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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 computationFri, 23 Dec 2016 08:45:00 +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/23/t1482479182kcy2eul010oqxq3.htm/, Retrieved Fri, 01 Nov 2024 03:46:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302756, Retrieved Fri, 01 Nov 2024 03:46:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact129
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Structural Time Series Models] [] [2016-12-23 07:45:00] [0b5bf205c55efce49027552c8371b570] [Current]
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Dataseries X:
3996.1
3984.2
4049
4032.8
4074.1
4114.4
4091.4
4166.6
4152.5
4112.7
4145.9
4174.4
4183.6
4172.5
4280.3
4327.4
4251.2
4256.5
4285.7
4257.4
4231.9
4274.3
4248.3
4310.5
4301.9
4336.5
4385.1
4310.4
4378.8
4338
4304.2
4266.9
4230.1
4230.6
4353.2
4371.2
4393.2
4250.2
4129.5
4124.9
4177.1
4156.9
4111.9
4167.4
4190.7
4165
4209.8
4250
4224.8
4322.7
4311.7
4373.8
4358.9
4441.2
4538.9
4444.8
4537.8
4490.2
4517.3
4561.9
4567
4588.3
4656.8
4677.7
4684.2
4752.8
4738.9
4785.6
4742.7
4711.4
4758.1
4800.5
4877.3
4885
4941.4
5009.4
5017.5
4984.1
4903.9
4968.6
4937.3
4987.1
5001.9
5094.6
5177.8
5206.1
5253.1
5284.3
5266.8
5225.1
5272.8
5529.8
5535.2
5715.9
5672.2
5475.7
5435.3
5458.5
5373.3
5395.3
5515
5410.9
5400.2
5424.2
5388.5
5482.1
5506.9
5377.2
5353.5
5401.1
5438.1
5510.2
5499
5606.5
5644
5440.7




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 time4 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302756&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]4 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=302756&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302756&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 time4 seconds
R ServerBig Analytics Cloud Computing Center







Structural Time Series Model -- Interpolation
tObservedLevelSlopeSeasonalStand. Residuals
13996.13996.1000
23984.23985.01059124444-0.618788285154742-0.616157182208652-0.105485173236787
340494046.18205247288-0.118759620223486-0.1962525431809740.972350174415284
44032.84033.65947388085-0.199966896766723-0.252628854115625-0.195280680055313
54074.14072.283135696550.0754111261164073-0.08140519884972920.61099243554484
64114.44112.352460435930.3844410771556860.09342039232610440.6291673895914
74091.44092.388324473930.2144281852108150.00522126687726708-0.319992681042011
84166.64162.864712771750.8448487229714670.3070220086209051.10448909157919
94152.54152.77277527540.7400920766149760.260496091405482-0.171857198545721
104112.74114.504504825470.3432856029829890.0962452370118734-0.612737422857474
114145.94144.249581391970.6594688777302330.2187105721070070.461669479730786
124174.44172.713732212430.9742894779140070.3332083494217690.436433596185952
134183.64182.484050938930.6694440899646470.6882867800832140.167104609441718
144172.54173.157535404920.351611479550886-0.310663046542206-0.13291790392044
154280.34275.369949673471.5720219867993-0.009647424527600761.5950700390643
164327.44324.985293330872.129738090505660.0827649851425110.75231073636477
174251.24254.761318287311.25326797838363-0.051356264182487-1.13261803712941
184256.54256.525644609831.25973101511007-0.05042204125979120.00799749584735755
194285.74284.412200626611.6103319355136-0.002393012429050210.416549650454789
204257.44258.770612848881.23768413703405-0.0508756149456269-0.426197966444214
214231.94233.290874632430.859175737974034-0.0977323244697032-0.417713780031446
224274.34272.477421316451.42051325604722-0.03150095158733120.599054580093838
234248.34249.550144553111.05260740447921-0.0729378236453646-0.380446162799069
244310.54307.717187793581.941355363246990.02274794524040540.892193508613842
254301.94303.801479846251.95805246132174-1.61947425367813-0.100909499129425
264336.54334.74779382072.766068584757290.6079854742339910.410298055476265
274385.14382.257217537533.523382847867760.6856003015148990.698108804323919
284310.44313.287556624252.304410615539920.608723291522096-1.13091698059634
294378.84375.254617559323.32979679375130.6691091858105350.93053263201173
3043384339.264689196152.639070320402820.630068497828255-0.613111029165435
314304.24305.365552718831.983756716577810.594443865790396-0.569611530974606
324266.94268.226734955161.26820781933240.556998540127781-0.609768561506717
334230.14231.411755835050.5586492030400760.521228407345194-0.593444452088545
344230.64230.167191581850.5244586062299390.519566886171079-0.0280935223494687
354353.24346.982227294752.76625555000280.6246503926822561.81141880676876
364371.24369.603156283523.155048754744330.6422397207481720.309211301055975
374393.24395.629405358833.38140316863724-3.52365783195450.380458780238474
384250.24257.42917230732-0.459189319332584-1.32591304390911-2.05760428508523
394129.54136.73398254369-2.93669158717133-1.46154830064334-1.871305504132
404124.94126.70647096457-3.08247653718039-1.46599937817569-0.110340355133033
414177.14176.01982991749-1.99269880754192-1.434961993456050.815200457345171
424156.94159.06180199943-2.3075877798856-1.4436245044291-0.232803309949418
434111.94115.35335864017-3.18834762487457-1.46707628788777-0.643946963495885
444167.44166.24325213522-2.02583690397284-1.437102974689730.84101492440337
454190.74190.84575070942-1.44773151436712-1.422664914402360.414064409149417
4641654167.48484957337-1.92794243975872-1.43428561021068-0.340701560706298
474209.84209.12348189798-0.964709162326632-1.411693553232050.677282116016817
4842504249.41378253021-0.044885026841939-1.390777892061410.641272048012429
494224.84215.13053020403-0.6172921597699311.3013707939303-0.559355543517827
504322.74318.31756154252.18153947172156-0.0789022817674321.53074885924714
514311.74312.183538695711.99066799875134-0.0853858435430821-0.129217092369789
524373.84371.136092369273.2962960271089-0.06357708678057560.884994866488834
534358.94359.67532190812.95595602036969-0.0688350349664777-0.22925155187904
544441.24437.651804501684.69688350639026-0.04278851414570431.1653422906649
554538.94534.501196144166.8479940121467-0.0115453891557531.43134246783007
564444.84449.249216697674.68608229902185-0.042036527601499-1.43040993223722
574537.84533.986102540376.57512408949331-0.01616074198846261.24317672103617
584490.24492.5291193335.43596070811877-0.0313179958676869-0.745875703620048
594517.34516.441833959895.87625783583812-0.02562651482849450.286899351187281
604561.94560.10694641996.78082930479525-0.01426526395413210.586729681713522
6145674566.848626988376.780023893410920.153235131513512-0.000632669897751662
624588.34587.596942335267.155027756803290.09103816390468160.207900510908194
634656.84653.850282203778.593127383712150.1245489972311430.917485298553706
644677.74676.881795568358.944051503924620.1279846176146520.224116709066942
654684.24684.152370818218.903244196079420.127620786192483-0.025974543593429
664752.84749.9414812011110.29499206638260.1396462169477510.882897714439931
674738.94739.743937389859.792048216490340.135421305642707-0.318039134162092
684785.64783.8193850699210.63597530365690.1423151781149110.532045229111566
694742.74744.933696916869.413481598086330.132603281246609-0.768494278003152
704711.44713.239368380768.395962261220890.124741277931074-0.637898201878816
714758.14756.312075518939.256487111165940.1312085201527120.538081207696796
724800.54798.7763286048610.08255257754960.1372475286681640.515267122253619
734877.34870.9479300459911.49720122052423.401680114984940.996249053936083
7448854885.1708289113611.5699946431129-0.2918595051809870.0408295597562266
754941.44939.625157581812.6467446216444-0.273382812713360.665411727395764
765009.45007.0489924699214.0206968004768-0.2651620511222430.84981865045174
775017.55017.916186781413.9414613481695-0.265583642638183-0.0489219143769746
784984.14986.5358052771112.8006799482621-0.271463286419262-0.703080789823936
794903.94908.5196833152710.5109068640171-0.282945083761032-1.40880876574541
804968.64966.6053692801811.71233233938-0.2770824491897950.73799148636553
814937.34939.4381810585110.7290028935457-0.281752230858592-0.603093613160383
824987.14985.6819011710511.6285226392545-0.2775947748167860.550886270057556
835001.95001.9552985507611.7463289074847-0.2770648410959180.0720473201386796
845094.65091.1699235263613.7136713420452-0.2684512317014131.20159613206678
855177.85167.5882639428615.22270343700817.233195836812381.00108064168804
865206.15205.6089567084715.8281952730708-0.5312082477666840.343109376498633
875253.15252.1543708426616.6124235822553-0.5207442533398710.476476921308785
885284.35284.0879115981217.0032555235798-0.5192764067545080.237623695245334
895266.85268.860431391916.1803181228228-0.521929846143454-0.499871551357138
905225.15228.3332474230514.7310544147578-0.526449661531735-0.879471315835648
915272.85271.9456614390415.4698346546964-0.5242073577391160.447911545862391
925529.85519.2415843318421.4049701242409-0.5066703952138223.59526335242547
935535.25535.9320368767221.2841728318691-0.507017884558752-0.0731138629808078
945715.95709.1448788270425.1799417068307-0.4961073091699142.35611537598963
955672.25675.5073902154523.6706407886714-0.500222683476452-0.912131556247816
965475.75486.3711093546618.2060758368066-0.514729646843697-3.30013761774246
975435.35436.9149473532616.5268599428191.59894214372295-1.07622186407647
985458.55458.3972169748816.6578073314231-0.1210763195999810.0748461627395399
995373.35378.0763786608614.1599204470466-0.14809536272154-1.50404608660315
1005395.35395.3016220619214.2388232368708-0.1479060745433430.047533981286555
10155155510.3329037254916.8345086339804-0.1428305759533941.56296157439048
1025410.95416.3370787729713.9788812733391-0.148216765258664-1.71860062056995
1035400.25401.7144254296313.2415870472167-0.149570266912267-0.44350862300413
1045424.25423.9213406227513.4728018297471-0.1491569682186030.139019431240541
1055388.55390.8712423449112.2724628492344-0.151246250024014-0.721394526437596
1065482.15478.6451825794614.221277964239-0.1479432102229981.17073448662832
1075506.95506.4015119304614.570775397614-0.1473663880777580.209874616116542
1085377.25383.8939728941911.0298805140096-0.153057146966318-2.12552366036794
1095353.55355.7745865825410.040766416605-0.414810996360083-0.620923909661056
1105401.15399.3891610724610.92423476973140.1852493580637810.50852386031654
1115438.15436.6517558278111.60579697592220.1914410830998860.408442150257846
1125510.25507.1940536618213.13016865930290.1938034066378020.91384487196088
11354995499.7867430589112.59884174937150.19318274485734-0.318441435479437
1145606.55602.027095252114.91858819328950.1957846241245541.38991864277627
11556445642.5803770274315.58213383320540.1965089022315810.39747185467195
1165440.75450.4211453502710.20350881866420.190791763347795-3.22106410633251

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Interpolation \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 3996.1 & 3996.1 & 0 & 0 & 0 \tabularnewline
2 & 3984.2 & 3985.01059124444 & -0.618788285154742 & -0.616157182208652 & -0.105485173236787 \tabularnewline
3 & 4049 & 4046.18205247288 & -0.118759620223486 & -0.196252543180974 & 0.972350174415284 \tabularnewline
4 & 4032.8 & 4033.65947388085 & -0.199966896766723 & -0.252628854115625 & -0.195280680055313 \tabularnewline
5 & 4074.1 & 4072.28313569655 & 0.0754111261164073 & -0.0814051988497292 & 0.61099243554484 \tabularnewline
6 & 4114.4 & 4112.35246043593 & 0.384441077155686 & 0.0934203923261044 & 0.6291673895914 \tabularnewline
7 & 4091.4 & 4092.38832447393 & 0.214428185210815 & 0.00522126687726708 & -0.319992681042011 \tabularnewline
8 & 4166.6 & 4162.86471277175 & 0.844848722971467 & 0.307022008620905 & 1.10448909157919 \tabularnewline
9 & 4152.5 & 4152.7727752754 & 0.740092076614976 & 0.260496091405482 & -0.171857198545721 \tabularnewline
10 & 4112.7 & 4114.50450482547 & 0.343285602982989 & 0.0962452370118734 & -0.612737422857474 \tabularnewline
11 & 4145.9 & 4144.24958139197 & 0.659468877730233 & 0.218710572107007 & 0.461669479730786 \tabularnewline
12 & 4174.4 & 4172.71373221243 & 0.974289477914007 & 0.333208349421769 & 0.436433596185952 \tabularnewline
13 & 4183.6 & 4182.48405093893 & 0.669444089964647 & 0.688286780083214 & 0.167104609441718 \tabularnewline
14 & 4172.5 & 4173.15753540492 & 0.351611479550886 & -0.310663046542206 & -0.13291790392044 \tabularnewline
15 & 4280.3 & 4275.36994967347 & 1.5720219867993 & -0.00964742452760076 & 1.5950700390643 \tabularnewline
16 & 4327.4 & 4324.98529333087 & 2.12973809050566 & 0.082764985142511 & 0.75231073636477 \tabularnewline
17 & 4251.2 & 4254.76131828731 & 1.25326797838363 & -0.051356264182487 & -1.13261803712941 \tabularnewline
18 & 4256.5 & 4256.52564460983 & 1.25973101511007 & -0.0504220412597912 & 0.00799749584735755 \tabularnewline
19 & 4285.7 & 4284.41220062661 & 1.6103319355136 & -0.00239301242905021 & 0.416549650454789 \tabularnewline
20 & 4257.4 & 4258.77061284888 & 1.23768413703405 & -0.0508756149456269 & -0.426197966444214 \tabularnewline
21 & 4231.9 & 4233.29087463243 & 0.859175737974034 & -0.0977323244697032 & -0.417713780031446 \tabularnewline
22 & 4274.3 & 4272.47742131645 & 1.42051325604722 & -0.0315009515873312 & 0.599054580093838 \tabularnewline
23 & 4248.3 & 4249.55014455311 & 1.05260740447921 & -0.0729378236453646 & -0.380446162799069 \tabularnewline
24 & 4310.5 & 4307.71718779358 & 1.94135536324699 & 0.0227479452404054 & 0.892193508613842 \tabularnewline
25 & 4301.9 & 4303.80147984625 & 1.95805246132174 & -1.61947425367813 & -0.100909499129425 \tabularnewline
26 & 4336.5 & 4334.7477938207 & 2.76606858475729 & 0.607985474233991 & 0.410298055476265 \tabularnewline
27 & 4385.1 & 4382.25721753753 & 3.52338284786776 & 0.685600301514899 & 0.698108804323919 \tabularnewline
28 & 4310.4 & 4313.28755662425 & 2.30441061553992 & 0.608723291522096 & -1.13091698059634 \tabularnewline
29 & 4378.8 & 4375.25461755932 & 3.3297967937513 & 0.669109185810535 & 0.93053263201173 \tabularnewline
30 & 4338 & 4339.26468919615 & 2.63907032040282 & 0.630068497828255 & -0.613111029165435 \tabularnewline
31 & 4304.2 & 4305.36555271883 & 1.98375671657781 & 0.594443865790396 & -0.569611530974606 \tabularnewline
32 & 4266.9 & 4268.22673495516 & 1.2682078193324 & 0.556998540127781 & -0.609768561506717 \tabularnewline
33 & 4230.1 & 4231.41175583505 & 0.558649203040076 & 0.521228407345194 & -0.593444452088545 \tabularnewline
34 & 4230.6 & 4230.16719158185 & 0.524458606229939 & 0.519566886171079 & -0.0280935223494687 \tabularnewline
35 & 4353.2 & 4346.98222729475 & 2.7662555500028 & 0.624650392682256 & 1.81141880676876 \tabularnewline
36 & 4371.2 & 4369.60315628352 & 3.15504875474433 & 0.642239720748172 & 0.309211301055975 \tabularnewline
37 & 4393.2 & 4395.62940535883 & 3.38140316863724 & -3.5236578319545 & 0.380458780238474 \tabularnewline
38 & 4250.2 & 4257.42917230732 & -0.459189319332584 & -1.32591304390911 & -2.05760428508523 \tabularnewline
39 & 4129.5 & 4136.73398254369 & -2.93669158717133 & -1.46154830064334 & -1.871305504132 \tabularnewline
40 & 4124.9 & 4126.70647096457 & -3.08247653718039 & -1.46599937817569 & -0.110340355133033 \tabularnewline
41 & 4177.1 & 4176.01982991749 & -1.99269880754192 & -1.43496199345605 & 0.815200457345171 \tabularnewline
42 & 4156.9 & 4159.06180199943 & -2.3075877798856 & -1.4436245044291 & -0.232803309949418 \tabularnewline
43 & 4111.9 & 4115.35335864017 & -3.18834762487457 & -1.46707628788777 & -0.643946963495885 \tabularnewline
44 & 4167.4 & 4166.24325213522 & -2.02583690397284 & -1.43710297468973 & 0.84101492440337 \tabularnewline
45 & 4190.7 & 4190.84575070942 & -1.44773151436712 & -1.42266491440236 & 0.414064409149417 \tabularnewline
46 & 4165 & 4167.48484957337 & -1.92794243975872 & -1.43428561021068 & -0.340701560706298 \tabularnewline
47 & 4209.8 & 4209.12348189798 & -0.964709162326632 & -1.41169355323205 & 0.677282116016817 \tabularnewline
48 & 4250 & 4249.41378253021 & -0.044885026841939 & -1.39077789206141 & 0.641272048012429 \tabularnewline
49 & 4224.8 & 4215.13053020403 & -0.61729215976993 & 11.3013707939303 & -0.559355543517827 \tabularnewline
50 & 4322.7 & 4318.3175615425 & 2.18153947172156 & -0.078902281767432 & 1.53074885924714 \tabularnewline
51 & 4311.7 & 4312.18353869571 & 1.99066799875134 & -0.0853858435430821 & -0.129217092369789 \tabularnewline
52 & 4373.8 & 4371.13609236927 & 3.2962960271089 & -0.0635770867805756 & 0.884994866488834 \tabularnewline
53 & 4358.9 & 4359.6753219081 & 2.95595602036969 & -0.0688350349664777 & -0.22925155187904 \tabularnewline
54 & 4441.2 & 4437.65180450168 & 4.69688350639026 & -0.0427885141457043 & 1.1653422906649 \tabularnewline
55 & 4538.9 & 4534.50119614416 & 6.8479940121467 & -0.011545389155753 & 1.43134246783007 \tabularnewline
56 & 4444.8 & 4449.24921669767 & 4.68608229902185 & -0.042036527601499 & -1.43040993223722 \tabularnewline
57 & 4537.8 & 4533.98610254037 & 6.57512408949331 & -0.0161607419884626 & 1.24317672103617 \tabularnewline
58 & 4490.2 & 4492.529119333 & 5.43596070811877 & -0.0313179958676869 & -0.745875703620048 \tabularnewline
59 & 4517.3 & 4516.44183395989 & 5.87625783583812 & -0.0256265148284945 & 0.286899351187281 \tabularnewline
60 & 4561.9 & 4560.1069464199 & 6.78082930479525 & -0.0142652639541321 & 0.586729681713522 \tabularnewline
61 & 4567 & 4566.84862698837 & 6.78002389341092 & 0.153235131513512 & -0.000632669897751662 \tabularnewline
62 & 4588.3 & 4587.59694233526 & 7.15502775680329 & 0.0910381639046816 & 0.207900510908194 \tabularnewline
63 & 4656.8 & 4653.85028220377 & 8.59312738371215 & 0.124548997231143 & 0.917485298553706 \tabularnewline
64 & 4677.7 & 4676.88179556835 & 8.94405150392462 & 0.127984617614652 & 0.224116709066942 \tabularnewline
65 & 4684.2 & 4684.15237081821 & 8.90324419607942 & 0.127620786192483 & -0.025974543593429 \tabularnewline
66 & 4752.8 & 4749.94148120111 & 10.2949920663826 & 0.139646216947751 & 0.882897714439931 \tabularnewline
67 & 4738.9 & 4739.74393738985 & 9.79204821649034 & 0.135421305642707 & -0.318039134162092 \tabularnewline
68 & 4785.6 & 4783.81938506992 & 10.6359753036569 & 0.142315178114911 & 0.532045229111566 \tabularnewline
69 & 4742.7 & 4744.93369691686 & 9.41348159808633 & 0.132603281246609 & -0.768494278003152 \tabularnewline
70 & 4711.4 & 4713.23936838076 & 8.39596226122089 & 0.124741277931074 & -0.637898201878816 \tabularnewline
71 & 4758.1 & 4756.31207551893 & 9.25648711116594 & 0.131208520152712 & 0.538081207696796 \tabularnewline
72 & 4800.5 & 4798.77632860486 & 10.0825525775496 & 0.137247528668164 & 0.515267122253619 \tabularnewline
73 & 4877.3 & 4870.94793004599 & 11.4972012205242 & 3.40168011498494 & 0.996249053936083 \tabularnewline
74 & 4885 & 4885.17082891136 & 11.5699946431129 & -0.291859505180987 & 0.0408295597562266 \tabularnewline
75 & 4941.4 & 4939.6251575818 & 12.6467446216444 & -0.27338281271336 & 0.665411727395764 \tabularnewline
76 & 5009.4 & 5007.04899246992 & 14.0206968004768 & -0.265162051122243 & 0.84981865045174 \tabularnewline
77 & 5017.5 & 5017.9161867814 & 13.9414613481695 & -0.265583642638183 & -0.0489219143769746 \tabularnewline
78 & 4984.1 & 4986.53580527711 & 12.8006799482621 & -0.271463286419262 & -0.703080789823936 \tabularnewline
79 & 4903.9 & 4908.51968331527 & 10.5109068640171 & -0.282945083761032 & -1.40880876574541 \tabularnewline
80 & 4968.6 & 4966.60536928018 & 11.71233233938 & -0.277082449189795 & 0.73799148636553 \tabularnewline
81 & 4937.3 & 4939.43818105851 & 10.7290028935457 & -0.281752230858592 & -0.603093613160383 \tabularnewline
82 & 4987.1 & 4985.68190117105 & 11.6285226392545 & -0.277594774816786 & 0.550886270057556 \tabularnewline
83 & 5001.9 & 5001.95529855076 & 11.7463289074847 & -0.277064841095918 & 0.0720473201386796 \tabularnewline
84 & 5094.6 & 5091.16992352636 & 13.7136713420452 & -0.268451231701413 & 1.20159613206678 \tabularnewline
85 & 5177.8 & 5167.58826394286 & 15.2227034370081 & 7.23319583681238 & 1.00108064168804 \tabularnewline
86 & 5206.1 & 5205.60895670847 & 15.8281952730708 & -0.531208247766684 & 0.343109376498633 \tabularnewline
87 & 5253.1 & 5252.15437084266 & 16.6124235822553 & -0.520744253339871 & 0.476476921308785 \tabularnewline
88 & 5284.3 & 5284.08791159812 & 17.0032555235798 & -0.519276406754508 & 0.237623695245334 \tabularnewline
89 & 5266.8 & 5268.8604313919 & 16.1803181228228 & -0.521929846143454 & -0.499871551357138 \tabularnewline
90 & 5225.1 & 5228.33324742305 & 14.7310544147578 & -0.526449661531735 & -0.879471315835648 \tabularnewline
91 & 5272.8 & 5271.94566143904 & 15.4698346546964 & -0.524207357739116 & 0.447911545862391 \tabularnewline
92 & 5529.8 & 5519.24158433184 & 21.4049701242409 & -0.506670395213822 & 3.59526335242547 \tabularnewline
93 & 5535.2 & 5535.93203687672 & 21.2841728318691 & -0.507017884558752 & -0.0731138629808078 \tabularnewline
94 & 5715.9 & 5709.14487882704 & 25.1799417068307 & -0.496107309169914 & 2.35611537598963 \tabularnewline
95 & 5672.2 & 5675.50739021545 & 23.6706407886714 & -0.500222683476452 & -0.912131556247816 \tabularnewline
96 & 5475.7 & 5486.37110935466 & 18.2060758368066 & -0.514729646843697 & -3.30013761774246 \tabularnewline
97 & 5435.3 & 5436.91494735326 & 16.526859942819 & 1.59894214372295 & -1.07622186407647 \tabularnewline
98 & 5458.5 & 5458.39721697488 & 16.6578073314231 & -0.121076319599981 & 0.0748461627395399 \tabularnewline
99 & 5373.3 & 5378.07637866086 & 14.1599204470466 & -0.14809536272154 & -1.50404608660315 \tabularnewline
100 & 5395.3 & 5395.30162206192 & 14.2388232368708 & -0.147906074543343 & 0.047533981286555 \tabularnewline
101 & 5515 & 5510.33290372549 & 16.8345086339804 & -0.142830575953394 & 1.56296157439048 \tabularnewline
102 & 5410.9 & 5416.33707877297 & 13.9788812733391 & -0.148216765258664 & -1.71860062056995 \tabularnewline
103 & 5400.2 & 5401.71442542963 & 13.2415870472167 & -0.149570266912267 & -0.44350862300413 \tabularnewline
104 & 5424.2 & 5423.92134062275 & 13.4728018297471 & -0.149156968218603 & 0.139019431240541 \tabularnewline
105 & 5388.5 & 5390.87124234491 & 12.2724628492344 & -0.151246250024014 & -0.721394526437596 \tabularnewline
106 & 5482.1 & 5478.64518257946 & 14.221277964239 & -0.147943210222998 & 1.17073448662832 \tabularnewline
107 & 5506.9 & 5506.40151193046 & 14.570775397614 & -0.147366388077758 & 0.209874616116542 \tabularnewline
108 & 5377.2 & 5383.89397289419 & 11.0298805140096 & -0.153057146966318 & -2.12552366036794 \tabularnewline
109 & 5353.5 & 5355.77458658254 & 10.040766416605 & -0.414810996360083 & -0.620923909661056 \tabularnewline
110 & 5401.1 & 5399.38916107246 & 10.9242347697314 & 0.185249358063781 & 0.50852386031654 \tabularnewline
111 & 5438.1 & 5436.65175582781 & 11.6057969759222 & 0.191441083099886 & 0.408442150257846 \tabularnewline
112 & 5510.2 & 5507.19405366182 & 13.1301686593029 & 0.193803406637802 & 0.91384487196088 \tabularnewline
113 & 5499 & 5499.78674305891 & 12.5988417493715 & 0.19318274485734 & -0.318441435479437 \tabularnewline
114 & 5606.5 & 5602.0270952521 & 14.9185881932895 & 0.195784624124554 & 1.38991864277627 \tabularnewline
115 & 5644 & 5642.58037702743 & 15.5821338332054 & 0.196508902231581 & 0.39747185467195 \tabularnewline
116 & 5440.7 & 5450.42114535027 & 10.2035088186642 & 0.190791763347795 & -3.22106410633251 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302756&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]3996.1[/C][C]3996.1[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]3984.2[/C][C]3985.01059124444[/C][C]-0.618788285154742[/C][C]-0.616157182208652[/C][C]-0.105485173236787[/C][/ROW]
[ROW][C]3[/C][C]4049[/C][C]4046.18205247288[/C][C]-0.118759620223486[/C][C]-0.196252543180974[/C][C]0.972350174415284[/C][/ROW]
[ROW][C]4[/C][C]4032.8[/C][C]4033.65947388085[/C][C]-0.199966896766723[/C][C]-0.252628854115625[/C][C]-0.195280680055313[/C][/ROW]
[ROW][C]5[/C][C]4074.1[/C][C]4072.28313569655[/C][C]0.0754111261164073[/C][C]-0.0814051988497292[/C][C]0.61099243554484[/C][/ROW]
[ROW][C]6[/C][C]4114.4[/C][C]4112.35246043593[/C][C]0.384441077155686[/C][C]0.0934203923261044[/C][C]0.6291673895914[/C][/ROW]
[ROW][C]7[/C][C]4091.4[/C][C]4092.38832447393[/C][C]0.214428185210815[/C][C]0.00522126687726708[/C][C]-0.319992681042011[/C][/ROW]
[ROW][C]8[/C][C]4166.6[/C][C]4162.86471277175[/C][C]0.844848722971467[/C][C]0.307022008620905[/C][C]1.10448909157919[/C][/ROW]
[ROW][C]9[/C][C]4152.5[/C][C]4152.7727752754[/C][C]0.740092076614976[/C][C]0.260496091405482[/C][C]-0.171857198545721[/C][/ROW]
[ROW][C]10[/C][C]4112.7[/C][C]4114.50450482547[/C][C]0.343285602982989[/C][C]0.0962452370118734[/C][C]-0.612737422857474[/C][/ROW]
[ROW][C]11[/C][C]4145.9[/C][C]4144.24958139197[/C][C]0.659468877730233[/C][C]0.218710572107007[/C][C]0.461669479730786[/C][/ROW]
[ROW][C]12[/C][C]4174.4[/C][C]4172.71373221243[/C][C]0.974289477914007[/C][C]0.333208349421769[/C][C]0.436433596185952[/C][/ROW]
[ROW][C]13[/C][C]4183.6[/C][C]4182.48405093893[/C][C]0.669444089964647[/C][C]0.688286780083214[/C][C]0.167104609441718[/C][/ROW]
[ROW][C]14[/C][C]4172.5[/C][C]4173.15753540492[/C][C]0.351611479550886[/C][C]-0.310663046542206[/C][C]-0.13291790392044[/C][/ROW]
[ROW][C]15[/C][C]4280.3[/C][C]4275.36994967347[/C][C]1.5720219867993[/C][C]-0.00964742452760076[/C][C]1.5950700390643[/C][/ROW]
[ROW][C]16[/C][C]4327.4[/C][C]4324.98529333087[/C][C]2.12973809050566[/C][C]0.082764985142511[/C][C]0.75231073636477[/C][/ROW]
[ROW][C]17[/C][C]4251.2[/C][C]4254.76131828731[/C][C]1.25326797838363[/C][C]-0.051356264182487[/C][C]-1.13261803712941[/C][/ROW]
[ROW][C]18[/C][C]4256.5[/C][C]4256.52564460983[/C][C]1.25973101511007[/C][C]-0.0504220412597912[/C][C]0.00799749584735755[/C][/ROW]
[ROW][C]19[/C][C]4285.7[/C][C]4284.41220062661[/C][C]1.6103319355136[/C][C]-0.00239301242905021[/C][C]0.416549650454789[/C][/ROW]
[ROW][C]20[/C][C]4257.4[/C][C]4258.77061284888[/C][C]1.23768413703405[/C][C]-0.0508756149456269[/C][C]-0.426197966444214[/C][/ROW]
[ROW][C]21[/C][C]4231.9[/C][C]4233.29087463243[/C][C]0.859175737974034[/C][C]-0.0977323244697032[/C][C]-0.417713780031446[/C][/ROW]
[ROW][C]22[/C][C]4274.3[/C][C]4272.47742131645[/C][C]1.42051325604722[/C][C]-0.0315009515873312[/C][C]0.599054580093838[/C][/ROW]
[ROW][C]23[/C][C]4248.3[/C][C]4249.55014455311[/C][C]1.05260740447921[/C][C]-0.0729378236453646[/C][C]-0.380446162799069[/C][/ROW]
[ROW][C]24[/C][C]4310.5[/C][C]4307.71718779358[/C][C]1.94135536324699[/C][C]0.0227479452404054[/C][C]0.892193508613842[/C][/ROW]
[ROW][C]25[/C][C]4301.9[/C][C]4303.80147984625[/C][C]1.95805246132174[/C][C]-1.61947425367813[/C][C]-0.100909499129425[/C][/ROW]
[ROW][C]26[/C][C]4336.5[/C][C]4334.7477938207[/C][C]2.76606858475729[/C][C]0.607985474233991[/C][C]0.410298055476265[/C][/ROW]
[ROW][C]27[/C][C]4385.1[/C][C]4382.25721753753[/C][C]3.52338284786776[/C][C]0.685600301514899[/C][C]0.698108804323919[/C][/ROW]
[ROW][C]28[/C][C]4310.4[/C][C]4313.28755662425[/C][C]2.30441061553992[/C][C]0.608723291522096[/C][C]-1.13091698059634[/C][/ROW]
[ROW][C]29[/C][C]4378.8[/C][C]4375.25461755932[/C][C]3.3297967937513[/C][C]0.669109185810535[/C][C]0.93053263201173[/C][/ROW]
[ROW][C]30[/C][C]4338[/C][C]4339.26468919615[/C][C]2.63907032040282[/C][C]0.630068497828255[/C][C]-0.613111029165435[/C][/ROW]
[ROW][C]31[/C][C]4304.2[/C][C]4305.36555271883[/C][C]1.98375671657781[/C][C]0.594443865790396[/C][C]-0.569611530974606[/C][/ROW]
[ROW][C]32[/C][C]4266.9[/C][C]4268.22673495516[/C][C]1.2682078193324[/C][C]0.556998540127781[/C][C]-0.609768561506717[/C][/ROW]
[ROW][C]33[/C][C]4230.1[/C][C]4231.41175583505[/C][C]0.558649203040076[/C][C]0.521228407345194[/C][C]-0.593444452088545[/C][/ROW]
[ROW][C]34[/C][C]4230.6[/C][C]4230.16719158185[/C][C]0.524458606229939[/C][C]0.519566886171079[/C][C]-0.0280935223494687[/C][/ROW]
[ROW][C]35[/C][C]4353.2[/C][C]4346.98222729475[/C][C]2.7662555500028[/C][C]0.624650392682256[/C][C]1.81141880676876[/C][/ROW]
[ROW][C]36[/C][C]4371.2[/C][C]4369.60315628352[/C][C]3.15504875474433[/C][C]0.642239720748172[/C][C]0.309211301055975[/C][/ROW]
[ROW][C]37[/C][C]4393.2[/C][C]4395.62940535883[/C][C]3.38140316863724[/C][C]-3.5236578319545[/C][C]0.380458780238474[/C][/ROW]
[ROW][C]38[/C][C]4250.2[/C][C]4257.42917230732[/C][C]-0.459189319332584[/C][C]-1.32591304390911[/C][C]-2.05760428508523[/C][/ROW]
[ROW][C]39[/C][C]4129.5[/C][C]4136.73398254369[/C][C]-2.93669158717133[/C][C]-1.46154830064334[/C][C]-1.871305504132[/C][/ROW]
[ROW][C]40[/C][C]4124.9[/C][C]4126.70647096457[/C][C]-3.08247653718039[/C][C]-1.46599937817569[/C][C]-0.110340355133033[/C][/ROW]
[ROW][C]41[/C][C]4177.1[/C][C]4176.01982991749[/C][C]-1.99269880754192[/C][C]-1.43496199345605[/C][C]0.815200457345171[/C][/ROW]
[ROW][C]42[/C][C]4156.9[/C][C]4159.06180199943[/C][C]-2.3075877798856[/C][C]-1.4436245044291[/C][C]-0.232803309949418[/C][/ROW]
[ROW][C]43[/C][C]4111.9[/C][C]4115.35335864017[/C][C]-3.18834762487457[/C][C]-1.46707628788777[/C][C]-0.643946963495885[/C][/ROW]
[ROW][C]44[/C][C]4167.4[/C][C]4166.24325213522[/C][C]-2.02583690397284[/C][C]-1.43710297468973[/C][C]0.84101492440337[/C][/ROW]
[ROW][C]45[/C][C]4190.7[/C][C]4190.84575070942[/C][C]-1.44773151436712[/C][C]-1.42266491440236[/C][C]0.414064409149417[/C][/ROW]
[ROW][C]46[/C][C]4165[/C][C]4167.48484957337[/C][C]-1.92794243975872[/C][C]-1.43428561021068[/C][C]-0.340701560706298[/C][/ROW]
[ROW][C]47[/C][C]4209.8[/C][C]4209.12348189798[/C][C]-0.964709162326632[/C][C]-1.41169355323205[/C][C]0.677282116016817[/C][/ROW]
[ROW][C]48[/C][C]4250[/C][C]4249.41378253021[/C][C]-0.044885026841939[/C][C]-1.39077789206141[/C][C]0.641272048012429[/C][/ROW]
[ROW][C]49[/C][C]4224.8[/C][C]4215.13053020403[/C][C]-0.61729215976993[/C][C]11.3013707939303[/C][C]-0.559355543517827[/C][/ROW]
[ROW][C]50[/C][C]4322.7[/C][C]4318.3175615425[/C][C]2.18153947172156[/C][C]-0.078902281767432[/C][C]1.53074885924714[/C][/ROW]
[ROW][C]51[/C][C]4311.7[/C][C]4312.18353869571[/C][C]1.99066799875134[/C][C]-0.0853858435430821[/C][C]-0.129217092369789[/C][/ROW]
[ROW][C]52[/C][C]4373.8[/C][C]4371.13609236927[/C][C]3.2962960271089[/C][C]-0.0635770867805756[/C][C]0.884994866488834[/C][/ROW]
[ROW][C]53[/C][C]4358.9[/C][C]4359.6753219081[/C][C]2.95595602036969[/C][C]-0.0688350349664777[/C][C]-0.22925155187904[/C][/ROW]
[ROW][C]54[/C][C]4441.2[/C][C]4437.65180450168[/C][C]4.69688350639026[/C][C]-0.0427885141457043[/C][C]1.1653422906649[/C][/ROW]
[ROW][C]55[/C][C]4538.9[/C][C]4534.50119614416[/C][C]6.8479940121467[/C][C]-0.011545389155753[/C][C]1.43134246783007[/C][/ROW]
[ROW][C]56[/C][C]4444.8[/C][C]4449.24921669767[/C][C]4.68608229902185[/C][C]-0.042036527601499[/C][C]-1.43040993223722[/C][/ROW]
[ROW][C]57[/C][C]4537.8[/C][C]4533.98610254037[/C][C]6.57512408949331[/C][C]-0.0161607419884626[/C][C]1.24317672103617[/C][/ROW]
[ROW][C]58[/C][C]4490.2[/C][C]4492.529119333[/C][C]5.43596070811877[/C][C]-0.0313179958676869[/C][C]-0.745875703620048[/C][/ROW]
[ROW][C]59[/C][C]4517.3[/C][C]4516.44183395989[/C][C]5.87625783583812[/C][C]-0.0256265148284945[/C][C]0.286899351187281[/C][/ROW]
[ROW][C]60[/C][C]4561.9[/C][C]4560.1069464199[/C][C]6.78082930479525[/C][C]-0.0142652639541321[/C][C]0.586729681713522[/C][/ROW]
[ROW][C]61[/C][C]4567[/C][C]4566.84862698837[/C][C]6.78002389341092[/C][C]0.153235131513512[/C][C]-0.000632669897751662[/C][/ROW]
[ROW][C]62[/C][C]4588.3[/C][C]4587.59694233526[/C][C]7.15502775680329[/C][C]0.0910381639046816[/C][C]0.207900510908194[/C][/ROW]
[ROW][C]63[/C][C]4656.8[/C][C]4653.85028220377[/C][C]8.59312738371215[/C][C]0.124548997231143[/C][C]0.917485298553706[/C][/ROW]
[ROW][C]64[/C][C]4677.7[/C][C]4676.88179556835[/C][C]8.94405150392462[/C][C]0.127984617614652[/C][C]0.224116709066942[/C][/ROW]
[ROW][C]65[/C][C]4684.2[/C][C]4684.15237081821[/C][C]8.90324419607942[/C][C]0.127620786192483[/C][C]-0.025974543593429[/C][/ROW]
[ROW][C]66[/C][C]4752.8[/C][C]4749.94148120111[/C][C]10.2949920663826[/C][C]0.139646216947751[/C][C]0.882897714439931[/C][/ROW]
[ROW][C]67[/C][C]4738.9[/C][C]4739.74393738985[/C][C]9.79204821649034[/C][C]0.135421305642707[/C][C]-0.318039134162092[/C][/ROW]
[ROW][C]68[/C][C]4785.6[/C][C]4783.81938506992[/C][C]10.6359753036569[/C][C]0.142315178114911[/C][C]0.532045229111566[/C][/ROW]
[ROW][C]69[/C][C]4742.7[/C][C]4744.93369691686[/C][C]9.41348159808633[/C][C]0.132603281246609[/C][C]-0.768494278003152[/C][/ROW]
[ROW][C]70[/C][C]4711.4[/C][C]4713.23936838076[/C][C]8.39596226122089[/C][C]0.124741277931074[/C][C]-0.637898201878816[/C][/ROW]
[ROW][C]71[/C][C]4758.1[/C][C]4756.31207551893[/C][C]9.25648711116594[/C][C]0.131208520152712[/C][C]0.538081207696796[/C][/ROW]
[ROW][C]72[/C][C]4800.5[/C][C]4798.77632860486[/C][C]10.0825525775496[/C][C]0.137247528668164[/C][C]0.515267122253619[/C][/ROW]
[ROW][C]73[/C][C]4877.3[/C][C]4870.94793004599[/C][C]11.4972012205242[/C][C]3.40168011498494[/C][C]0.996249053936083[/C][/ROW]
[ROW][C]74[/C][C]4885[/C][C]4885.17082891136[/C][C]11.5699946431129[/C][C]-0.291859505180987[/C][C]0.0408295597562266[/C][/ROW]
[ROW][C]75[/C][C]4941.4[/C][C]4939.6251575818[/C][C]12.6467446216444[/C][C]-0.27338281271336[/C][C]0.665411727395764[/C][/ROW]
[ROW][C]76[/C][C]5009.4[/C][C]5007.04899246992[/C][C]14.0206968004768[/C][C]-0.265162051122243[/C][C]0.84981865045174[/C][/ROW]
[ROW][C]77[/C][C]5017.5[/C][C]5017.9161867814[/C][C]13.9414613481695[/C][C]-0.265583642638183[/C][C]-0.0489219143769746[/C][/ROW]
[ROW][C]78[/C][C]4984.1[/C][C]4986.53580527711[/C][C]12.8006799482621[/C][C]-0.271463286419262[/C][C]-0.703080789823936[/C][/ROW]
[ROW][C]79[/C][C]4903.9[/C][C]4908.51968331527[/C][C]10.5109068640171[/C][C]-0.282945083761032[/C][C]-1.40880876574541[/C][/ROW]
[ROW][C]80[/C][C]4968.6[/C][C]4966.60536928018[/C][C]11.71233233938[/C][C]-0.277082449189795[/C][C]0.73799148636553[/C][/ROW]
[ROW][C]81[/C][C]4937.3[/C][C]4939.43818105851[/C][C]10.7290028935457[/C][C]-0.281752230858592[/C][C]-0.603093613160383[/C][/ROW]
[ROW][C]82[/C][C]4987.1[/C][C]4985.68190117105[/C][C]11.6285226392545[/C][C]-0.277594774816786[/C][C]0.550886270057556[/C][/ROW]
[ROW][C]83[/C][C]5001.9[/C][C]5001.95529855076[/C][C]11.7463289074847[/C][C]-0.277064841095918[/C][C]0.0720473201386796[/C][/ROW]
[ROW][C]84[/C][C]5094.6[/C][C]5091.16992352636[/C][C]13.7136713420452[/C][C]-0.268451231701413[/C][C]1.20159613206678[/C][/ROW]
[ROW][C]85[/C][C]5177.8[/C][C]5167.58826394286[/C][C]15.2227034370081[/C][C]7.23319583681238[/C][C]1.00108064168804[/C][/ROW]
[ROW][C]86[/C][C]5206.1[/C][C]5205.60895670847[/C][C]15.8281952730708[/C][C]-0.531208247766684[/C][C]0.343109376498633[/C][/ROW]
[ROW][C]87[/C][C]5253.1[/C][C]5252.15437084266[/C][C]16.6124235822553[/C][C]-0.520744253339871[/C][C]0.476476921308785[/C][/ROW]
[ROW][C]88[/C][C]5284.3[/C][C]5284.08791159812[/C][C]17.0032555235798[/C][C]-0.519276406754508[/C][C]0.237623695245334[/C][/ROW]
[ROW][C]89[/C][C]5266.8[/C][C]5268.8604313919[/C][C]16.1803181228228[/C][C]-0.521929846143454[/C][C]-0.499871551357138[/C][/ROW]
[ROW][C]90[/C][C]5225.1[/C][C]5228.33324742305[/C][C]14.7310544147578[/C][C]-0.526449661531735[/C][C]-0.879471315835648[/C][/ROW]
[ROW][C]91[/C][C]5272.8[/C][C]5271.94566143904[/C][C]15.4698346546964[/C][C]-0.524207357739116[/C][C]0.447911545862391[/C][/ROW]
[ROW][C]92[/C][C]5529.8[/C][C]5519.24158433184[/C][C]21.4049701242409[/C][C]-0.506670395213822[/C][C]3.59526335242547[/C][/ROW]
[ROW][C]93[/C][C]5535.2[/C][C]5535.93203687672[/C][C]21.2841728318691[/C][C]-0.507017884558752[/C][C]-0.0731138629808078[/C][/ROW]
[ROW][C]94[/C][C]5715.9[/C][C]5709.14487882704[/C][C]25.1799417068307[/C][C]-0.496107309169914[/C][C]2.35611537598963[/C][/ROW]
[ROW][C]95[/C][C]5672.2[/C][C]5675.50739021545[/C][C]23.6706407886714[/C][C]-0.500222683476452[/C][C]-0.912131556247816[/C][/ROW]
[ROW][C]96[/C][C]5475.7[/C][C]5486.37110935466[/C][C]18.2060758368066[/C][C]-0.514729646843697[/C][C]-3.30013761774246[/C][/ROW]
[ROW][C]97[/C][C]5435.3[/C][C]5436.91494735326[/C][C]16.526859942819[/C][C]1.59894214372295[/C][C]-1.07622186407647[/C][/ROW]
[ROW][C]98[/C][C]5458.5[/C][C]5458.39721697488[/C][C]16.6578073314231[/C][C]-0.121076319599981[/C][C]0.0748461627395399[/C][/ROW]
[ROW][C]99[/C][C]5373.3[/C][C]5378.07637866086[/C][C]14.1599204470466[/C][C]-0.14809536272154[/C][C]-1.50404608660315[/C][/ROW]
[ROW][C]100[/C][C]5395.3[/C][C]5395.30162206192[/C][C]14.2388232368708[/C][C]-0.147906074543343[/C][C]0.047533981286555[/C][/ROW]
[ROW][C]101[/C][C]5515[/C][C]5510.33290372549[/C][C]16.8345086339804[/C][C]-0.142830575953394[/C][C]1.56296157439048[/C][/ROW]
[ROW][C]102[/C][C]5410.9[/C][C]5416.33707877297[/C][C]13.9788812733391[/C][C]-0.148216765258664[/C][C]-1.71860062056995[/C][/ROW]
[ROW][C]103[/C][C]5400.2[/C][C]5401.71442542963[/C][C]13.2415870472167[/C][C]-0.149570266912267[/C][C]-0.44350862300413[/C][/ROW]
[ROW][C]104[/C][C]5424.2[/C][C]5423.92134062275[/C][C]13.4728018297471[/C][C]-0.149156968218603[/C][C]0.139019431240541[/C][/ROW]
[ROW][C]105[/C][C]5388.5[/C][C]5390.87124234491[/C][C]12.2724628492344[/C][C]-0.151246250024014[/C][C]-0.721394526437596[/C][/ROW]
[ROW][C]106[/C][C]5482.1[/C][C]5478.64518257946[/C][C]14.221277964239[/C][C]-0.147943210222998[/C][C]1.17073448662832[/C][/ROW]
[ROW][C]107[/C][C]5506.9[/C][C]5506.40151193046[/C][C]14.570775397614[/C][C]-0.147366388077758[/C][C]0.209874616116542[/C][/ROW]
[ROW][C]108[/C][C]5377.2[/C][C]5383.89397289419[/C][C]11.0298805140096[/C][C]-0.153057146966318[/C][C]-2.12552366036794[/C][/ROW]
[ROW][C]109[/C][C]5353.5[/C][C]5355.77458658254[/C][C]10.040766416605[/C][C]-0.414810996360083[/C][C]-0.620923909661056[/C][/ROW]
[ROW][C]110[/C][C]5401.1[/C][C]5399.38916107246[/C][C]10.9242347697314[/C][C]0.185249358063781[/C][C]0.50852386031654[/C][/ROW]
[ROW][C]111[/C][C]5438.1[/C][C]5436.65175582781[/C][C]11.6057969759222[/C][C]0.191441083099886[/C][C]0.408442150257846[/C][/ROW]
[ROW][C]112[/C][C]5510.2[/C][C]5507.19405366182[/C][C]13.1301686593029[/C][C]0.193803406637802[/C][C]0.91384487196088[/C][/ROW]
[ROW][C]113[/C][C]5499[/C][C]5499.78674305891[/C][C]12.5988417493715[/C][C]0.19318274485734[/C][C]-0.318441435479437[/C][/ROW]
[ROW][C]114[/C][C]5606.5[/C][C]5602.0270952521[/C][C]14.9185881932895[/C][C]0.195784624124554[/C][C]1.38991864277627[/C][/ROW]
[ROW][C]115[/C][C]5644[/C][C]5642.58037702743[/C][C]15.5821338332054[/C][C]0.196508902231581[/C][C]0.39747185467195[/C][/ROW]
[ROW][C]116[/C][C]5440.7[/C][C]5450.42114535027[/C][C]10.2035088186642[/C][C]0.190791763347795[/C][C]-3.22106410633251[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302756&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302756&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
13996.13996.1000
23984.23985.01059124444-0.618788285154742-0.616157182208652-0.105485173236787
340494046.18205247288-0.118759620223486-0.1962525431809740.972350174415284
44032.84033.65947388085-0.199966896766723-0.252628854115625-0.195280680055313
54074.14072.283135696550.0754111261164073-0.08140519884972920.61099243554484
64114.44112.352460435930.3844410771556860.09342039232610440.6291673895914
74091.44092.388324473930.2144281852108150.00522126687726708-0.319992681042011
84166.64162.864712771750.8448487229714670.3070220086209051.10448909157919
94152.54152.77277527540.7400920766149760.260496091405482-0.171857198545721
104112.74114.504504825470.3432856029829890.0962452370118734-0.612737422857474
114145.94144.249581391970.6594688777302330.2187105721070070.461669479730786
124174.44172.713732212430.9742894779140070.3332083494217690.436433596185952
134183.64182.484050938930.6694440899646470.6882867800832140.167104609441718
144172.54173.157535404920.351611479550886-0.310663046542206-0.13291790392044
154280.34275.369949673471.5720219867993-0.009647424527600761.5950700390643
164327.44324.985293330872.129738090505660.0827649851425110.75231073636477
174251.24254.761318287311.25326797838363-0.051356264182487-1.13261803712941
184256.54256.525644609831.25973101511007-0.05042204125979120.00799749584735755
194285.74284.412200626611.6103319355136-0.002393012429050210.416549650454789
204257.44258.770612848881.23768413703405-0.0508756149456269-0.426197966444214
214231.94233.290874632430.859175737974034-0.0977323244697032-0.417713780031446
224274.34272.477421316451.42051325604722-0.03150095158733120.599054580093838
234248.34249.550144553111.05260740447921-0.0729378236453646-0.380446162799069
244310.54307.717187793581.941355363246990.02274794524040540.892193508613842
254301.94303.801479846251.95805246132174-1.61947425367813-0.100909499129425
264336.54334.74779382072.766068584757290.6079854742339910.410298055476265
274385.14382.257217537533.523382847867760.6856003015148990.698108804323919
284310.44313.287556624252.304410615539920.608723291522096-1.13091698059634
294378.84375.254617559323.32979679375130.6691091858105350.93053263201173
3043384339.264689196152.639070320402820.630068497828255-0.613111029165435
314304.24305.365552718831.983756716577810.594443865790396-0.569611530974606
324266.94268.226734955161.26820781933240.556998540127781-0.609768561506717
334230.14231.411755835050.5586492030400760.521228407345194-0.593444452088545
344230.64230.167191581850.5244586062299390.519566886171079-0.0280935223494687
354353.24346.982227294752.76625555000280.6246503926822561.81141880676876
364371.24369.603156283523.155048754744330.6422397207481720.309211301055975
374393.24395.629405358833.38140316863724-3.52365783195450.380458780238474
384250.24257.42917230732-0.459189319332584-1.32591304390911-2.05760428508523
394129.54136.73398254369-2.93669158717133-1.46154830064334-1.871305504132
404124.94126.70647096457-3.08247653718039-1.46599937817569-0.110340355133033
414177.14176.01982991749-1.99269880754192-1.434961993456050.815200457345171
424156.94159.06180199943-2.3075877798856-1.4436245044291-0.232803309949418
434111.94115.35335864017-3.18834762487457-1.46707628788777-0.643946963495885
444167.44166.24325213522-2.02583690397284-1.437102974689730.84101492440337
454190.74190.84575070942-1.44773151436712-1.422664914402360.414064409149417
4641654167.48484957337-1.92794243975872-1.43428561021068-0.340701560706298
474209.84209.12348189798-0.964709162326632-1.411693553232050.677282116016817
4842504249.41378253021-0.044885026841939-1.390777892061410.641272048012429
494224.84215.13053020403-0.6172921597699311.3013707939303-0.559355543517827
504322.74318.31756154252.18153947172156-0.0789022817674321.53074885924714
514311.74312.183538695711.99066799875134-0.0853858435430821-0.129217092369789
524373.84371.136092369273.2962960271089-0.06357708678057560.884994866488834
534358.94359.67532190812.95595602036969-0.0688350349664777-0.22925155187904
544441.24437.651804501684.69688350639026-0.04278851414570431.1653422906649
554538.94534.501196144166.8479940121467-0.0115453891557531.43134246783007
564444.84449.249216697674.68608229902185-0.042036527601499-1.43040993223722
574537.84533.986102540376.57512408949331-0.01616074198846261.24317672103617
584490.24492.5291193335.43596070811877-0.0313179958676869-0.745875703620048
594517.34516.441833959895.87625783583812-0.02562651482849450.286899351187281
604561.94560.10694641996.78082930479525-0.01426526395413210.586729681713522
6145674566.848626988376.780023893410920.153235131513512-0.000632669897751662
624588.34587.596942335267.155027756803290.09103816390468160.207900510908194
634656.84653.850282203778.593127383712150.1245489972311430.917485298553706
644677.74676.881795568358.944051503924620.1279846176146520.224116709066942
654684.24684.152370818218.903244196079420.127620786192483-0.025974543593429
664752.84749.9414812011110.29499206638260.1396462169477510.882897714439931
674738.94739.743937389859.792048216490340.135421305642707-0.318039134162092
684785.64783.8193850699210.63597530365690.1423151781149110.532045229111566
694742.74744.933696916869.413481598086330.132603281246609-0.768494278003152
704711.44713.239368380768.395962261220890.124741277931074-0.637898201878816
714758.14756.312075518939.256487111165940.1312085201527120.538081207696796
724800.54798.7763286048610.08255257754960.1372475286681640.515267122253619
734877.34870.9479300459911.49720122052423.401680114984940.996249053936083
7448854885.1708289113611.5699946431129-0.2918595051809870.0408295597562266
754941.44939.625157581812.6467446216444-0.273382812713360.665411727395764
765009.45007.0489924699214.0206968004768-0.2651620511222430.84981865045174
775017.55017.916186781413.9414613481695-0.265583642638183-0.0489219143769746
784984.14986.5358052771112.8006799482621-0.271463286419262-0.703080789823936
794903.94908.5196833152710.5109068640171-0.282945083761032-1.40880876574541
804968.64966.6053692801811.71233233938-0.2770824491897950.73799148636553
814937.34939.4381810585110.7290028935457-0.281752230858592-0.603093613160383
824987.14985.6819011710511.6285226392545-0.2775947748167860.550886270057556
835001.95001.9552985507611.7463289074847-0.2770648410959180.0720473201386796
845094.65091.1699235263613.7136713420452-0.2684512317014131.20159613206678
855177.85167.5882639428615.22270343700817.233195836812381.00108064168804
865206.15205.6089567084715.8281952730708-0.5312082477666840.343109376498633
875253.15252.1543708426616.6124235822553-0.5207442533398710.476476921308785
885284.35284.0879115981217.0032555235798-0.5192764067545080.237623695245334
895266.85268.860431391916.1803181228228-0.521929846143454-0.499871551357138
905225.15228.3332474230514.7310544147578-0.526449661531735-0.879471315835648
915272.85271.9456614390415.4698346546964-0.5242073577391160.447911545862391
925529.85519.2415843318421.4049701242409-0.5066703952138223.59526335242547
935535.25535.9320368767221.2841728318691-0.507017884558752-0.0731138629808078
945715.95709.1448788270425.1799417068307-0.4961073091699142.35611537598963
955672.25675.5073902154523.6706407886714-0.500222683476452-0.912131556247816
965475.75486.3711093546618.2060758368066-0.514729646843697-3.30013761774246
975435.35436.9149473532616.5268599428191.59894214372295-1.07622186407647
985458.55458.3972169748816.6578073314231-0.1210763195999810.0748461627395399
995373.35378.0763786608614.1599204470466-0.14809536272154-1.50404608660315
1005395.35395.3016220619214.2388232368708-0.1479060745433430.047533981286555
10155155510.3329037254916.8345086339804-0.1428305759533941.56296157439048
1025410.95416.3370787729713.9788812733391-0.148216765258664-1.71860062056995
1035400.25401.7144254296313.2415870472167-0.149570266912267-0.44350862300413
1045424.25423.9213406227513.4728018297471-0.1491569682186030.139019431240541
1055388.55390.8712423449112.2724628492344-0.151246250024014-0.721394526437596
1065482.15478.6451825794614.221277964239-0.1479432102229981.17073448662832
1075506.95506.4015119304614.570775397614-0.1473663880777580.209874616116542
1085377.25383.8939728941911.0298805140096-0.153057146966318-2.12552366036794
1095353.55355.7745865825410.040766416605-0.414810996360083-0.620923909661056
1105401.15399.3891610724610.92423476973140.1852493580637810.50852386031654
1115438.15436.6517558278111.60579697592220.1914410830998860.408442150257846
1125510.25507.1940536618213.13016865930290.1938034066378020.91384487196088
11354995499.7867430589112.59884174937150.19318274485734-0.318441435479437
1145606.55602.027095252114.91858819328950.1957846241245541.38991864277627
11556445642.5803770274315.58213383320540.1965089022315810.39747185467195
1165440.75450.4211453502710.20350881866420.190791763347795-3.22106410633251







Structural Time Series Model -- Extrapolation
tObservedLevelSeasonal
15428.553078978165442.15322508728-13.60014610912
25399.198543429935403.08424635131-3.88570292137871
35372.750638825425364.015267615348.73537121007686
45319.92047913185324.94628887938-5.02580974757548
55278.737551331425285.87731014341-7.13975881198891
65235.950720443485246.80833140745-10.8576109639627
75205.469855960935207.73935267148-2.26949671055025
85176.904959690625168.670373935518.2345857551086
95143.63603320785129.6013951995514.0346380082526
105099.55307750455090.532416463589.02066104091645
115050.086091843635051.46343772762-1.3773458839842
125016.525074125865012.394458991654.13061513420586

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Extrapolation \tabularnewline
t & Observed & Level & Seasonal \tabularnewline
1 & 5428.55307897816 & 5442.15322508728 & -13.60014610912 \tabularnewline
2 & 5399.19854342993 & 5403.08424635131 & -3.88570292137871 \tabularnewline
3 & 5372.75063882542 & 5364.01526761534 & 8.73537121007686 \tabularnewline
4 & 5319.9204791318 & 5324.94628887938 & -5.02580974757548 \tabularnewline
5 & 5278.73755133142 & 5285.87731014341 & -7.13975881198891 \tabularnewline
6 & 5235.95072044348 & 5246.80833140745 & -10.8576109639627 \tabularnewline
7 & 5205.46985596093 & 5207.73935267148 & -2.26949671055025 \tabularnewline
8 & 5176.90495969062 & 5168.67037393551 & 8.2345857551086 \tabularnewline
9 & 5143.6360332078 & 5129.60139519955 & 14.0346380082526 \tabularnewline
10 & 5099.5530775045 & 5090.53241646358 & 9.02066104091645 \tabularnewline
11 & 5050.08609184363 & 5051.46343772762 & -1.3773458839842 \tabularnewline
12 & 5016.52507412586 & 5012.39445899165 & 4.13061513420586 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302756&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]5428.55307897816[/C][C]5442.15322508728[/C][C]-13.60014610912[/C][/ROW]
[ROW][C]2[/C][C]5399.19854342993[/C][C]5403.08424635131[/C][C]-3.88570292137871[/C][/ROW]
[ROW][C]3[/C][C]5372.75063882542[/C][C]5364.01526761534[/C][C]8.73537121007686[/C][/ROW]
[ROW][C]4[/C][C]5319.9204791318[/C][C]5324.94628887938[/C][C]-5.02580974757548[/C][/ROW]
[ROW][C]5[/C][C]5278.73755133142[/C][C]5285.87731014341[/C][C]-7.13975881198891[/C][/ROW]
[ROW][C]6[/C][C]5235.95072044348[/C][C]5246.80833140745[/C][C]-10.8576109639627[/C][/ROW]
[ROW][C]7[/C][C]5205.46985596093[/C][C]5207.73935267148[/C][C]-2.26949671055025[/C][/ROW]
[ROW][C]8[/C][C]5176.90495969062[/C][C]5168.67037393551[/C][C]8.2345857551086[/C][/ROW]
[ROW][C]9[/C][C]5143.6360332078[/C][C]5129.60139519955[/C][C]14.0346380082526[/C][/ROW]
[ROW][C]10[/C][C]5099.5530775045[/C][C]5090.53241646358[/C][C]9.02066104091645[/C][/ROW]
[ROW][C]11[/C][C]5050.08609184363[/C][C]5051.46343772762[/C][C]-1.3773458839842[/C][/ROW]
[ROW][C]12[/C][C]5016.52507412586[/C][C]5012.39445899165[/C][C]4.13061513420586[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302756&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302756&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
15428.553078978165442.15322508728-13.60014610912
25399.198543429935403.08424635131-3.88570292137871
35372.750638825425364.015267615348.73537121007686
45319.92047913185324.94628887938-5.02580974757548
55278.737551331425285.87731014341-7.13975881198891
65235.950720443485246.80833140745-10.8576109639627
75205.469855960935207.73935267148-2.26949671055025
85176.904959690625168.670373935518.2345857551086
95143.63603320785129.6013951995514.0346380082526
105099.55307750455090.532416463589.02066104091645
115050.086091843635051.46343772762-1.3773458839842
125016.525074125865012.394458991654.13061513420586



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')