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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 computationWed, 07 Dec 2016 16:07:56 +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/07/t1481123314cdg0pd2aizf056s.htm/, Retrieved Tue, 07 May 2024 12:35:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298188, Retrieved Tue, 07 May 2024 12:35:36 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact70
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Structural Time Series Models] [Paper N2163] [2016-12-07 15:07:56] [1e2703d0f11438bcd65480dae45a3781] [Current]
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Dataseries X:
3875
3755
4670
4335
4945
4600
4395
4345
4390
4490
4395
4690
4590
4630
5375
4655
4975
4810
4445
4660
4215
4825
4250
3945
4390
4315
4835
4835
4970
4690
4700
4855
4610
4900
4250
4105
4740
4565
5155
5320
5430
4690
4540
4575
4660
4850
4200
4360
4655
4585
5315
5115
5100
5735
5260
5050
5165
5190
4720
5275
4605
4825
5595
5160
5320
5540
4970
5445
5305
5145
4895
4555
4980
4930
5810
5210
5450
5510
5010
5495
5125
5190
4565
4255
4875
4650
5295
5045
5430
5325
4920
5445
4895
5175
4545
4220
4595
4360
4750
4985
5140
4995
5150
5240
4875
5170
4715
4370
5160
4930
5600
5385
5425
5375
5365




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time5 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 time5 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298188&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]5 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=298188&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298188&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 time5 seconds
R ServerBig Analytics Cloud Computing Center







Structural Time Series Model -- Interpolation
tObservedLevelSlopeSeasonalStand. Residuals
138753875000
237553819.06444131369-2.54689135563457-43.7276932861133-0.457255806692532
346704211.671873429125.5209463783593356.1834558611932.69436379945182
443354323.601778261130.5279822728339-16.37348501639610.6989795614056
549454592.5374387557640.3968106046809265.0320628736322.11397964025451
646004648.9846846815340.886709424785-55.16683655452310.14691343366562
743954561.3070545373937.6625298193098-115.975673853129-1.18826676936251
843454458.8243795573534.4676379542809-58.6871074338999-1.29870751932354
943904410.9810627357332.65983192689711.4390232506234-0.763065605390626
1044904432.354100561132.415322848342362.0913444945915-0.104611755328755
1143954422.2456600696831.5007431221942-10.5012868849873-0.394015117206595
1246904525.5243794867733.0342594749988136.2175935341710.664918394034674
1345904648.6407833656729.6531972945702-96.24714094905510.945777535103339
1446304796.1837804196930.3262246828926-210.3737522243151.09472552970129
1553754964.7425231926234.3730577907151365.0621633676231.16044222522539
1646554950.9757791181132.7401051540658-280.210544614787-0.409608815405487
1749754875.0498550110829.4223922864567137.277645510226-0.962178467693239
1848104841.9786459103827.8318326117792-9.74140986628501-0.567930041778181
1944454714.6321169318924.5030555914561-213.424452775317-1.42735293577913
2046604685.2178879387323.4761766889242-5.53853498457322-0.498313672091422
2142154507.9018477341919.9106084584796-219.395201253462-1.85877040760365
2248254571.3965524227820.6392607361525237.6276632322470.403573547764655
2342504497.9892968454719.2566538460591-213.469065971803-0.870585002135194
2439454265.5505248784816.7634726694494-227.760311003838-2.33519323761066
2543904331.3573413490216.756415471871140.19280109777820.466090110047585
2643154436.0890431523717.5310112530421-153.2170543707630.81257233660119
2748354455.0415887133517.5585247530214379.4664594208010.0125930378665814
2848354688.7601926005522.827146152246672.7432334209681.89954372658524
2949704772.289079278424.3310825802202176.7895646100060.541197174362687
3046904736.7266535235422.9577613477502-25.6717561556342-0.542808000500836
3147004783.3413898615823.4450569788933-91.77766824141420.216704225306899
3248554789.9432948702523.13216237853671.1118937797258-0.155129221806541
3346104810.7955216619423.093595009367-199.97256700427-0.0210446495884632
3449004731.3460007953921.5285800079281205.737659264523-0.946878855607596
3542504580.6300724054919.2595319005699-268.259686748138-1.59037067655188
3641054488.3399680864218.0814578253585-342.846968252426-1.03168705948357
3747404579.5985845133418.7129992077229133.7384832902710.67931491822186
3845654673.5117613290119.603419805374-135.5625217463610.690067573905558
3951554786.6795106292521.1682717164723335.4476867061120.842855678599011
4053204998.1328337894224.990571267553255.8779222056921.701219707576
4154305132.5595971202327.3142218610323259.3856654941340.98319948006815
4246905021.2076267312724.4344651976643-282.495968313303-1.25751529674917
4345404865.7162902682120.9236281304676-261.884467259013-1.64454559256925
4445754702.5616253341417.60522400435-61.8174009025794-1.69038500730633
4546604699.345050845617.2610623052781-31.8809739996128-0.191591410554701
4648504641.1646813962116.1277521005379235.925999438364-0.69447549305831
4742004558.6481006430514.7949851087817-323.191687161973-0.908132173622011
4843604627.2732257268115.4544261425688-286.6404572096080.495843566217642
4946554636.6025644861215.381164165709920.6002391825563-0.0563949024843131
5045854712.9449250199816.2072401005733-149.7150340855470.557826010222992
5153154875.0577421237218.5480507693462388.443413753921.32289825684452
5251154911.458772647518.8713386543533197.2902494127060.161063612974659
5351004852.852478661317.3893850953832274.26920066906-0.700070189100449
5457355224.2049375454724.1658376626745386.247111084043.21503321113977
5552605363.8661620235526.3008398131693-144.7620715170081.05456537254187
5650505294.7342472157424.6328480068837-210.776697305709-0.874431567944267
5751655236.2525608589823.2746796556599-41.5924869585725-0.762796169189006
5851905118.4396277763121.1293637199514121.978643079489-1.29541600144223
5947205093.5299453647520.4753113420564-357.066764503161-0.422752134119991
6052755276.3844566738822.6789032873732-59.46485304721741.49107549857462
6146055092.1652942136419.861907278643-413.242774279803-1.89786730561768
6248255060.5340883797119.1142266746578-217.213478224681-0.470626722522297
6355955126.8604583326419.8647397403066451.448391707790.429357598324425
6451605103.2457969742519.119104713698572.0518958470748-0.394195338586589
6553205165.9973471287319.8996555482547138.6631930124140.395754287199351
6655405193.6764449830520.0399282653686343.5813637957560.0707660648314951
6749705148.4973505799218.8864062993779-155.418609968795-0.595259390081596
6854455305.3999672179821.237517093295190.59791047124351.26275409467654
6953055327.0133895664821.2436233092941-22.14713357641310.00344344550043087
7051455227.3738211802819.3751293810965-39.319524480176-1.10776382781413
7148955243.6001929479119.3284848019652-347.478206239396-0.0288570936484577
7245554980.6255789043215.2442328410009-325.033141491253-2.5868249231038
7349805085.0120413570816.5417443972381-136.745101385040.816090607208056
7449305140.1887920250217.1249861132272-223.9066113354440.352917162936594
7558105231.6571725758918.3067222966153552.042219993020.677170964454983
7652105230.628316469117.9846014502653-13.8076869157078-0.175791030249933
7754505268.7594271758318.3302902242192174.1390178270570.183175177077134
7855105243.18643277917.5706181847038282.310715488809-0.399827171611092
7950105242.6379989384517.2603713469614-226.22714907187-0.165354845555974
8054955296.5643209158417.8731382351892185.4342186949160.335157943131665
8151255226.6016125169916.4512705901364-70.4103728265699-0.803589708148707
8251905202.7017663874815.81916923022891.6380879123038-0.369276982738943
8345655051.6709844837213.2740736542808-427.357852733595-1.52702812281898
8442554884.4797459163210.5576748294319-565.330562324306-1.65137663590092
8548754920.741495886910.9463817177915-54.87196576747580.235054350219272
8646504928.4283886449710.8960198791325-277.272423508803-0.0297662030464448
8752954862.974037498869.67985496402496459.045115294147-0.696075082943121
8850454927.7551850316410.5834201879697.7795307573360.501772532322159
8954305052.6813597758212.495744752992336.947316336591.04119818152538
9053255071.2187813110412.5974816574884251.6464924560230.0550661049868094
9149205103.8486155762212.9329004094597-190.9368032209250.182816826436345
9254455143.0562236341513.3661516230863292.6337674049220.240038704751202
9348955063.2785627496711.8617705939844-135.242227411466-0.851447379179981
9451755046.361301207511.406714978452138.85148727647-0.263136905693229
9545454986.1281423005710.2927280396828-415.699918581103-0.655056371872135
9642204911.401410855448.98117657290306-661.226098755534-0.777296481548303
9745954804.022057012597.18073417891318-167.742778929481-1.06336173081834
9843604721.364261119425.77265267925919-329.525391183083-0.820299191436334
9947504574.753822910843.34004271043394229.180985827628-1.38997972546312
10049854690.246066852215.16299468567013255.1010721521221.02228445548351
10151404755.782470372416.1570001937089362.8797462191310.550275308932787
10249954767.697453354056.2522780777757225.2666908010960.0525091257526726
10351504976.612095645369.59551445873451101.6709133813581.84960189380561
10452404979.865190607679.49187845461149262.381222486155-0.0579234925291633
10548754978.973699804259.32443992799307-100.293643242129-0.0948668616655604
10651704974.672956379399.10768116336842200.157817846749-0.124506720453977
10747155003.275471015649.41456207499419-295.1883314401190.178149171273912
10843704987.765359062949.0241450967811-608.927506644343-0.227747594119279
10951605086.5771761259510.433111556720341.59559011502040.820190807477796
11049305152.13948906211.3049632144321-241.6692294288240.503331151198428
11156005279.1683664492613.1556909205764279.868270293561.05591562665568
11253855271.8904869308412.8252156875576120.337714518799-0.186363111526886
11354255218.007296454511.7373764605989230.584271188329-0.608372293081858
11453755230.4016404259911.748127421422144.3659712217990.00599328841574651
11553655247.607595561711.8372962637446115.4608175370030.049813700566938

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Interpolation \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 3875 & 3875 & 0 & 0 & 0 \tabularnewline
2 & 3755 & 3819.06444131369 & -2.54689135563457 & -43.7276932861133 & -0.457255806692532 \tabularnewline
3 & 4670 & 4211.6718734291 & 25.5209463783593 & 356.183455861193 & 2.69436379945182 \tabularnewline
4 & 4335 & 4323.6017782611 & 30.5279822728339 & -16.3734850163961 & 0.6989795614056 \tabularnewline
5 & 4945 & 4592.53743875576 & 40.3968106046809 & 265.032062873632 & 2.11397964025451 \tabularnewline
6 & 4600 & 4648.98468468153 & 40.886709424785 & -55.1668365545231 & 0.14691343366562 \tabularnewline
7 & 4395 & 4561.30705453739 & 37.6625298193098 & -115.975673853129 & -1.18826676936251 \tabularnewline
8 & 4345 & 4458.82437955735 & 34.4676379542809 & -58.6871074338999 & -1.29870751932354 \tabularnewline
9 & 4390 & 4410.98106273573 & 32.659831926897 & 11.4390232506234 & -0.763065605390626 \tabularnewline
10 & 4490 & 4432.3541005611 & 32.4153228483423 & 62.0913444945915 & -0.104611755328755 \tabularnewline
11 & 4395 & 4422.24566006968 & 31.5007431221942 & -10.5012868849873 & -0.394015117206595 \tabularnewline
12 & 4690 & 4525.52437948677 & 33.0342594749988 & 136.217593534171 & 0.664918394034674 \tabularnewline
13 & 4590 & 4648.64078336567 & 29.6531972945702 & -96.2471409490551 & 0.945777535103339 \tabularnewline
14 & 4630 & 4796.18378041969 & 30.3262246828926 & -210.373752224315 & 1.09472552970129 \tabularnewline
15 & 5375 & 4964.74252319262 & 34.3730577907151 & 365.062163367623 & 1.16044222522539 \tabularnewline
16 & 4655 & 4950.97577911811 & 32.7401051540658 & -280.210544614787 & -0.409608815405487 \tabularnewline
17 & 4975 & 4875.04985501108 & 29.4223922864567 & 137.277645510226 & -0.962178467693239 \tabularnewline
18 & 4810 & 4841.97864591038 & 27.8318326117792 & -9.74140986628501 & -0.567930041778181 \tabularnewline
19 & 4445 & 4714.63211693189 & 24.5030555914561 & -213.424452775317 & -1.42735293577913 \tabularnewline
20 & 4660 & 4685.21788793873 & 23.4761766889242 & -5.53853498457322 & -0.498313672091422 \tabularnewline
21 & 4215 & 4507.90184773419 & 19.9106084584796 & -219.395201253462 & -1.85877040760365 \tabularnewline
22 & 4825 & 4571.39655242278 & 20.6392607361525 & 237.627663232247 & 0.403573547764655 \tabularnewline
23 & 4250 & 4497.98929684547 & 19.2566538460591 & -213.469065971803 & -0.870585002135194 \tabularnewline
24 & 3945 & 4265.55052487848 & 16.7634726694494 & -227.760311003838 & -2.33519323761066 \tabularnewline
25 & 4390 & 4331.35734134902 & 16.7564154718711 & 40.1928010977782 & 0.466090110047585 \tabularnewline
26 & 4315 & 4436.08904315237 & 17.5310112530421 & -153.217054370763 & 0.81257233660119 \tabularnewline
27 & 4835 & 4455.04158871335 & 17.5585247530214 & 379.466459420801 & 0.0125930378665814 \tabularnewline
28 & 4835 & 4688.76019260055 & 22.8271461522466 & 72.743233420968 & 1.89954372658524 \tabularnewline
29 & 4970 & 4772.2890792784 & 24.3310825802202 & 176.789564610006 & 0.541197174362687 \tabularnewline
30 & 4690 & 4736.72665352354 & 22.9577613477502 & -25.6717561556342 & -0.542808000500836 \tabularnewline
31 & 4700 & 4783.34138986158 & 23.4450569788933 & -91.7776682414142 & 0.216704225306899 \tabularnewline
32 & 4855 & 4789.94329487025 & 23.132162378536 & 71.1118937797258 & -0.155129221806541 \tabularnewline
33 & 4610 & 4810.79552166194 & 23.093595009367 & -199.97256700427 & -0.0210446495884632 \tabularnewline
34 & 4900 & 4731.34600079539 & 21.5285800079281 & 205.737659264523 & -0.946878855607596 \tabularnewline
35 & 4250 & 4580.63007240549 & 19.2595319005699 & -268.259686748138 & -1.59037067655188 \tabularnewline
36 & 4105 & 4488.33996808642 & 18.0814578253585 & -342.846968252426 & -1.03168705948357 \tabularnewline
37 & 4740 & 4579.59858451334 & 18.7129992077229 & 133.738483290271 & 0.67931491822186 \tabularnewline
38 & 4565 & 4673.51176132901 & 19.603419805374 & -135.562521746361 & 0.690067573905558 \tabularnewline
39 & 5155 & 4786.67951062925 & 21.1682717164723 & 335.447686706112 & 0.842855678599011 \tabularnewline
40 & 5320 & 4998.13283378942 & 24.990571267553 & 255.877922205692 & 1.701219707576 \tabularnewline
41 & 5430 & 5132.55959712023 & 27.3142218610323 & 259.385665494134 & 0.98319948006815 \tabularnewline
42 & 4690 & 5021.20762673127 & 24.4344651976643 & -282.495968313303 & -1.25751529674917 \tabularnewline
43 & 4540 & 4865.71629026821 & 20.9236281304676 & -261.884467259013 & -1.64454559256925 \tabularnewline
44 & 4575 & 4702.56162533414 & 17.60522400435 & -61.8174009025794 & -1.69038500730633 \tabularnewline
45 & 4660 & 4699.3450508456 & 17.2610623052781 & -31.8809739996128 & -0.191591410554701 \tabularnewline
46 & 4850 & 4641.16468139621 & 16.1277521005379 & 235.925999438364 & -0.69447549305831 \tabularnewline
47 & 4200 & 4558.64810064305 & 14.7949851087817 & -323.191687161973 & -0.908132173622011 \tabularnewline
48 & 4360 & 4627.27322572681 & 15.4544261425688 & -286.640457209608 & 0.495843566217642 \tabularnewline
49 & 4655 & 4636.60256448612 & 15.3811641657099 & 20.6002391825563 & -0.0563949024843131 \tabularnewline
50 & 4585 & 4712.94492501998 & 16.2072401005733 & -149.715034085547 & 0.557826010222992 \tabularnewline
51 & 5315 & 4875.05774212372 & 18.5480507693462 & 388.44341375392 & 1.32289825684452 \tabularnewline
52 & 5115 & 4911.4587726475 & 18.8713386543533 & 197.290249412706 & 0.161063612974659 \tabularnewline
53 & 5100 & 4852.8524786613 & 17.3893850953832 & 274.26920066906 & -0.700070189100449 \tabularnewline
54 & 5735 & 5224.20493754547 & 24.1658376626745 & 386.24711108404 & 3.21503321113977 \tabularnewline
55 & 5260 & 5363.86616202355 & 26.3008398131693 & -144.762071517008 & 1.05456537254187 \tabularnewline
56 & 5050 & 5294.73424721574 & 24.6328480068837 & -210.776697305709 & -0.874431567944267 \tabularnewline
57 & 5165 & 5236.25256085898 & 23.2746796556599 & -41.5924869585725 & -0.762796169189006 \tabularnewline
58 & 5190 & 5118.43962777631 & 21.1293637199514 & 121.978643079489 & -1.29541600144223 \tabularnewline
59 & 4720 & 5093.52994536475 & 20.4753113420564 & -357.066764503161 & -0.422752134119991 \tabularnewline
60 & 5275 & 5276.38445667388 & 22.6789032873732 & -59.4648530472174 & 1.49107549857462 \tabularnewline
61 & 4605 & 5092.16529421364 & 19.861907278643 & -413.242774279803 & -1.89786730561768 \tabularnewline
62 & 4825 & 5060.53408837971 & 19.1142266746578 & -217.213478224681 & -0.470626722522297 \tabularnewline
63 & 5595 & 5126.86045833264 & 19.8647397403066 & 451.44839170779 & 0.429357598324425 \tabularnewline
64 & 5160 & 5103.24579697425 & 19.1191047136985 & 72.0518958470748 & -0.394195338586589 \tabularnewline
65 & 5320 & 5165.99734712873 & 19.8996555482547 & 138.663193012414 & 0.395754287199351 \tabularnewline
66 & 5540 & 5193.67644498305 & 20.0399282653686 & 343.581363795756 & 0.0707660648314951 \tabularnewline
67 & 4970 & 5148.49735057992 & 18.8864062993779 & -155.418609968795 & -0.595259390081596 \tabularnewline
68 & 5445 & 5305.39996721798 & 21.2375170932951 & 90.5979104712435 & 1.26275409467654 \tabularnewline
69 & 5305 & 5327.01338956648 & 21.2436233092941 & -22.1471335764131 & 0.00344344550043087 \tabularnewline
70 & 5145 & 5227.37382118028 & 19.3751293810965 & -39.319524480176 & -1.10776382781413 \tabularnewline
71 & 4895 & 5243.60019294791 & 19.3284848019652 & -347.478206239396 & -0.0288570936484577 \tabularnewline
72 & 4555 & 4980.62557890432 & 15.2442328410009 & -325.033141491253 & -2.5868249231038 \tabularnewline
73 & 4980 & 5085.01204135708 & 16.5417443972381 & -136.74510138504 & 0.816090607208056 \tabularnewline
74 & 4930 & 5140.18879202502 & 17.1249861132272 & -223.906611335444 & 0.352917162936594 \tabularnewline
75 & 5810 & 5231.65717257589 & 18.3067222966153 & 552.04221999302 & 0.677170964454983 \tabularnewline
76 & 5210 & 5230.6283164691 & 17.9846014502653 & -13.8076869157078 & -0.175791030249933 \tabularnewline
77 & 5450 & 5268.75942717583 & 18.3302902242192 & 174.139017827057 & 0.183175177077134 \tabularnewline
78 & 5510 & 5243.186432779 & 17.5706181847038 & 282.310715488809 & -0.399827171611092 \tabularnewline
79 & 5010 & 5242.63799893845 & 17.2603713469614 & -226.22714907187 & -0.165354845555974 \tabularnewline
80 & 5495 & 5296.56432091584 & 17.8731382351892 & 185.434218694916 & 0.335157943131665 \tabularnewline
81 & 5125 & 5226.60161251699 & 16.4512705901364 & -70.4103728265699 & -0.803589708148707 \tabularnewline
82 & 5190 & 5202.70176638748 & 15.8191692302289 & 1.6380879123038 & -0.369276982738943 \tabularnewline
83 & 4565 & 5051.67098448372 & 13.2740736542808 & -427.357852733595 & -1.52702812281898 \tabularnewline
84 & 4255 & 4884.47974591632 & 10.5576748294319 & -565.330562324306 & -1.65137663590092 \tabularnewline
85 & 4875 & 4920.7414958869 & 10.9463817177915 & -54.8719657674758 & 0.235054350219272 \tabularnewline
86 & 4650 & 4928.42838864497 & 10.8960198791325 & -277.272423508803 & -0.0297662030464448 \tabularnewline
87 & 5295 & 4862.97403749886 & 9.67985496402496 & 459.045115294147 & -0.696075082943121 \tabularnewline
88 & 5045 & 4927.75518503164 & 10.58342018796 & 97.779530757336 & 0.501772532322159 \tabularnewline
89 & 5430 & 5052.68135977582 & 12.495744752992 & 336.94731633659 & 1.04119818152538 \tabularnewline
90 & 5325 & 5071.21878131104 & 12.5974816574884 & 251.646492456023 & 0.0550661049868094 \tabularnewline
91 & 4920 & 5103.84861557622 & 12.9329004094597 & -190.936803220925 & 0.182816826436345 \tabularnewline
92 & 5445 & 5143.05622363415 & 13.3661516230863 & 292.633767404922 & 0.240038704751202 \tabularnewline
93 & 4895 & 5063.27856274967 & 11.8617705939844 & -135.242227411466 & -0.851447379179981 \tabularnewline
94 & 5175 & 5046.3613012075 & 11.406714978452 & 138.85148727647 & -0.263136905693229 \tabularnewline
95 & 4545 & 4986.12814230057 & 10.2927280396828 & -415.699918581103 & -0.655056371872135 \tabularnewline
96 & 4220 & 4911.40141085544 & 8.98117657290306 & -661.226098755534 & -0.777296481548303 \tabularnewline
97 & 4595 & 4804.02205701259 & 7.18073417891318 & -167.742778929481 & -1.06336173081834 \tabularnewline
98 & 4360 & 4721.36426111942 & 5.77265267925919 & -329.525391183083 & -0.820299191436334 \tabularnewline
99 & 4750 & 4574.75382291084 & 3.34004271043394 & 229.180985827628 & -1.38997972546312 \tabularnewline
100 & 4985 & 4690.24606685221 & 5.16299468567013 & 255.101072152122 & 1.02228445548351 \tabularnewline
101 & 5140 & 4755.78247037241 & 6.1570001937089 & 362.879746219131 & 0.550275308932787 \tabularnewline
102 & 4995 & 4767.69745335405 & 6.2522780777757 & 225.266690801096 & 0.0525091257526726 \tabularnewline
103 & 5150 & 4976.61209564536 & 9.59551445873451 & 101.670913381358 & 1.84960189380561 \tabularnewline
104 & 5240 & 4979.86519060767 & 9.49187845461149 & 262.381222486155 & -0.0579234925291633 \tabularnewline
105 & 4875 & 4978.97369980425 & 9.32443992799307 & -100.293643242129 & -0.0948668616655604 \tabularnewline
106 & 5170 & 4974.67295637939 & 9.10768116336842 & 200.157817846749 & -0.124506720453977 \tabularnewline
107 & 4715 & 5003.27547101564 & 9.41456207499419 & -295.188331440119 & 0.178149171273912 \tabularnewline
108 & 4370 & 4987.76535906294 & 9.0241450967811 & -608.927506644343 & -0.227747594119279 \tabularnewline
109 & 5160 & 5086.57717612595 & 10.4331115567203 & 41.5955901150204 & 0.820190807477796 \tabularnewline
110 & 4930 & 5152.139489062 & 11.3049632144321 & -241.669229428824 & 0.503331151198428 \tabularnewline
111 & 5600 & 5279.16836644926 & 13.1556909205764 & 279.86827029356 & 1.05591562665568 \tabularnewline
112 & 5385 & 5271.89048693084 & 12.8252156875576 & 120.337714518799 & -0.186363111526886 \tabularnewline
113 & 5425 & 5218.0072964545 & 11.7373764605989 & 230.584271188329 & -0.608372293081858 \tabularnewline
114 & 5375 & 5230.40164042599 & 11.748127421422 & 144.365971221799 & 0.00599328841574651 \tabularnewline
115 & 5365 & 5247.6075955617 & 11.8372962637446 & 115.460817537003 & 0.049813700566938 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298188&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]3875[/C][C]3875[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]3755[/C][C]3819.06444131369[/C][C]-2.54689135563457[/C][C]-43.7276932861133[/C][C]-0.457255806692532[/C][/ROW]
[ROW][C]3[/C][C]4670[/C][C]4211.6718734291[/C][C]25.5209463783593[/C][C]356.183455861193[/C][C]2.69436379945182[/C][/ROW]
[ROW][C]4[/C][C]4335[/C][C]4323.6017782611[/C][C]30.5279822728339[/C][C]-16.3734850163961[/C][C]0.6989795614056[/C][/ROW]
[ROW][C]5[/C][C]4945[/C][C]4592.53743875576[/C][C]40.3968106046809[/C][C]265.032062873632[/C][C]2.11397964025451[/C][/ROW]
[ROW][C]6[/C][C]4600[/C][C]4648.98468468153[/C][C]40.886709424785[/C][C]-55.1668365545231[/C][C]0.14691343366562[/C][/ROW]
[ROW][C]7[/C][C]4395[/C][C]4561.30705453739[/C][C]37.6625298193098[/C][C]-115.975673853129[/C][C]-1.18826676936251[/C][/ROW]
[ROW][C]8[/C][C]4345[/C][C]4458.82437955735[/C][C]34.4676379542809[/C][C]-58.6871074338999[/C][C]-1.29870751932354[/C][/ROW]
[ROW][C]9[/C][C]4390[/C][C]4410.98106273573[/C][C]32.659831926897[/C][C]11.4390232506234[/C][C]-0.763065605390626[/C][/ROW]
[ROW][C]10[/C][C]4490[/C][C]4432.3541005611[/C][C]32.4153228483423[/C][C]62.0913444945915[/C][C]-0.104611755328755[/C][/ROW]
[ROW][C]11[/C][C]4395[/C][C]4422.24566006968[/C][C]31.5007431221942[/C][C]-10.5012868849873[/C][C]-0.394015117206595[/C][/ROW]
[ROW][C]12[/C][C]4690[/C][C]4525.52437948677[/C][C]33.0342594749988[/C][C]136.217593534171[/C][C]0.664918394034674[/C][/ROW]
[ROW][C]13[/C][C]4590[/C][C]4648.64078336567[/C][C]29.6531972945702[/C][C]-96.2471409490551[/C][C]0.945777535103339[/C][/ROW]
[ROW][C]14[/C][C]4630[/C][C]4796.18378041969[/C][C]30.3262246828926[/C][C]-210.373752224315[/C][C]1.09472552970129[/C][/ROW]
[ROW][C]15[/C][C]5375[/C][C]4964.74252319262[/C][C]34.3730577907151[/C][C]365.062163367623[/C][C]1.16044222522539[/C][/ROW]
[ROW][C]16[/C][C]4655[/C][C]4950.97577911811[/C][C]32.7401051540658[/C][C]-280.210544614787[/C][C]-0.409608815405487[/C][/ROW]
[ROW][C]17[/C][C]4975[/C][C]4875.04985501108[/C][C]29.4223922864567[/C][C]137.277645510226[/C][C]-0.962178467693239[/C][/ROW]
[ROW][C]18[/C][C]4810[/C][C]4841.97864591038[/C][C]27.8318326117792[/C][C]-9.74140986628501[/C][C]-0.567930041778181[/C][/ROW]
[ROW][C]19[/C][C]4445[/C][C]4714.63211693189[/C][C]24.5030555914561[/C][C]-213.424452775317[/C][C]-1.42735293577913[/C][/ROW]
[ROW][C]20[/C][C]4660[/C][C]4685.21788793873[/C][C]23.4761766889242[/C][C]-5.53853498457322[/C][C]-0.498313672091422[/C][/ROW]
[ROW][C]21[/C][C]4215[/C][C]4507.90184773419[/C][C]19.9106084584796[/C][C]-219.395201253462[/C][C]-1.85877040760365[/C][/ROW]
[ROW][C]22[/C][C]4825[/C][C]4571.39655242278[/C][C]20.6392607361525[/C][C]237.627663232247[/C][C]0.403573547764655[/C][/ROW]
[ROW][C]23[/C][C]4250[/C][C]4497.98929684547[/C][C]19.2566538460591[/C][C]-213.469065971803[/C][C]-0.870585002135194[/C][/ROW]
[ROW][C]24[/C][C]3945[/C][C]4265.55052487848[/C][C]16.7634726694494[/C][C]-227.760311003838[/C][C]-2.33519323761066[/C][/ROW]
[ROW][C]25[/C][C]4390[/C][C]4331.35734134902[/C][C]16.7564154718711[/C][C]40.1928010977782[/C][C]0.466090110047585[/C][/ROW]
[ROW][C]26[/C][C]4315[/C][C]4436.08904315237[/C][C]17.5310112530421[/C][C]-153.217054370763[/C][C]0.81257233660119[/C][/ROW]
[ROW][C]27[/C][C]4835[/C][C]4455.04158871335[/C][C]17.5585247530214[/C][C]379.466459420801[/C][C]0.0125930378665814[/C][/ROW]
[ROW][C]28[/C][C]4835[/C][C]4688.76019260055[/C][C]22.8271461522466[/C][C]72.743233420968[/C][C]1.89954372658524[/C][/ROW]
[ROW][C]29[/C][C]4970[/C][C]4772.2890792784[/C][C]24.3310825802202[/C][C]176.789564610006[/C][C]0.541197174362687[/C][/ROW]
[ROW][C]30[/C][C]4690[/C][C]4736.72665352354[/C][C]22.9577613477502[/C][C]-25.6717561556342[/C][C]-0.542808000500836[/C][/ROW]
[ROW][C]31[/C][C]4700[/C][C]4783.34138986158[/C][C]23.4450569788933[/C][C]-91.7776682414142[/C][C]0.216704225306899[/C][/ROW]
[ROW][C]32[/C][C]4855[/C][C]4789.94329487025[/C][C]23.132162378536[/C][C]71.1118937797258[/C][C]-0.155129221806541[/C][/ROW]
[ROW][C]33[/C][C]4610[/C][C]4810.79552166194[/C][C]23.093595009367[/C][C]-199.97256700427[/C][C]-0.0210446495884632[/C][/ROW]
[ROW][C]34[/C][C]4900[/C][C]4731.34600079539[/C][C]21.5285800079281[/C][C]205.737659264523[/C][C]-0.946878855607596[/C][/ROW]
[ROW][C]35[/C][C]4250[/C][C]4580.63007240549[/C][C]19.2595319005699[/C][C]-268.259686748138[/C][C]-1.59037067655188[/C][/ROW]
[ROW][C]36[/C][C]4105[/C][C]4488.33996808642[/C][C]18.0814578253585[/C][C]-342.846968252426[/C][C]-1.03168705948357[/C][/ROW]
[ROW][C]37[/C][C]4740[/C][C]4579.59858451334[/C][C]18.7129992077229[/C][C]133.738483290271[/C][C]0.67931491822186[/C][/ROW]
[ROW][C]38[/C][C]4565[/C][C]4673.51176132901[/C][C]19.603419805374[/C][C]-135.562521746361[/C][C]0.690067573905558[/C][/ROW]
[ROW][C]39[/C][C]5155[/C][C]4786.67951062925[/C][C]21.1682717164723[/C][C]335.447686706112[/C][C]0.842855678599011[/C][/ROW]
[ROW][C]40[/C][C]5320[/C][C]4998.13283378942[/C][C]24.990571267553[/C][C]255.877922205692[/C][C]1.701219707576[/C][/ROW]
[ROW][C]41[/C][C]5430[/C][C]5132.55959712023[/C][C]27.3142218610323[/C][C]259.385665494134[/C][C]0.98319948006815[/C][/ROW]
[ROW][C]42[/C][C]4690[/C][C]5021.20762673127[/C][C]24.4344651976643[/C][C]-282.495968313303[/C][C]-1.25751529674917[/C][/ROW]
[ROW][C]43[/C][C]4540[/C][C]4865.71629026821[/C][C]20.9236281304676[/C][C]-261.884467259013[/C][C]-1.64454559256925[/C][/ROW]
[ROW][C]44[/C][C]4575[/C][C]4702.56162533414[/C][C]17.60522400435[/C][C]-61.8174009025794[/C][C]-1.69038500730633[/C][/ROW]
[ROW][C]45[/C][C]4660[/C][C]4699.3450508456[/C][C]17.2610623052781[/C][C]-31.8809739996128[/C][C]-0.191591410554701[/C][/ROW]
[ROW][C]46[/C][C]4850[/C][C]4641.16468139621[/C][C]16.1277521005379[/C][C]235.925999438364[/C][C]-0.69447549305831[/C][/ROW]
[ROW][C]47[/C][C]4200[/C][C]4558.64810064305[/C][C]14.7949851087817[/C][C]-323.191687161973[/C][C]-0.908132173622011[/C][/ROW]
[ROW][C]48[/C][C]4360[/C][C]4627.27322572681[/C][C]15.4544261425688[/C][C]-286.640457209608[/C][C]0.495843566217642[/C][/ROW]
[ROW][C]49[/C][C]4655[/C][C]4636.60256448612[/C][C]15.3811641657099[/C][C]20.6002391825563[/C][C]-0.0563949024843131[/C][/ROW]
[ROW][C]50[/C][C]4585[/C][C]4712.94492501998[/C][C]16.2072401005733[/C][C]-149.715034085547[/C][C]0.557826010222992[/C][/ROW]
[ROW][C]51[/C][C]5315[/C][C]4875.05774212372[/C][C]18.5480507693462[/C][C]388.44341375392[/C][C]1.32289825684452[/C][/ROW]
[ROW][C]52[/C][C]5115[/C][C]4911.4587726475[/C][C]18.8713386543533[/C][C]197.290249412706[/C][C]0.161063612974659[/C][/ROW]
[ROW][C]53[/C][C]5100[/C][C]4852.8524786613[/C][C]17.3893850953832[/C][C]274.26920066906[/C][C]-0.700070189100449[/C][/ROW]
[ROW][C]54[/C][C]5735[/C][C]5224.20493754547[/C][C]24.1658376626745[/C][C]386.24711108404[/C][C]3.21503321113977[/C][/ROW]
[ROW][C]55[/C][C]5260[/C][C]5363.86616202355[/C][C]26.3008398131693[/C][C]-144.762071517008[/C][C]1.05456537254187[/C][/ROW]
[ROW][C]56[/C][C]5050[/C][C]5294.73424721574[/C][C]24.6328480068837[/C][C]-210.776697305709[/C][C]-0.874431567944267[/C][/ROW]
[ROW][C]57[/C][C]5165[/C][C]5236.25256085898[/C][C]23.2746796556599[/C][C]-41.5924869585725[/C][C]-0.762796169189006[/C][/ROW]
[ROW][C]58[/C][C]5190[/C][C]5118.43962777631[/C][C]21.1293637199514[/C][C]121.978643079489[/C][C]-1.29541600144223[/C][/ROW]
[ROW][C]59[/C][C]4720[/C][C]5093.52994536475[/C][C]20.4753113420564[/C][C]-357.066764503161[/C][C]-0.422752134119991[/C][/ROW]
[ROW][C]60[/C][C]5275[/C][C]5276.38445667388[/C][C]22.6789032873732[/C][C]-59.4648530472174[/C][C]1.49107549857462[/C][/ROW]
[ROW][C]61[/C][C]4605[/C][C]5092.16529421364[/C][C]19.861907278643[/C][C]-413.242774279803[/C][C]-1.89786730561768[/C][/ROW]
[ROW][C]62[/C][C]4825[/C][C]5060.53408837971[/C][C]19.1142266746578[/C][C]-217.213478224681[/C][C]-0.470626722522297[/C][/ROW]
[ROW][C]63[/C][C]5595[/C][C]5126.86045833264[/C][C]19.8647397403066[/C][C]451.44839170779[/C][C]0.429357598324425[/C][/ROW]
[ROW][C]64[/C][C]5160[/C][C]5103.24579697425[/C][C]19.1191047136985[/C][C]72.0518958470748[/C][C]-0.394195338586589[/C][/ROW]
[ROW][C]65[/C][C]5320[/C][C]5165.99734712873[/C][C]19.8996555482547[/C][C]138.663193012414[/C][C]0.395754287199351[/C][/ROW]
[ROW][C]66[/C][C]5540[/C][C]5193.67644498305[/C][C]20.0399282653686[/C][C]343.581363795756[/C][C]0.0707660648314951[/C][/ROW]
[ROW][C]67[/C][C]4970[/C][C]5148.49735057992[/C][C]18.8864062993779[/C][C]-155.418609968795[/C][C]-0.595259390081596[/C][/ROW]
[ROW][C]68[/C][C]5445[/C][C]5305.39996721798[/C][C]21.2375170932951[/C][C]90.5979104712435[/C][C]1.26275409467654[/C][/ROW]
[ROW][C]69[/C][C]5305[/C][C]5327.01338956648[/C][C]21.2436233092941[/C][C]-22.1471335764131[/C][C]0.00344344550043087[/C][/ROW]
[ROW][C]70[/C][C]5145[/C][C]5227.37382118028[/C][C]19.3751293810965[/C][C]-39.319524480176[/C][C]-1.10776382781413[/C][/ROW]
[ROW][C]71[/C][C]4895[/C][C]5243.60019294791[/C][C]19.3284848019652[/C][C]-347.478206239396[/C][C]-0.0288570936484577[/C][/ROW]
[ROW][C]72[/C][C]4555[/C][C]4980.62557890432[/C][C]15.2442328410009[/C][C]-325.033141491253[/C][C]-2.5868249231038[/C][/ROW]
[ROW][C]73[/C][C]4980[/C][C]5085.01204135708[/C][C]16.5417443972381[/C][C]-136.74510138504[/C][C]0.816090607208056[/C][/ROW]
[ROW][C]74[/C][C]4930[/C][C]5140.18879202502[/C][C]17.1249861132272[/C][C]-223.906611335444[/C][C]0.352917162936594[/C][/ROW]
[ROW][C]75[/C][C]5810[/C][C]5231.65717257589[/C][C]18.3067222966153[/C][C]552.04221999302[/C][C]0.677170964454983[/C][/ROW]
[ROW][C]76[/C][C]5210[/C][C]5230.6283164691[/C][C]17.9846014502653[/C][C]-13.8076869157078[/C][C]-0.175791030249933[/C][/ROW]
[ROW][C]77[/C][C]5450[/C][C]5268.75942717583[/C][C]18.3302902242192[/C][C]174.139017827057[/C][C]0.183175177077134[/C][/ROW]
[ROW][C]78[/C][C]5510[/C][C]5243.186432779[/C][C]17.5706181847038[/C][C]282.310715488809[/C][C]-0.399827171611092[/C][/ROW]
[ROW][C]79[/C][C]5010[/C][C]5242.63799893845[/C][C]17.2603713469614[/C][C]-226.22714907187[/C][C]-0.165354845555974[/C][/ROW]
[ROW][C]80[/C][C]5495[/C][C]5296.56432091584[/C][C]17.8731382351892[/C][C]185.434218694916[/C][C]0.335157943131665[/C][/ROW]
[ROW][C]81[/C][C]5125[/C][C]5226.60161251699[/C][C]16.4512705901364[/C][C]-70.4103728265699[/C][C]-0.803589708148707[/C][/ROW]
[ROW][C]82[/C][C]5190[/C][C]5202.70176638748[/C][C]15.8191692302289[/C][C]1.6380879123038[/C][C]-0.369276982738943[/C][/ROW]
[ROW][C]83[/C][C]4565[/C][C]5051.67098448372[/C][C]13.2740736542808[/C][C]-427.357852733595[/C][C]-1.52702812281898[/C][/ROW]
[ROW][C]84[/C][C]4255[/C][C]4884.47974591632[/C][C]10.5576748294319[/C][C]-565.330562324306[/C][C]-1.65137663590092[/C][/ROW]
[ROW][C]85[/C][C]4875[/C][C]4920.7414958869[/C][C]10.9463817177915[/C][C]-54.8719657674758[/C][C]0.235054350219272[/C][/ROW]
[ROW][C]86[/C][C]4650[/C][C]4928.42838864497[/C][C]10.8960198791325[/C][C]-277.272423508803[/C][C]-0.0297662030464448[/C][/ROW]
[ROW][C]87[/C][C]5295[/C][C]4862.97403749886[/C][C]9.67985496402496[/C][C]459.045115294147[/C][C]-0.696075082943121[/C][/ROW]
[ROW][C]88[/C][C]5045[/C][C]4927.75518503164[/C][C]10.58342018796[/C][C]97.779530757336[/C][C]0.501772532322159[/C][/ROW]
[ROW][C]89[/C][C]5430[/C][C]5052.68135977582[/C][C]12.495744752992[/C][C]336.94731633659[/C][C]1.04119818152538[/C][/ROW]
[ROW][C]90[/C][C]5325[/C][C]5071.21878131104[/C][C]12.5974816574884[/C][C]251.646492456023[/C][C]0.0550661049868094[/C][/ROW]
[ROW][C]91[/C][C]4920[/C][C]5103.84861557622[/C][C]12.9329004094597[/C][C]-190.936803220925[/C][C]0.182816826436345[/C][/ROW]
[ROW][C]92[/C][C]5445[/C][C]5143.05622363415[/C][C]13.3661516230863[/C][C]292.633767404922[/C][C]0.240038704751202[/C][/ROW]
[ROW][C]93[/C][C]4895[/C][C]5063.27856274967[/C][C]11.8617705939844[/C][C]-135.242227411466[/C][C]-0.851447379179981[/C][/ROW]
[ROW][C]94[/C][C]5175[/C][C]5046.3613012075[/C][C]11.406714978452[/C][C]138.85148727647[/C][C]-0.263136905693229[/C][/ROW]
[ROW][C]95[/C][C]4545[/C][C]4986.12814230057[/C][C]10.2927280396828[/C][C]-415.699918581103[/C][C]-0.655056371872135[/C][/ROW]
[ROW][C]96[/C][C]4220[/C][C]4911.40141085544[/C][C]8.98117657290306[/C][C]-661.226098755534[/C][C]-0.777296481548303[/C][/ROW]
[ROW][C]97[/C][C]4595[/C][C]4804.02205701259[/C][C]7.18073417891318[/C][C]-167.742778929481[/C][C]-1.06336173081834[/C][/ROW]
[ROW][C]98[/C][C]4360[/C][C]4721.36426111942[/C][C]5.77265267925919[/C][C]-329.525391183083[/C][C]-0.820299191436334[/C][/ROW]
[ROW][C]99[/C][C]4750[/C][C]4574.75382291084[/C][C]3.34004271043394[/C][C]229.180985827628[/C][C]-1.38997972546312[/C][/ROW]
[ROW][C]100[/C][C]4985[/C][C]4690.24606685221[/C][C]5.16299468567013[/C][C]255.101072152122[/C][C]1.02228445548351[/C][/ROW]
[ROW][C]101[/C][C]5140[/C][C]4755.78247037241[/C][C]6.1570001937089[/C][C]362.879746219131[/C][C]0.550275308932787[/C][/ROW]
[ROW][C]102[/C][C]4995[/C][C]4767.69745335405[/C][C]6.2522780777757[/C][C]225.266690801096[/C][C]0.0525091257526726[/C][/ROW]
[ROW][C]103[/C][C]5150[/C][C]4976.61209564536[/C][C]9.59551445873451[/C][C]101.670913381358[/C][C]1.84960189380561[/C][/ROW]
[ROW][C]104[/C][C]5240[/C][C]4979.86519060767[/C][C]9.49187845461149[/C][C]262.381222486155[/C][C]-0.0579234925291633[/C][/ROW]
[ROW][C]105[/C][C]4875[/C][C]4978.97369980425[/C][C]9.32443992799307[/C][C]-100.293643242129[/C][C]-0.0948668616655604[/C][/ROW]
[ROW][C]106[/C][C]5170[/C][C]4974.67295637939[/C][C]9.10768116336842[/C][C]200.157817846749[/C][C]-0.124506720453977[/C][/ROW]
[ROW][C]107[/C][C]4715[/C][C]5003.27547101564[/C][C]9.41456207499419[/C][C]-295.188331440119[/C][C]0.178149171273912[/C][/ROW]
[ROW][C]108[/C][C]4370[/C][C]4987.76535906294[/C][C]9.0241450967811[/C][C]-608.927506644343[/C][C]-0.227747594119279[/C][/ROW]
[ROW][C]109[/C][C]5160[/C][C]5086.57717612595[/C][C]10.4331115567203[/C][C]41.5955901150204[/C][C]0.820190807477796[/C][/ROW]
[ROW][C]110[/C][C]4930[/C][C]5152.139489062[/C][C]11.3049632144321[/C][C]-241.669229428824[/C][C]0.503331151198428[/C][/ROW]
[ROW][C]111[/C][C]5600[/C][C]5279.16836644926[/C][C]13.1556909205764[/C][C]279.86827029356[/C][C]1.05591562665568[/C][/ROW]
[ROW][C]112[/C][C]5385[/C][C]5271.89048693084[/C][C]12.8252156875576[/C][C]120.337714518799[/C][C]-0.186363111526886[/C][/ROW]
[ROW][C]113[/C][C]5425[/C][C]5218.0072964545[/C][C]11.7373764605989[/C][C]230.584271188329[/C][C]-0.608372293081858[/C][/ROW]
[ROW][C]114[/C][C]5375[/C][C]5230.40164042599[/C][C]11.748127421422[/C][C]144.365971221799[/C][C]0.00599328841574651[/C][/ROW]
[ROW][C]115[/C][C]5365[/C][C]5247.6075955617[/C][C]11.8372962637446[/C][C]115.460817537003[/C][C]0.049813700566938[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298188&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298188&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
138753875000
237553819.06444131369-2.54689135563457-43.7276932861133-0.457255806692532
346704211.671873429125.5209463783593356.1834558611932.69436379945182
443354323.601778261130.5279822728339-16.37348501639610.6989795614056
549454592.5374387557640.3968106046809265.0320628736322.11397964025451
646004648.9846846815340.886709424785-55.16683655452310.14691343366562
743954561.3070545373937.6625298193098-115.975673853129-1.18826676936251
843454458.8243795573534.4676379542809-58.6871074338999-1.29870751932354
943904410.9810627357332.65983192689711.4390232506234-0.763065605390626
1044904432.354100561132.415322848342362.0913444945915-0.104611755328755
1143954422.2456600696831.5007431221942-10.5012868849873-0.394015117206595
1246904525.5243794867733.0342594749988136.2175935341710.664918394034674
1345904648.6407833656729.6531972945702-96.24714094905510.945777535103339
1446304796.1837804196930.3262246828926-210.3737522243151.09472552970129
1553754964.7425231926234.3730577907151365.0621633676231.16044222522539
1646554950.9757791181132.7401051540658-280.210544614787-0.409608815405487
1749754875.0498550110829.4223922864567137.277645510226-0.962178467693239
1848104841.9786459103827.8318326117792-9.74140986628501-0.567930041778181
1944454714.6321169318924.5030555914561-213.424452775317-1.42735293577913
2046604685.2178879387323.4761766889242-5.53853498457322-0.498313672091422
2142154507.9018477341919.9106084584796-219.395201253462-1.85877040760365
2248254571.3965524227820.6392607361525237.6276632322470.403573547764655
2342504497.9892968454719.2566538460591-213.469065971803-0.870585002135194
2439454265.5505248784816.7634726694494-227.760311003838-2.33519323761066
2543904331.3573413490216.756415471871140.19280109777820.466090110047585
2643154436.0890431523717.5310112530421-153.2170543707630.81257233660119
2748354455.0415887133517.5585247530214379.4664594208010.0125930378665814
2848354688.7601926005522.827146152246672.7432334209681.89954372658524
2949704772.289079278424.3310825802202176.7895646100060.541197174362687
3046904736.7266535235422.9577613477502-25.6717561556342-0.542808000500836
3147004783.3413898615823.4450569788933-91.77766824141420.216704225306899
3248554789.9432948702523.13216237853671.1118937797258-0.155129221806541
3346104810.7955216619423.093595009367-199.97256700427-0.0210446495884632
3449004731.3460007953921.5285800079281205.737659264523-0.946878855607596
3542504580.6300724054919.2595319005699-268.259686748138-1.59037067655188
3641054488.3399680864218.0814578253585-342.846968252426-1.03168705948357
3747404579.5985845133418.7129992077229133.7384832902710.67931491822186
3845654673.5117613290119.603419805374-135.5625217463610.690067573905558
3951554786.6795106292521.1682717164723335.4476867061120.842855678599011
4053204998.1328337894224.990571267553255.8779222056921.701219707576
4154305132.5595971202327.3142218610323259.3856654941340.98319948006815
4246905021.2076267312724.4344651976643-282.495968313303-1.25751529674917
4345404865.7162902682120.9236281304676-261.884467259013-1.64454559256925
4445754702.5616253341417.60522400435-61.8174009025794-1.69038500730633
4546604699.345050845617.2610623052781-31.8809739996128-0.191591410554701
4648504641.1646813962116.1277521005379235.925999438364-0.69447549305831
4742004558.6481006430514.7949851087817-323.191687161973-0.908132173622011
4843604627.2732257268115.4544261425688-286.6404572096080.495843566217642
4946554636.6025644861215.381164165709920.6002391825563-0.0563949024843131
5045854712.9449250199816.2072401005733-149.7150340855470.557826010222992
5153154875.0577421237218.5480507693462388.443413753921.32289825684452
5251154911.458772647518.8713386543533197.2902494127060.161063612974659
5351004852.852478661317.3893850953832274.26920066906-0.700070189100449
5457355224.2049375454724.1658376626745386.247111084043.21503321113977
5552605363.8661620235526.3008398131693-144.7620715170081.05456537254187
5650505294.7342472157424.6328480068837-210.776697305709-0.874431567944267
5751655236.2525608589823.2746796556599-41.5924869585725-0.762796169189006
5851905118.4396277763121.1293637199514121.978643079489-1.29541600144223
5947205093.5299453647520.4753113420564-357.066764503161-0.422752134119991
6052755276.3844566738822.6789032873732-59.46485304721741.49107549857462
6146055092.1652942136419.861907278643-413.242774279803-1.89786730561768
6248255060.5340883797119.1142266746578-217.213478224681-0.470626722522297
6355955126.8604583326419.8647397403066451.448391707790.429357598324425
6451605103.2457969742519.119104713698572.0518958470748-0.394195338586589
6553205165.9973471287319.8996555482547138.6631930124140.395754287199351
6655405193.6764449830520.0399282653686343.5813637957560.0707660648314951
6749705148.4973505799218.8864062993779-155.418609968795-0.595259390081596
6854455305.3999672179821.237517093295190.59791047124351.26275409467654
6953055327.0133895664821.2436233092941-22.14713357641310.00344344550043087
7051455227.3738211802819.3751293810965-39.319524480176-1.10776382781413
7148955243.6001929479119.3284848019652-347.478206239396-0.0288570936484577
7245554980.6255789043215.2442328410009-325.033141491253-2.5868249231038
7349805085.0120413570816.5417443972381-136.745101385040.816090607208056
7449305140.1887920250217.1249861132272-223.9066113354440.352917162936594
7558105231.6571725758918.3067222966153552.042219993020.677170964454983
7652105230.628316469117.9846014502653-13.8076869157078-0.175791030249933
7754505268.7594271758318.3302902242192174.1390178270570.183175177077134
7855105243.18643277917.5706181847038282.310715488809-0.399827171611092
7950105242.6379989384517.2603713469614-226.22714907187-0.165354845555974
8054955296.5643209158417.8731382351892185.4342186949160.335157943131665
8151255226.6016125169916.4512705901364-70.4103728265699-0.803589708148707
8251905202.7017663874815.81916923022891.6380879123038-0.369276982738943
8345655051.6709844837213.2740736542808-427.357852733595-1.52702812281898
8442554884.4797459163210.5576748294319-565.330562324306-1.65137663590092
8548754920.741495886910.9463817177915-54.87196576747580.235054350219272
8646504928.4283886449710.8960198791325-277.272423508803-0.0297662030464448
8752954862.974037498869.67985496402496459.045115294147-0.696075082943121
8850454927.7551850316410.5834201879697.7795307573360.501772532322159
8954305052.6813597758212.495744752992336.947316336591.04119818152538
9053255071.2187813110412.5974816574884251.6464924560230.0550661049868094
9149205103.8486155762212.9329004094597-190.9368032209250.182816826436345
9254455143.0562236341513.3661516230863292.6337674049220.240038704751202
9348955063.2785627496711.8617705939844-135.242227411466-0.851447379179981
9451755046.361301207511.406714978452138.85148727647-0.263136905693229
9545454986.1281423005710.2927280396828-415.699918581103-0.655056371872135
9642204911.401410855448.98117657290306-661.226098755534-0.777296481548303
9745954804.022057012597.18073417891318-167.742778929481-1.06336173081834
9843604721.364261119425.77265267925919-329.525391183083-0.820299191436334
9947504574.753822910843.34004271043394229.180985827628-1.38997972546312
10049854690.246066852215.16299468567013255.1010721521221.02228445548351
10151404755.782470372416.1570001937089362.8797462191310.550275308932787
10249954767.697453354056.2522780777757225.2666908010960.0525091257526726
10351504976.612095645369.59551445873451101.6709133813581.84960189380561
10452404979.865190607679.49187845461149262.381222486155-0.0579234925291633
10548754978.973699804259.32443992799307-100.293643242129-0.0948668616655604
10651704974.672956379399.10768116336842200.157817846749-0.124506720453977
10747155003.275471015649.41456207499419-295.1883314401190.178149171273912
10843704987.765359062949.0241450967811-608.927506644343-0.227747594119279
10951605086.5771761259510.433111556720341.59559011502040.820190807477796
11049305152.13948906211.3049632144321-241.6692294288240.503331151198428
11156005279.1683664492613.1556909205764279.868270293561.05591562665568
11253855271.8904869308412.8252156875576120.337714518799-0.186363111526886
11354255218.007296454511.7373764605989230.584271188329-0.608372293081858
11453755230.4016404259911.748127421422144.3659712217990.00599328841574651
11553655247.607595561711.8372962637446115.4608175370030.049813700566938







Structural Time Series Model -- Extrapolation
tObservedLevelSeasonal
15498.868511643655192.18029024596306.688221397693
25093.395767206695199.59767320094-106.201905994244
35362.643262096595207.01505615592155.628205940673
44866.162707465745214.4324391109-348.269731645159
54469.90009893635221.84982206588-751.949723129574
65192.556932023875229.26720502086-36.7102729969862
74920.093080300475236.68458797584-316.591507675364
85581.208599654815244.10197093082337.106628723993
95410.792840449845251.5193538858159.273486564039
105490.658095142785258.93673684078231.721358301999
115455.422267599675266.35411979576189.06814780391
125454.008595459765273.77150275074180.237092709021
135587.877107103415281.18888570572306.688221397693
145182.404362666455288.6062686607-106.201905994244
155451.651857556355296.02365161568155.628205940673
164955.17130292555303.44103457066-348.269731645159
174558.908694396065310.85841752564-751.949723129574
185281.565527483635318.27580048062-36.7102729969861

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Extrapolation \tabularnewline
t & Observed & Level & Seasonal \tabularnewline
1 & 5498.86851164365 & 5192.18029024596 & 306.688221397693 \tabularnewline
2 & 5093.39576720669 & 5199.59767320094 & -106.201905994244 \tabularnewline
3 & 5362.64326209659 & 5207.01505615592 & 155.628205940673 \tabularnewline
4 & 4866.16270746574 & 5214.4324391109 & -348.269731645159 \tabularnewline
5 & 4469.9000989363 & 5221.84982206588 & -751.949723129574 \tabularnewline
6 & 5192.55693202387 & 5229.26720502086 & -36.7102729969862 \tabularnewline
7 & 4920.09308030047 & 5236.68458797584 & -316.591507675364 \tabularnewline
8 & 5581.20859965481 & 5244.10197093082 & 337.106628723993 \tabularnewline
9 & 5410.79284044984 & 5251.5193538858 & 159.273486564039 \tabularnewline
10 & 5490.65809514278 & 5258.93673684078 & 231.721358301999 \tabularnewline
11 & 5455.42226759967 & 5266.35411979576 & 189.06814780391 \tabularnewline
12 & 5454.00859545976 & 5273.77150275074 & 180.237092709021 \tabularnewline
13 & 5587.87710710341 & 5281.18888570572 & 306.688221397693 \tabularnewline
14 & 5182.40436266645 & 5288.6062686607 & -106.201905994244 \tabularnewline
15 & 5451.65185755635 & 5296.02365161568 & 155.628205940673 \tabularnewline
16 & 4955.1713029255 & 5303.44103457066 & -348.269731645159 \tabularnewline
17 & 4558.90869439606 & 5310.85841752564 & -751.949723129574 \tabularnewline
18 & 5281.56552748363 & 5318.27580048062 & -36.7102729969861 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298188&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]5498.86851164365[/C][C]5192.18029024596[/C][C]306.688221397693[/C][/ROW]
[ROW][C]2[/C][C]5093.39576720669[/C][C]5199.59767320094[/C][C]-106.201905994244[/C][/ROW]
[ROW][C]3[/C][C]5362.64326209659[/C][C]5207.01505615592[/C][C]155.628205940673[/C][/ROW]
[ROW][C]4[/C][C]4866.16270746574[/C][C]5214.4324391109[/C][C]-348.269731645159[/C][/ROW]
[ROW][C]5[/C][C]4469.9000989363[/C][C]5221.84982206588[/C][C]-751.949723129574[/C][/ROW]
[ROW][C]6[/C][C]5192.55693202387[/C][C]5229.26720502086[/C][C]-36.7102729969862[/C][/ROW]
[ROW][C]7[/C][C]4920.09308030047[/C][C]5236.68458797584[/C][C]-316.591507675364[/C][/ROW]
[ROW][C]8[/C][C]5581.20859965481[/C][C]5244.10197093082[/C][C]337.106628723993[/C][/ROW]
[ROW][C]9[/C][C]5410.79284044984[/C][C]5251.5193538858[/C][C]159.273486564039[/C][/ROW]
[ROW][C]10[/C][C]5490.65809514278[/C][C]5258.93673684078[/C][C]231.721358301999[/C][/ROW]
[ROW][C]11[/C][C]5455.42226759967[/C][C]5266.35411979576[/C][C]189.06814780391[/C][/ROW]
[ROW][C]12[/C][C]5454.00859545976[/C][C]5273.77150275074[/C][C]180.237092709021[/C][/ROW]
[ROW][C]13[/C][C]5587.87710710341[/C][C]5281.18888570572[/C][C]306.688221397693[/C][/ROW]
[ROW][C]14[/C][C]5182.40436266645[/C][C]5288.6062686607[/C][C]-106.201905994244[/C][/ROW]
[ROW][C]15[/C][C]5451.65185755635[/C][C]5296.02365161568[/C][C]155.628205940673[/C][/ROW]
[ROW][C]16[/C][C]4955.1713029255[/C][C]5303.44103457066[/C][C]-348.269731645159[/C][/ROW]
[ROW][C]17[/C][C]4558.90869439606[/C][C]5310.85841752564[/C][C]-751.949723129574[/C][/ROW]
[ROW][C]18[/C][C]5281.56552748363[/C][C]5318.27580048062[/C][C]-36.7102729969861[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298188&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298188&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
15498.868511643655192.18029024596306.688221397693
25093.395767206695199.59767320094-106.201905994244
35362.643262096595207.01505615592155.628205940673
44866.162707465745214.4324391109-348.269731645159
54469.90009893635221.84982206588-751.949723129574
65192.556932023875229.26720502086-36.7102729969862
74920.093080300475236.68458797584-316.591507675364
85581.208599654815244.10197093082337.106628723993
95410.792840449845251.5193538858159.273486564039
105490.658095142785258.93673684078231.721358301999
115455.422267599675266.35411979576189.06814780391
125454.008595459765273.77150275074180.237092709021
135587.877107103415281.18888570572306.688221397693
145182.404362666455288.6062686607-106.201905994244
155451.651857556355296.02365161568155.628205940673
164955.17130292555303.44103457066-348.269731645159
174558.908694396065310.85841752564-751.949723129574
185281.565527483635318.27580048062-36.7102729969861



Parameters (Session):
par1 = additive ; par2 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = 18 ; 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')