487830107432 \tabularnewline
104 & 3495.2 & 3550.27735309067 & 5.02953352306291 & -70.3543719852092 & 0.224839676094544 \tabularnewline
105 & 3478.96 & 3536.57768907802 & 4.89380056926872 & -33.0655750220341 & -0.361117407027946 \tabularnewline
106 & 3559.28 & 3555.45764659435 & 4.98551807814426 & -14.5537316740467 & 0.270103891676816 \tabularnewline
107 & 3887.1 & 3669.40566759235 & 5.62681045288042 & 74.293390272237 & 2.10660171049546 \tabularnewline
108 & 4083.16 & 3649.18256634885 & 5.48758507916516 & 468.022999684324 & -0.499945644425356 \tabularnewline
109 & 3659.52 & 3685.7335266369 & 5.65168127923871 & -67.0932315148761 & 0.600260908314419 \tabularnewline
110 & 3693.48 & 3710.18205014385 & 5.75914767001235 & -41.3694630091151 & 0.362352534492515 \tabularnewline
111 & 3779.52 & 3756.14080874711 & 6.01817089513207 & -29.1838893432527 & 0.772717729883143 \tabularnewline
112 & 3891.62 & 3827.48161178006 & 6.4832048156523 & -21.0433135678372 & 1.25323839770523 \tabularnewline
113 & 3895.86 & 3834.54616815013 & 6.48758705261175 & 60.5564006222939 & 0.0111497449496931 \tabularnewline
114 & 3745.04 & 3821.49558010824 & 6.33814331225989 & -50.9785354137769 & -0.375096756142522 \tabularnewline
115 & 3884.46 & 3867.0602679812 & 6.63190973613377 & -33.846639527186 & 0.754372893009938 \tabularnewline
116 & 3862.98 & 3894.71027945393 & 6.78170619836819 & -59.2512141433154 & 0.404964906425558 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299140&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]2669.94[/C][C]2669.94[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]2778.72[/C][C]2704.36975548424[/C][C]3.29823941305202[/C][C]23.7482728060319[/C][C]0.647820173413504[/C][/ROW]
[ROW][C]3[/C][C]2648.44[/C][C]2689.6940466017[/C][C]1.51751759680943[/C][C]-22.5771216644125[/C][C]-0.265169460081158[/C][/ROW]
[ROW][C]4[/C][C]2631.32[/C][C]2668.28352557744[/C][C]-0.322518484738259[/C][C]-11.1492346693359[/C][C]-0.361124139476437[/C][/ROW]
[ROW][C]5[/C][C]3057.32[/C][C]2794.88449527968[/C][C]7.91243701354016[/C][C]107.32075197255[/C][C]2.12817798296401[/C][/ROW]
[ROW][C]6[/C][C]2730.66[/C][C]2789.97790302866[/C][C]7.21607452121146[/C][C]-42.8131250927816[/C][C]-0.223651446999778[/C][/ROW]
[ROW][C]7[/C][C]2730.62[/C][C]2772.43791871627[/C][C]6.04633794314354[/C][C]-8.90314680892791[/C][C]-0.442645465409495[/C][/ROW]
[ROW][C]8[/C][C]2738.7[/C][C]2761.42546544542[/C][C]5.32251078626948[/C][C]0.419478685840408[/C][C]-0.309778616775546[/C][/ROW]
[ROW][C]9[/C][C]2616.36[/C][C]2716.37032236376[/C][C]3.35613830280771[/C][C]-30.7515260554086[/C][C]-0.924102936172828[/C][/ROW]
[ROW][C]10[/C][C]2773.54[/C][C]2729.79188574291[/C][C]3.72384216393419[/C][C]29.7864247277814[/C][C]0.18589404217281[/C][/ROW]
[ROW][C]11[/C][C]2872.76[/C][C]2776.51804884742[/C][C]5.21191008633982[/C][C]36.2187041279697[/C][C]0.797983604482272[/C][/ROW]
[ROW][C]12[/C][C]2999.42[/C][C]2852.04691053799[/C][C]7.53603167050531[/C][C]48.7700595741813[/C][C]1.30941575965909[/C][/ROW]
[ROW][C]13[/C][C]2730.62[/C][C]2854.51075475307[/C][C]7.92201203732867[/C][C]-115.111530261332[/C][C]-0.126087097027341[/C][/ROW]
[ROW][C]14[/C][C]2907.22[/C][C]2866.48059122506[/C][C]8.01053395663016[/C][C]35.6809403742265[/C][C]0.0716968091687369[/C][/ROW]
[ROW][C]15[/C][C]2778.04[/C][C]2849.58588428783[/C][C]7.0229941804[/C][C]-43.7030134573384[/C][C]-0.408107150829358[/C][/ROW]
[ROW][C]16[/C][C]2833.94[/C][C]2862.64027838217[/C][C]7.25661856843064[/C][C]-35.7060792951148[/C][C]0.102522400366516[/C][/ROW]
[ROW][C]17[/C][C]2914.44[/C][C]2850.17488994153[/C][C]6.58635034675012[/C][C]88.3810642127776[/C][C]-0.349682934890082[/C][/ROW]
[ROW][C]18[/C][C]2788.86[/C][C]2843.67426401037[/C][C]6.20041712480794[/C][C]-38.2360433560792[/C][C]-0.238669365734011[/C][/ROW]
[ROW][C]19[/C][C]2742.8[/C][C]2816.68778854788[/C][C]5.33399573214404[/C][C]-30.9367425323706[/C][C]-0.615544272712959[/C][/ROW]
[ROW][C]20[/C][C]2726.52[/C][C]2784.02445571363[/C][C]4.43188116284639[/C][C]-7.69476281870835[/C][C]-0.711863096985823[/C][/ROW]
[ROW][C]21[/C][C]2746.44[/C][C]2781.18265294426[/C][C]4.27117657245048[/C][C]-25.1329354528218[/C][C]-0.137102367421469[/C][/ROW]
[ROW][C]22[/C][C]2927.42[/C][C]2821.85254303072[/C][C]5.02850271576135[/C][C]57.2278024665378[/C][C]0.688811115298779[/C][/ROW]
[ROW][C]23[/C][C]2879.56[/C][C]2844.77469923211[/C][C]5.36990660624033[/C][C]10.9017766116322[/C][C]0.339765278050792[/C][/ROW]
[ROW][C]24[/C][C]3262.02[/C][C]2954.36445619445[/C][C]6.76134451744516[/C][C]166.793722725162[/C][C]1.99474300548986[/C][/ROW]
[ROW][C]25[/C][C]2883.14[/C][C]2982.36799024404[/C][C]6.38787563913507[/C][C]-130.201745727977[/C][C]0.444306846825402[/C][/ROW]
[ROW][C]26[/C][C]2903.2[/C][C]2955.49446712015[/C][C]6.0384249978359[/C][C]-8.93822590265787[/C][C]-0.625153904066007[/C][/ROW]
[ROW][C]27[/C][C]2877.7[/C][C]2945.70036298011[/C][C]5.66307001672155[/C][C]-48.8709490139709[/C][C]-0.280863427009957[/C][/ROW]
[ROW][C]28[/C][C]2874.3[/C][C]2933.50885885172[/C][C]5.19522465624047[/C][C]-37.6619955968902[/C][C]-0.317936117754429[/C][/ROW]
[ROW][C]29[/C][C]3026.66[/C][C]2932.56366038356[/C][C]5.04378828996718[/C][C]101.681471995668[/C][C]-0.11163647374267[/C][/ROW]
[ROW][C]30[/C][C]2979.42[/C][C]2952.57116645528[/C][C]5.37556406685941[/C][C]7.94654829364713[/C][C]0.277136224260959[/C][/ROW]
[ROW][C]31[/C][C]3109.68[/C][C]3004.65564865234[/C][C]6.30470290307621[/C][C]45.0733577313753[/C][C]0.87626220136397[/C][/ROW]
[ROW][C]32[/C][C]2966.76[/C][C]3007.19091736177[/C][C]6.23646838311134[/C][C]-35.5422065360707[/C][C]-0.0713009148787499[/C][/ROW]
[ROW][C]33[/C][C]2961.04[/C][C]3012.28060790262[/C][C]6.21732145401595[/C][C]-49.743148943594[/C][C]-0.0218066220004299[/C][/ROW]
[ROW][C]34[/C][C]3103.84[/C][C]3032.52464703656[/C][C]6.4320542104048[/C][C]52.9066160437796[/C][C]0.267698205739095[/C][/ROW]
[ROW][C]35[/C][C]3359.12[/C][C]3141.40446557162[/C][C]7.77334457606377[/C][C]82.5174220950502[/C][C]1.96201865587221[/C][/ROW]
[ROW][C]36[/C][C]3976.24[/C][C]3345.99731264384[/C][C]9.35025306617607[/C][C]367.635356332385[/C][C]3.79877090079792[/C][/ROW]
[ROW][C]37[/C][C]3049.42[/C][C]3333.82897961333[/C][C]9.41635074311275[/C][C]-254.811952770193[/C][C]-0.42839595827487[/C][/ROW]
[ROW][C]38[/C][C]3089.14[/C][C]3274.28211732186[/C][C]8.87191796126904[/C][C]-94.7862342079443[/C][C]-1.31367895491492[/C][/ROW]
[ROW][C]39[/C][C]3166.26[/C][C]3252.29959741519[/C][C]8.36722591568769[/C][C]-47.4313605568745[/C][C]-0.566983280128905[/C][/ROW]
[ROW][C]40[/C][C]3459.04[/C][C]3321.8074539668[/C][C]9.55100133111093[/C][C]61.4884093320132[/C][C]1.11792828696314[/C][/ROW]
[ROW][C]41[/C][C]3457.32[/C][C]3347.99701636443[/C][C]9.87184015628469[/C][C]88.5052619884118[/C][C]0.30726624736154[/C][/ROW]
[ROW][C]42[/C][C]3292.66[/C][C]3345.34838343425[/C][C]9.64661211330184[/C][C]-36.8009249015344[/C][C]-0.234055786252355[/C][/ROW]
[ROW][C]43[/C][C]3432.86[/C][C]3361.28498437026[/C][C]9.75002562256694[/C][C]63.4972253797602[/C][C]0.118755881007052[/C][/ROW]
[ROW][C]44[/C][C]3388.4[/C][C]3387.54978954603[/C][C]9.9977242338773[/C][C]-20.5461640728437[/C][C]0.314007130489364[/C][/ROW]
[ROW][C]45[/C][C]3312.9[/C][C]3398.62900845032[/C][C]10.0125003794953[/C][C]-87.1390347513367[/C][C]0.0206624871125288[/C][/ROW]
[ROW][C]46[/C][C]3390.04[/C][C]3412.6105451185[/C][C]10.0608402866013[/C][C]-27.7709005796908[/C][C]0.0760920263736206[/C][/ROW]
[ROW][C]47[/C][C]3757.44[/C][C]3518.99408747882[/C][C]11.026558899239[/C][C]111.596977035091[/C][C]1.85262643464074[/C][/ROW]
[ROW][C]48[/C][C]4612.38[/C][C]3730.14133609452[/C][C]12.3221035406035[/C][C]616.656959316532[/C][C]3.87072950803034[/C][/ROW]
[ROW][C]49[/C][C]3613.34[/C][C]3795.51445576687[/C][C]12.4327919809691[/C][C]-253.399695799791[/C][C]1.03705655862781[/C][/ROW]
[ROW][C]50[/C][C]3525.14[/C][C]3767.53344554351[/C][C]12.1440773398968[/C][C]-189.444060226266[/C][C]-0.773145851303354[/C][/ROW]
[ROW][C]51[/C][C]3473.06[/C][C]3714.59634035749[/C][C]11.3323364778593[/C][C]-158.620480757004[/C][C]-1.21785474333287[/C][/ROW]
[ROW][C]52[/C][C]3662.22[/C][C]3684.47097154502[/C][C]10.7056510529168[/C][C]30.0252885775976[/C][C]-0.770848446525712[/C][/ROW]
[ROW][C]53[/C][C]3717.4[/C][C]3668.73771165582[/C][C]10.2921840818603[/C][C]82.1188978804096[/C][C]-0.493797660007479[/C][/ROW]
[ROW][C]54[/C][C]3466.9[/C][C]3627.76086519311[/C][C]9.52118289187554[/C][C]-95.4126011915877[/C][C]-0.965205482235862[/C][/ROW]
[ROW][C]55[/C][C]3443.4[/C][C]3562.70267237851[/C][C]8.47765132282181[/C][C]-23.2454270251754[/C][C]-1.41467673421793[/C][/ROW]
[ROW][C]56[/C][C]3383.16[/C][C]3518.48261887563[/C][C]7.80190016035197[/C][C]-66.9503421824742[/C][C]-1.00552365178622[/C][/ROW]
[ROW][C]57[/C][C]3843.64[/C][C]3637.20705722601[/C][C]9.08781979437387[/C][C]61.703481781395[/C][C]2.12559013669234[/C][/ROW]
[ROW][C]58[/C][C]3692.4[/C][C]3704.45009990908[/C][C]9.67985974912019[/C][C]-88.2738889726009[/C][C]1.11791621538671[/C][/ROW]
[ROW][C]59[/C][C]3558.38[/C][C]3681.85441824135[/C][C]9.41022721412378[/C][C]-80.9895099516086[/C][C]-0.622155649275723[/C][/ROW]
[ROW][C]60[/C][C]3811.02[/C][C]3558.25523402873[/C][C]8.6109568839427[/C][C]428.722819519866[/C][C]-2.57309912669851[/C][/ROW]
[ROW][C]61[/C][C]3470.54[/C][C]3579.85489379538[/C][C]8.66487885041606[/C][C]-126.563928781911[/C][C]0.252042779400757[/C][/ROW]
[ROW][C]62[/C][C]3354.68[/C][C]3562.58992132845[/C][C]8.4885374799148[/C][C]-173.948317492253[/C][C]-0.497133514402728[/C][/ROW]
[ROW][C]63[/C][C]3499.96[/C][C]3581.61201864134[/C][C]8.59606330799252[/C][C]-95.2089510929034[/C][C]0.19917161580204[/C][/ROW]
[ROW][C]64[/C][C]3537.36[/C][C]3560.12373798345[/C][C]8.22560552291314[/C][C]15.6259390180648[/C][C]-0.56563569839928[/C][/ROW]
[ROW][C]65[/C][C]3414.98[/C][C]3488.64613143581[/C][C]7.18792413305177[/C][C]28.109918047532[/C][C]-1.5012363944095[/C][/ROW]
[ROW][C]66[/C][C]3649[/C][C]3542.60699203311[/C][C]7.78659416960209[/C][C]46.3420634902489[/C][C]0.885565287731873[/C][/ROW]
[ROW][C]67[/C][C]3549.72[/C][C]3560.00889582263[/C][C]7.90285642092666[/C][C]-22.7148956493028[/C][C]0.183081461574685[/C][/ROW]
[ROW][C]68[/C][C]3680.78[/C][C]3635.77289123652[/C][C]8.65964816548334[/C][C]-43.2128066947596[/C][C]1.29835754906848[/C][/ROW]
[ROW][C]69[/C][C]3484.64[/C][C]3598.02340286054[/C][C]8.19220699968695[/C][C]-52.7572965430772[/C][C]-0.891204670442932[/C][/ROW]
[ROW][C]70[/C][C]3451.92[/C][C]3572.3129755996[/C][C]7.89290764327012[/C][C]-75.9293535680058[/C][C]-0.652832278125242[/C][/ROW]
[ROW][C]71[/C][C]3831.14[/C][C]3645.63084333122[/C][C]8.37503931004141[/C][C]99.4070063863929[/C][C]1.26268417930231[/C][/ROW]
[ROW][C]72[/C][C]3906.02[/C][C]3614.72257626986[/C][C]8.1461785956706[/C][C]343.157191324263[/C][C]-0.759760537089086[/C][/ROW]
[ROW][C]73[/C][C]3499.54[/C][C]3614.66267730226[/C][C]8.10518527276361[/C][C]-104.281285562277[/C][C]-0.158756858182438[/C][/ROW]
[ROW][C]74[/C][C]3620.62[/C][C]3666.7284712175[/C][C]8.39228355552831[/C][C]-103.689777720645[/C][C]0.844181672666972[/C][/ROW]
[ROW][C]75[/C][C]3473.64[/C][C]3644.33712094987[/C][C]8.12250420669459[/C][C]-130.829441047706[/C][C]-0.585863795185463[/C][/ROW]
[ROW][C]76[/C][C]3494.32[/C][C]3592.73088924069[/C][C]7.50283219872434[/C][C]-21.5641309662383[/C][C]-1.13164374551659[/C][/ROW]
[ROW][C]77[/C][C]3799.66[/C][C]3647.61575766581[/C][C]8.02755150983404[/C][C]91.1133393263404[/C][C]0.898185120120902[/C][/ROW]
[ROW][C]78[/C][C]3476.4[/C][C]3603.24618768391[/C][C]7.44853283695644[/C][C]-59.2393397077459[/C][C]-0.996623638548705[/C][/ROW]
[ROW][C]79[/C][C]3446.86[/C][C]3573.60821165776[/C][C]7.05657075138614[/C][C]-78.6667787865612[/C][C]-0.708379124944555[/C][/ROW]
[ROW][C]80[/C][C]3441.94[/C][C]3542.57673223596[/C][C]6.68247449527648[/C][C]-51.0227500871561[/C][C]-0.730323959868199[/C][/ROW]
[ROW][C]81[/C][C]3514.68[/C][C]3546.59040344117[/C][C]6.65870082447615[/C][C]-28.4197934268916[/C][C]-0.0513320840651294[/C][/ROW]
[ROW][C]82[/C][C]3464.96[/C][C]3556.71577037225[/C][C]6.68595561879857[/C][C]-96.3051127248457[/C][C]0.0668350084834451[/C][/ROW]
[ROW][C]83[/C][C]3579.48[/C][C]3535.37376461442[/C][C]6.49742429159993[/C][C]80.9879709353984[/C][C]-0.541330730484405[/C][/ROW]
[ROW][C]84[/C][C]3944.24[/C][C]3553.79654277187[/C][C]6.56531967112899[/C][C]374.720818914427[/C][C]0.230602833312652[/C][/ROW]
[ROW][C]85[/C][C]3702.42[/C][C]3631.1982210427[/C][C]6.94096203555184[/C][C]-22.1326379389265[/C][C]1.36888410940752[/C][/ROW]
[ROW][C]86[/C][C]3716.28[/C][C]3688.75978517456[/C][C]7.25801261903792[/C][C]-38.8133826994724[/C][C]0.973443694139236[/C][/ROW]
[ROW][C]87[/C][C]3538.36[/C][C]3687.89839415485[/C][C]7.19496768183315[/C][C]-138.978754613273[/C][C]-0.155206571294685[/C][/ROW]
[ROW][C]88[/C][C]3482.58[/C][C]3646.17402609416[/C][C]6.75586398724442[/C][C]-100.28516438868[/C][C]-0.931925698260496[/C][/ROW]
[ROW][C]89[/C][C]3665.5[/C][C]3615.50716912121[/C][C]6.39680091489427[/C][C]98.3796021251941[/C][C]-0.712879209220765[/C][/ROW]
[ROW][C]90[/C][C]3484.5[/C][C]3588.43253518827[/C][C]6.07335279760328[/C][C]-60.5640911921858[/C][C]-0.639032790099266[/C][/ROW]
[ROW][C]91[/C][C]3425.08[/C][C]3559.73474566299[/C][C]5.74882210049311[/C][C]-89.4445499587059[/C][C]-0.665918891768819[/C][/ROW]
[ROW][C]92[/C][C]3421.44[/C][C]3535.31301619703[/C][C]5.48500917282066[/C][C]-74.4982092270346[/C][C]-0.579580538821365[/C][/ROW]
[ROW][C]93[/C][C]3602.34[/C][C]3560.98290731338[/C][C]5.64627792528883[/C][C]14.9258900471446[/C][C]0.388748228730408[/C][/ROW]
[ROW][C]94[/C][C]3593.44[/C][C]3600.10562695833[/C][C]5.8850845297298[/C][C]-50.6232338911639[/C][C]0.64600301700112[/C][/ROW]
[ROW][C]95[/C][C]3478.5[/C][C]3560.1255754498[/C][C]5.59801675264418[/C][C]-21.2721286127429[/C][C]-0.886311773268556[/C][/ROW]
[ROW][C]96[/C][C]4365.26[/C][C]3686.2614886799[/C][C]6.267007757141[/C][C]520.194935736919[/C][C]2.33086547556881[/C][/ROW]
[ROW][C]97[/C][C]3445.2[/C][C]3651.95152928597[/C][C]6.04967309041848[/C][C]-153.333567926421[/C][C]-0.783948739176382[/C][/ROW]
[ROW][C]98[/C][C]3473.48[/C][C]3609.47633506852[/C][C]5.75899429019933[/C][C]-72.3665839604834[/C][C]-0.934337752871104[/C][/ROW]
[ROW][C]99[/C][C]3472.32[/C][C]3597.78935752371[/C][C]5.63645418064414[/C][C]-102.711031066213[/C][C]-0.334545501387434[/C][/ROW]
[ROW][C]100[/C][C]3403.82[/C][C]3565.82475966324[/C][C]5.33831306507101[/C][C]-113.133095330339[/C][C]-0.719196476985106[/C][/ROW]
[ROW][C]101[/C][C]3575.4[/C][C]3533.76329100641[/C][C]5.02242230274698[/C][C]90.2002307421626[/C][C]-0.715153790208139[/C][/ROW]
[ROW][C]102[/C][C]3512.96[/C][C]3537.317904923[/C][C]5.00987151900283[/C][C]-22.4494588112716[/C][C]-0.028108863552876[/C][/ROW]
[ROW][C]103[/C][C]3433.04[/C][C]3533.65406813389[/C][C]4.93768561862153[/C][C]-89.3076021563027[/C][C]-0.166487830107432[/C][/ROW]
[ROW][C]104[/C][C]3495.2[/C][C]3550.27735309067[/C][C]5.02953352306291[/C][C]-70.3543719852092[/C][C]0.224839676094544[/C][/ROW]
[ROW][C]105[/C][C]3478.96[/C][C]3536.57768907802[/C][C]4.89380056926872[/C][C]-33.0655750220341[/C][C]-0.361117407027946[/C][/ROW]
[ROW][C]106[/C][C]3559.28[/C][C]3555.45764659435[/C][C]4.98551807814426[/C][C]-14.5537316740467[/C][C]0.270103891676816[/C][/ROW]
[ROW][C]107[/C][C]3887.1[/C][C]3669.40566759235[/C][C]5.62681045288042[/C][C]74.293390272237[/C][C]2.10660171049546[/C][/ROW]
[ROW][C]108[/C][C]4083.16[/C][C]3649.18256634885[/C][C]5.48758507916516[/C][C]468.022999684324[/C][C]-0.499945644425356[/C][/ROW]
[ROW][C]109[/C][C]3659.52[/C][C]3685.7335266369[/C][C]5.65168127923871[/C][C]-67.0932315148761[/C][C]0.600260908314419[/C][/ROW]
[ROW][C]110[/C][C]3693.48[/C][C]3710.18205014385[/C][C]5.75914767001235[/C][C]-41.3694630091151[/C][C]0.362352534492515[/C][/ROW]
[ROW][C]111[/C][C]3779.52[/C][C]3756.14080874711[/C][C]6.01817089513207[/C][C]-29.1838893432527[/C][C]0.772717729883143[/C][/ROW]
[ROW][C]112[/C][C]3891.62[/C][C]3827.48161178006[/C][C]6.4832048156523[/C][C]-21.0433135678372[/C][C]1.25323839770523[/C][/ROW]
[ROW][C]113[/C][C]3895.86[/C][C]3834.54616815013[/C][C]6.48758705261175[/C][C]60.5564006222939[/C][C]0.0111497449496931[/C][/ROW]
[ROW][C]114[/C][C]3745.04[/C][C]3821.49558010824[/C][C]6.33814331225989[/C][C]-50.9785354137769[/C][C]-0.375096756142522[/C][/ROW]
[ROW][C]115[/C][C]3884.46[/C][C]3867.0602679812[/C][C]6.63190973613377[/C][C]-33.846639527186[/C][C]0.754372893009938[/C][/ROW]
[ROW][C]116[/C][C]3862.98[/C][C]3894.71027945393[/C][C]6.78170619836819[/C][C]-59.2512141433154[/C][C]0.404964906425558[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299140&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299140&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
12669.942669.94000
22778.722704.369755484243.2982394130520223.74827280603190.647820173413504
32648.442689.69404660171.51751759680943-22.5771216644125-0.265169460081158
42631.322668.28352557744-0.322518484738259-11.1492346693359-0.361124139476437
53057.322794.884495279687.91243701354016107.320751972552.12817798296401
62730.662789.977903028667.21607452121146-42.8131250927816-0.223651446999778
72730.622772.437918716276.04633794314354-8.90314680892791-0.442645465409495
82738.72761.425465445425.322510786269480.419478685840408-0.309778616775546
92616.362716.370322363763.35613830280771-30.7515260554086-0.924102936172828
102773.542729.791885742913.7238421639341929.78642472778140.18589404217281
112872.762776.518048847425.2119100863398236.21870412796970.797983604482272
122999.422852.046910537997.5360316705053148.77005957418131.30941575965909
132730.622854.510754753077.92201203732867-115.111530261332-0.126087097027341
142907.222866.480591225068.0105339566301635.68094037422650.0716968091687369
152778.042849.585884287837.0229941804-43.7030134573384-0.408107150829358
162833.942862.640278382177.25661856843064-35.70607929511480.102522400366516
172914.442850.174889941536.5863503467501288.3810642127776-0.349682934890082
182788.862843.674264010376.20041712480794-38.2360433560792-0.238669365734011
192742.82816.687788547885.33399573214404-30.9367425323706-0.615544272712959
202726.522784.024455713634.43188116284639-7.69476281870835-0.711863096985823
212746.442781.182652944264.27117657245048-25.1329354528218-0.137102367421469
222927.422821.852543030725.0285027157613557.22780246653780.688811115298779
232879.562844.774699232115.3699066062403310.90177661163220.339765278050792
243262.022954.364456194456.76134451744516166.7937227251621.99474300548986
252883.142982.367990244046.38787563913507-130.2017457279770.444306846825402
262903.22955.494467120156.0384249978359-8.93822590265787-0.625153904066007
272877.72945.700362980115.66307001672155-48.8709490139709-0.280863427009957
282874.32933.508858851725.19522465624047-37.6619955968902-0.317936117754429
293026.662932.563660383565.04378828996718101.681471995668-0.11163647374267
302979.422952.571166455285.375564066859417.946548293647130.277136224260959
313109.683004.655648652346.3047029030762145.07335773137530.87626220136397
322966.763007.190917361776.23646838311134-35.5422065360707-0.0713009148787499
332961.043012.280607902626.21732145401595-49.743148943594-0.0218066220004299
343103.843032.524647036566.432054210404852.90661604377960.267698205739095
353359.123141.404465571627.7733445760637782.51742209505021.96201865587221
363976.243345.997312643849.35025306617607367.6353563323853.79877090079792
373049.423333.828979613339.41635074311275-254.811952770193-0.42839595827487
383089.143274.282117321868.87191796126904-94.7862342079443-1.31367895491492
393166.263252.299597415198.36722591568769-47.4313605568745-0.566983280128905
403459.043321.80745396689.5510013311109361.48840933201321.11792828696314
413457.323347.997016364439.8718401562846988.50526198841180.30726624736154
423292.663345.348383434259.64661211330184-36.8009249015344-0.234055786252355
433432.863361.284984370269.7500256225669463.49722537976020.118755881007052
443388.43387.549789546039.9977242338773-20.54616407284370.314007130489364
453312.93398.6290084503210.0125003794953-87.13903475133670.0206624871125288
463390.043412.610545118510.0608402866013-27.77090057969080.0760920263736206
473757.443518.9940874788211.026558899239111.5969770350911.85262643464074
484612.383730.1413360945212.3221035406035616.6569593165323.87072950803034
493613.343795.5144557668712.4327919809691-253.3996957997911.03705655862781
503525.143767.5334455435112.1440773398968-189.444060226266-0.773145851303354
513473.063714.5963403574911.3323364778593-158.620480757004-1.21785474333287
523662.223684.4709715450210.705651052916830.0252885775976-0.770848446525712
533717.43668.7377116558210.292184081860382.1188978804096-0.493797660007479
543466.93627.760865193119.52118289187554-95.4126011915877-0.965205482235862
553443.43562.702672378518.47765132282181-23.2454270251754-1.41467673421793
563383.163518.482618875637.80190016035197-66.9503421824742-1.00552365178622
573843.643637.207057226019.0878197943738761.7034817813952.12559013669234
583692.43704.450099909089.67985974912019-88.27388897260091.11791621538671
593558.383681.854418241359.41022721412378-80.9895099516086-0.622155649275723
603811.023558.255234028738.6109568839427428.722819519866-2.57309912669851
613470.543579.854893795388.66487885041606-126.5639287819110.252042779400757
623354.683562.589921328458.4885374799148-173.948317492253-0.497133514402728
633499.963581.612018641348.59606330799252-95.20895109290340.19917161580204
643537.363560.123737983458.2256055229131415.6259390180648-0.56563569839928
653414.983488.646131435817.1879241330517728.109918047532-1.5012363944095
6636493542.606992033117.7865941696020946.34206349024890.885565287731873
673549.723560.008895822637.90285642092666-22.71489564930280.183081461574685
683680.783635.772891236528.65964816548334-43.21280669475961.29835754906848
693484.643598.023402860548.19220699968695-52.7572965430772-0.891204670442932
703451.923572.31297559967.89290764327012-75.9293535680058-0.652832278125242
713831.143645.630843331228.3750393100414199.40700638639291.26268417930231
723906.023614.722576269868.1461785956706343.157191324263-0.759760537089086
733499.543614.662677302268.10518527276361-104.281285562277-0.158756858182438
743620.623666.72847121758.39228355552831-103.6897777206450.844181672666972
753473.643644.337120949878.12250420669459-130.829441047706-0.585863795185463
763494.323592.730889240697.50283219872434-21.5641309662383-1.13164374551659
773799.663647.615757665818.0275515098340491.11333932634040.898185120120902
783476.43603.246187683917.44853283695644-59.2393397077459-0.996623638548705
793446.863573.608211657767.05657075138614-78.6667787865612-0.708379124944555
803441.943542.576732235966.68247449527648-51.0227500871561-0.730323959868199
813514.683546.590403441176.65870082447615-28.4197934268916-0.0513320840651294
823464.963556.715770372256.68595561879857-96.30511272484570.0668350084834451
833579.483535.373764614426.4974242915999380.9879709353984-0.541330730484405
843944.243553.796542771876.56531967112899374.7208189144270.230602833312652
853702.423631.19822104276.94096203555184-22.13263793892651.36888410940752
863716.283688.759785174567.25801261903792-38.81338269947240.973443694139236
873538.363687.898394154857.19496768183315-138.978754613273-0.155206571294685
883482.583646.174026094166.75586398724442-100.28516438868-0.931925698260496
893665.53615.507169121216.3968009148942798.3796021251941-0.712879209220765
903484.53588.432535188276.07335279760328-60.5640911921858-0.639032790099266
913425.083559.734745662995.74882210049311-89.4445499587059-0.665918891768819
923421.443535.313016197035.48500917282066-74.4982092270346-0.579580538821365
933602.343560.982907313385.6462779252888314.92589004714460.388748228730408
943593.443600.105626958335.8850845297298-50.62323389116390.64600301700112
953478.53560.12557544985.59801675264418-21.2721286127429-0.886311773268556
964365.263686.26148867996.267007757141520.1949357369192.33086547556881
973445.23651.951529285976.04967309041848-153.333567926421-0.783948739176382
983473.483609.476335068525.75899429019933-72.3665839604834-0.934337752871104
993472.323597.789357523715.63645418064414-102.711031066213-0.334545501387434
1003403.823565.824759663245.33831306507101-113.133095330339-0.719196476985106
1013575.43533.763291006415.0224223027469890.2002307421626-0.715153790208139
1023512.963537.3179049235.00987151900283-22.4494588112716-0.028108863552876
1033433.043533.654068133894.93768561862153-89.3076021563027-0.166487830107432
1043495.23550.277353090675.02953352306291-70.35437198520920.224839676094544
1053478.963536.577689078024.89380056926872-33.0655750220341-0.361117407027946
1063559.283555.457646594354.98551807814426-14.55373167404670.270103891676816
1073887.13669.405667592355.6268104528804274.2933902722372.10660171049546
1084083.163649.182566348855.48758507916516468.022999684324-0.499945644425356
1093659.523685.73352663695.65168127923871-67.09323151487610.600260908314419
1103693.483710.182050143855.75914767001235-41.36946300911510.362352534492515
1113779.523756.140808747116.01817089513207-29.18388934325270.772717729883143
1123891.623827.481611780066.4832048156523-21.04331356783721.25323839770523
1133895.863834.546168150136.4875870526117560.55640062229390.0111497449496931
1143745.043821.495580108246.33814331225989-50.9785354137769-0.375096756142522
1153884.463867.06026798126.63190973613377-33.8466395271860.754372893009938
1163862.983894.710279453936.78170619836819-59.25121414331540.404964906425558







Structural Time Series Model -- Extrapolation
tObservedLevelSeasonal
13832.011217375753939.60932932207-107.598111946315
23878.679244509243950.01145647106-71.3322119618185
34113.240647769593960.41358362006152.827064149531
44417.853556696313970.81571076905447.037845927255
53921.687979807833981.21783791804-59.5298581102126
63922.408404023483991.61996506704-69.2115610435607
73950.283856730364002.02209221603-51.7382354856752
84008.412865268824012.42421936502-4.01135409620547
94046.999120261214022.8263465140224.1727737471893
103905.975051866584033.22847366301-127.253421796436
113989.593581140614043.63060081201-54.0370196713927
123974.706818248644054.032727961-79.3259097123601

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Extrapolation \tabularnewline
t & Observed & Level & Seasonal \tabularnewline
1 & 3832.01121737575 & 3939.60932932207 & -107.598111946315 \tabularnewline
2 & 3878.67924450924 & 3950.01145647106 & -71.3322119618185 \tabularnewline
3 & 4113.24064776959 & 3960.41358362006 & 152.827064149531 \tabularnewline
4 & 4417.85355669631 & 3970.81571076905 & 447.037845927255 \tabularnewline
5 & 3921.68797980783 & 3981.21783791804 & -59.5298581102126 \tabularnewline
6 & 3922.40840402348 & 3991.61996506704 & -69.2115610435607 \tabularnewline
7 & 3950.28385673036 & 4002.02209221603 & -51.7382354856752 \tabularnewline
8 & 4008.41286526882 & 4012.42421936502 & -4.01135409620547 \tabularnewline
9 & 4046.99912026121 & 4022.82634651402 & 24.1727737471893 \tabularnewline
10 & 3905.97505186658 & 4033.22847366301 & -127.253421796436 \tabularnewline
11 & 3989.59358114061 & 4043.63060081201 & -54.0370196713927 \tabularnewline
12 & 3974.70681824864 & 4054.032727961 & -79.3259097123601 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299140&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]3832.01121737575[/C][C]3939.60932932207[/C][C]-107.598111946315[/C][/ROW]
[ROW][C]2[/C][C]3878.67924450924[/C][C]3950.01145647106[/C][C]-71.3322119618185[/C][/ROW]
[ROW][C]3[/C][C]4113.24064776959[/C][C]3960.41358362006[/C][C]152.827064149531[/C][/ROW]
[ROW][C]4[/C][C]4417.85355669631[/C][C]3970.81571076905[/C][C]447.037845927255[/C][/ROW]
[ROW][C]5[/C][C]3921.68797980783[/C][C]3981.21783791804[/C][C]-59.5298581102126[/C][/ROW]
[ROW][C]6[/C][C]3922.40840402348[/C][C]3991.61996506704[/C][C]-69.2115610435607[/C][/ROW]
[ROW][C]7[/C][C]3950.28385673036[/C][C]4002.02209221603[/C][C]-51.7382354856752[/C][/ROW]
[ROW][C]8[/C][C]4008.41286526882[/C][C]4012.42421936502[/C][C]-4.01135409620547[/C][/ROW]
[ROW][C]9[/C][C]4046.99912026121[/C][C]4022.82634651402[/C][C]24.1727737471893[/C][/ROW]
[ROW][C]10[/C][C]3905.97505186658[/C][C]4033.22847366301[/C][C]-127.253421796436[/C][/ROW]
[ROW][C]11[/C][C]3989.59358114061[/C][C]4043.63060081201[/C][C]-54.0370196713927[/C][/ROW]
[ROW][C]12[/C][C]3974.70681824864[/C][C]4054.032727961[/C][C]-79.3259097123601[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299140&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299140&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
13832.011217375753939.60932932207-107.598111946315
23878.679244509243950.01145647106-71.3322119618185
34113.240647769593960.41358362006152.827064149531
44417.853556696313970.81571076905447.037845927255
53921.687979807833981.21783791804-59.5298581102126
63922.408404023483991.61996506704-69.2115610435607
73950.283856730364002.02209221603-51.7382354856752
84008.412865268824012.42421936502-4.01135409620547
94046.999120261214022.8263465140224.1727737471893
103905.975051866584033.22847366301-127.253421796436
113989.593581140614043.63060081201-54.0370196713927
123974.706818248644054.032727961-79.3259097123601



Parameters (Session):
par1 = 12 ; par2 = periodic ; par3 = 0 ; par5 = 1 ; par7 = 1 ; par8 = FALSE ;
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')