Free Statistics

of Irreproducible Research!

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 16:24:12 +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/t1481124515u2jgp7qyhcl6nat.htm/, Retrieved Tue, 07 May 2024 21:38:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298198, Retrieved Tue, 07 May 2024 21:38:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact63
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Structural Time Series Models] [N2474 F1 comp] [2016-12-07 15:24:12] [fe6e63930acb843607fc81833855c27b] [Current]
Feedback Forum

Post a new message
Dataseries X:
6788
6783
6795
6835
6889
6926
6957
6984
7159
7121
7165
7208
7217
7250
7281
7298
7310
7362
7387
7414
7449
7473
7513
7522
7588
7602
7643
7651
7661
7688
7728
7750
7759
7760
7806
7864
7859
7926
7978
7999
8056
8104
8146
8171
8199
8212
8242
8269
8279
8323
8350
8372
8403
8412
8460
8484
8498
8527
8519
8537
8526
8549
8594
8767
8690
8657
8680
8714
8746
8671
8654
8677
8765
8760
8812
8822
8837
8997
8875
8905
8927
8950
9010
9086
9161
9248
9285
9335
9354
9267
9403
9469
9464
9630
9724
9764
9806
9869
9907
9914
9922
9950
9982
9981
10045
10067
10080
10051
9962
9896
9849
9854
9847
9845





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R ServerBig Analytics Cloud Computing Center
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time3 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=298198&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]3 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [ROW]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=298198&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298198&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R ServerBig Analytics Cloud Computing Center
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.







Structural Time Series Model -- Interpolation
tObservedLevelSlopeSeasonalStand. Residuals
167886788000
267836783.63380667356-0.321907213784065-0.251405098497128-0.0772685672841303
367956793.201336911360.519652235911834-0.1225434478351180.267632112996357
468356828.396230561944.449682393901850.02776782642385510.922034772041571
568896880.1860841538710.94882410399060.1450188779803471.2326030069995
669266920.5541160813615.50322976349790.1996728039647020.754173410785821
769576953.688486863618.44680345698170.2260116028940730.447050405341169
869846982.0492646378520.18300244387630.2380357597212040.249488665940831
971597135.7623724644444.28935118481280.3692236259408933.34329209050907
1071217129.3108686177434.94977712240720.328977883295168-1.26613734930941
1171657164.6113150879635.01512643465280.3292018488865790.00873063555989765
1272087206.5036196286636.30689894203320.3327324470748620.170967861202134
1372177229.7340178001933.9977460946878-10.622378925111-0.382172311214925
1472507250.9101561989931.61327699185410.647746508037618-0.267392355585926
1572817280.6705176528931.26266721096230.640962638740705-0.0459537485076501
1672987299.4603032478228.89296034480660.641492947617775-0.309275061793948
1773107312.0875919104525.79969176500310.650723915524036-0.403010772665712
1873627357.9784908071329.62214627827390.6396596628631880.497757263812632
1973877386.5386218031729.42003476269090.640146671557412-0.0263127531303979
2074147413.7335924706828.99649901167680.64097123194966-0.0551324846880421
2174497447.5491826611229.91393380595570.6395374969857280.119414363687561
2274737473.0948404455529.08223624941910.640579320533524-0.108248959176606
2375137510.8935677796630.74193865777230.6389133922230770.216009944057723
2475227524.2804425130927.43718314231230.641571261088412-0.430103887882354
2575887582.0643671806533.10546577481850.9554865373166230.820959671355896
2676027603.833454760430.9855386344985-0.27087441506386-0.252657621570641
2776437642.0403478675832.3575899939408-0.2544668273859220.17900508702984
2876517654.5872444487728.5842164668218-0.251791000609647-0.490964069849694
2976617664.4018595121525.0088480645454-0.243172352490002-0.464973640896671
3076887688.4109891909224.8184382943353-0.242741458867861-0.0247666705193028
3177287726.0837524378127.2665107649664-0.2473266353790390.318480027100886
3277507750.6937397856926.7606038973335-0.246561944243131-0.0658240511694493
3377597761.8670133928723.7922067360138-0.242961049129781-0.38625382002359
3477607763.9018933862219.6488195982451-0.238932262066665-0.539175302125059
3578067802.9719894444923.3473632390009-0.2418140065363550.481305087844675
3678647858.7802637914629.5292088441012-0.2456734005526140.804484420022479
3778597864.4372218457525.0381290884232-1.48601739543939-0.628461024984163
3879267920.9074799817330.94160037202030.5159031753823110.721138473523295
3979787973.7615353224335.1074293914570.5528376456682230.543163438901915
4079997999.9482107569733.40829022625650.55378506620236-0.221087302145651
4180568052.2694862970637.01086521480760.5472284694758660.468587656861943
4281048101.4143403158539.32194069500040.5432873199943730.300640504309245
4381468144.7775228538140.09159676621770.542201403270540.100136261087256
4481718172.5320275464737.74207055809160.544876409512039-0.30571596878861
4581998200.1566924319335.81529492494560.546636914158954-0.250724765457788
4682128214.9840485270831.81832172791110.549564187444266-0.520134360935204
4782428242.2212466996630.94588185577140.550076189088343-0.113535459842938
4882698269.1294102166430.17692361038260.550437776792762-0.10007055181791
4982798288.3231312841428.1041708594633-7.49732570592677-0.285046562665964
5083238321.5063992085329.06079853306780.7306811500856710.118466715831756
5183508349.4575036093128.84975482667720.729188203485359-0.0275066198714499
5283728372.284398591927.70259597875620.729699835457174-0.149270770703015
5384038401.9417933334228.0749390195040.7291592434726440.0484361135422353
5484128413.9681826843225.01830732427010.733316948277596-0.397661483444413
5584608456.3477273717828.32478112034990.7295960271434630.430213906695405
5684848483.472263931328.09619878179710.72980359792786-0.0297438019993816
5784988499.3291489172425.76528834020690.731502261427332-0.303320632562613
5885278526.0994039169525.95667855734060.7313904656041620.0249063819985957
5985198523.1355058461920.44889758882960.733968478756268-0.716765208745451
6085378537.3203162194319.25592603766880.734415896131432-0.155251692848206
6185268538.8840589881515.9108773603426-9.93532016595321-0.455139881200011
6285498549.0271646122614.82249691857770.856823391901911-0.135974870811678
6385948588.9001556206619.58780543004890.8847698021672560.620935404902812
6487678743.4073592289945.28529542161930.8752406287730033.34389791799696
6586908703.4541023878229.04965884328510.894836570732049-2.11216372054679
6686578667.1011324096816.59303621438350.908922174958669-1.62067320228254
6786808679.7537549325315.8425756522410.909624233509276-0.097648079483688
6887148710.5713203256618.69453308641480.9074713343840420.371114147492799
6987468742.8131598576221.27456926669560.9059083208388560.335744586514037
7086718683.633046513565.952274821845280.913348503638678-1.99397228397239
7186548658.344557947710.002569287912588260.915663536278134-0.774280916109927
7286778673.52892869682.893910090178360.9147621006436580.376276726794295
7387658755.0611610937717.7802466926281-3.190386338751742.01095852254534
7487608761.5438449046915.64553977972070.212244614354223-0.268341372350793
7588128806.7799663503221.2754741464490.2404840033510670.733467554650225
7688228822.6665661417120.24908708954270.24080965520026-0.133561525979471
7788378837.6453832214719.24525638564760.241846337768138-0.130599542431184
7889978976.6232731981742.04952013334240.2197826503126512.96707685280601
7988758895.4987891606818.59069371095390.238560066602611-3.05248708902154
8089058906.1048026210117.07001809935420.239542265152621-0.197883069894946
8189278926.243999380617.65453636369240.2392392838968280.0760652309875495
8289508948.9162905439218.61015594498870.2388422526296680.124360794425303
8390109003.6765386006425.49487422750760.2365501865508020.895965463612855
8490869077.6097887898134.71991242340150.2340893511389271.20054249543735
8591619153.5891910300142.53721501875330.5137662397601611.05054932408264
8692489240.7664294652750.98051345831780.222026463148361.06618712113575
8792859285.7861263604849.8462558094590.217051396172911-0.147751236249862
8893359334.9053316281849.70777955201450.217089788117069-0.0180198607366465
8993549358.2214554290544.68099786466270.221626168286903-0.654015955628227
9092679286.3771976477822.48767144433140.24038982586176-2.88767490081837
9194039389.2384399985837.79506888815340.2296829707349621.99185480152133
9294699462.7590877703644.59900503849240.2258427831161860.885396825720449
9394649470.0522593879537.49415424872460.229060895046048-0.924584721489595
9496309612.1630833369857.41825981469620.2218274303215312.59286332540615
9597249715.969832421566.25290651337560.2192572854948141.14972979596327
9697649766.4379290186763.2466923534260.219958032894122-0.391228285395051
9798069812.4351092798259.9763441663596-3.54898046890897-0.43777341133578
9898699869.2025909880359.36894283197070.30547936576458-0.0769683960879275
9999079909.8579849323355.80766665674730.291618585258371-0.463852539153868
10099149921.1944463118747.33758186995320.293703771591952-1.10222042356786
10199229928.4484876985939.70298368684830.299821738065744-0.993339722758893
10299509952.3570502118536.69479459143320.302080138326844-0.391418401336358
10399829982.7570082895435.49592146095220.30282475523976-0.15600421980329
10499819986.1066189275729.37363605887140.305893096891951-0.796701627041405
1051004510040.485713567934.13591491903630.303977702714450.619739823708681
1061006710067.837851092532.8439481420480.304394203223489-0.168133384317733
1071008010082.719278560229.42298859164070.305277919154801-0.445200564590337
1081005110059.54856087419.40649177218230.307351178182198-1.30354772825866
10999629986.288228328451.82878810951457-8.77244631005813-2.34576592779511
11098969908.30411709871-13.28825101599910.413602805535598-1.92089857344148
11198499855.29795329796-20.84736115261730.387150848510304-0.984484615891793
11298549850.85184983692-17.72355175784820.3864593034068980.406507799705957
11398479844.67168497451-15.52492886662980.3848749294803110.286070439205617
11498459842.38757604747-13.00310027591290.3831723918073940.328140489975303

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Interpolation \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 6788 & 6788 & 0 & 0 & 0 \tabularnewline
2 & 6783 & 6783.63380667356 & -0.321907213784065 & -0.251405098497128 & -0.0772685672841303 \tabularnewline
3 & 6795 & 6793.20133691136 & 0.519652235911834 & -0.122543447835118 & 0.267632112996357 \tabularnewline
4 & 6835 & 6828.39623056194 & 4.44968239390185 & 0.0277678264238551 & 0.922034772041571 \tabularnewline
5 & 6889 & 6880.18608415387 & 10.9488241039906 & 0.145018877980347 & 1.2326030069995 \tabularnewline
6 & 6926 & 6920.55411608136 & 15.5032297634979 & 0.199672803964702 & 0.754173410785821 \tabularnewline
7 & 6957 & 6953.6884868636 & 18.4468034569817 & 0.226011602894073 & 0.447050405341169 \tabularnewline
8 & 6984 & 6982.04926463785 & 20.1830024438763 & 0.238035759721204 & 0.249488665940831 \tabularnewline
9 & 7159 & 7135.76237246444 & 44.2893511848128 & 0.369223625940893 & 3.34329209050907 \tabularnewline
10 & 7121 & 7129.31086861774 & 34.9497771224072 & 0.328977883295168 & -1.26613734930941 \tabularnewline
11 & 7165 & 7164.61131508796 & 35.0151264346528 & 0.329201848886579 & 0.00873063555989765 \tabularnewline
12 & 7208 & 7206.50361962866 & 36.3068989420332 & 0.332732447074862 & 0.170967861202134 \tabularnewline
13 & 7217 & 7229.73401780019 & 33.9977460946878 & -10.622378925111 & -0.382172311214925 \tabularnewline
14 & 7250 & 7250.91015619899 & 31.6132769918541 & 0.647746508037618 & -0.267392355585926 \tabularnewline
15 & 7281 & 7280.67051765289 & 31.2626672109623 & 0.640962638740705 & -0.0459537485076501 \tabularnewline
16 & 7298 & 7299.46030324782 & 28.8929603448066 & 0.641492947617775 & -0.309275061793948 \tabularnewline
17 & 7310 & 7312.08759191045 & 25.7996917650031 & 0.650723915524036 & -0.403010772665712 \tabularnewline
18 & 7362 & 7357.97849080713 & 29.6221462782739 & 0.639659662863188 & 0.497757263812632 \tabularnewline
19 & 7387 & 7386.53862180317 & 29.4200347626909 & 0.640146671557412 & -0.0263127531303979 \tabularnewline
20 & 7414 & 7413.73359247068 & 28.9964990116768 & 0.64097123194966 & -0.0551324846880421 \tabularnewline
21 & 7449 & 7447.54918266112 & 29.9139338059557 & 0.639537496985728 & 0.119414363687561 \tabularnewline
22 & 7473 & 7473.09484044555 & 29.0822362494191 & 0.640579320533524 & -0.108248959176606 \tabularnewline
23 & 7513 & 7510.89356777966 & 30.7419386577723 & 0.638913392223077 & 0.216009944057723 \tabularnewline
24 & 7522 & 7524.28044251309 & 27.4371831423123 & 0.641571261088412 & -0.430103887882354 \tabularnewline
25 & 7588 & 7582.06436718065 & 33.1054657748185 & 0.955486537316623 & 0.820959671355896 \tabularnewline
26 & 7602 & 7603.8334547604 & 30.9855386344985 & -0.27087441506386 & -0.252657621570641 \tabularnewline
27 & 7643 & 7642.04034786758 & 32.3575899939408 & -0.254466827385922 & 0.17900508702984 \tabularnewline
28 & 7651 & 7654.58724444877 & 28.5842164668218 & -0.251791000609647 & -0.490964069849694 \tabularnewline
29 & 7661 & 7664.40185951215 & 25.0088480645454 & -0.243172352490002 & -0.464973640896671 \tabularnewline
30 & 7688 & 7688.41098919092 & 24.8184382943353 & -0.242741458867861 & -0.0247666705193028 \tabularnewline
31 & 7728 & 7726.08375243781 & 27.2665107649664 & -0.247326635379039 & 0.318480027100886 \tabularnewline
32 & 7750 & 7750.69373978569 & 26.7606038973335 & -0.246561944243131 & -0.0658240511694493 \tabularnewline
33 & 7759 & 7761.86701339287 & 23.7922067360138 & -0.242961049129781 & -0.38625382002359 \tabularnewline
34 & 7760 & 7763.90189338622 & 19.6488195982451 & -0.238932262066665 & -0.539175302125059 \tabularnewline
35 & 7806 & 7802.97198944449 & 23.3473632390009 & -0.241814006536355 & 0.481305087844675 \tabularnewline
36 & 7864 & 7858.78026379146 & 29.5292088441012 & -0.245673400552614 & 0.804484420022479 \tabularnewline
37 & 7859 & 7864.43722184575 & 25.0381290884232 & -1.48601739543939 & -0.628461024984163 \tabularnewline
38 & 7926 & 7920.90747998173 & 30.9416003720203 & 0.515903175382311 & 0.721138473523295 \tabularnewline
39 & 7978 & 7973.76153532243 & 35.107429391457 & 0.552837645668223 & 0.543163438901915 \tabularnewline
40 & 7999 & 7999.94821075697 & 33.4082902262565 & 0.55378506620236 & -0.221087302145651 \tabularnewline
41 & 8056 & 8052.26948629706 & 37.0108652148076 & 0.547228469475866 & 0.468587656861943 \tabularnewline
42 & 8104 & 8101.41434031585 & 39.3219406950004 & 0.543287319994373 & 0.300640504309245 \tabularnewline
43 & 8146 & 8144.77752285381 & 40.0915967662177 & 0.54220140327054 & 0.100136261087256 \tabularnewline
44 & 8171 & 8172.53202754647 & 37.7420705580916 & 0.544876409512039 & -0.30571596878861 \tabularnewline
45 & 8199 & 8200.15669243193 & 35.8152949249456 & 0.546636914158954 & -0.250724765457788 \tabularnewline
46 & 8212 & 8214.98404852708 & 31.8183217279111 & 0.549564187444266 & -0.520134360935204 \tabularnewline
47 & 8242 & 8242.22124669966 & 30.9458818557714 & 0.550076189088343 & -0.113535459842938 \tabularnewline
48 & 8269 & 8269.12941021664 & 30.1769236103826 & 0.550437776792762 & -0.10007055181791 \tabularnewline
49 & 8279 & 8288.32313128414 & 28.1041708594633 & -7.49732570592677 & -0.285046562665964 \tabularnewline
50 & 8323 & 8321.50639920853 & 29.0607985330678 & 0.730681150085671 & 0.118466715831756 \tabularnewline
51 & 8350 & 8349.45750360931 & 28.8497548266772 & 0.729188203485359 & -0.0275066198714499 \tabularnewline
52 & 8372 & 8372.2843985919 & 27.7025959787562 & 0.729699835457174 & -0.149270770703015 \tabularnewline
53 & 8403 & 8401.94179333342 & 28.074939019504 & 0.729159243472644 & 0.0484361135422353 \tabularnewline
54 & 8412 & 8413.96818268432 & 25.0183073242701 & 0.733316948277596 & -0.397661483444413 \tabularnewline
55 & 8460 & 8456.34772737178 & 28.3247811203499 & 0.729596027143463 & 0.430213906695405 \tabularnewline
56 & 8484 & 8483.4722639313 & 28.0961987817971 & 0.72980359792786 & -0.0297438019993816 \tabularnewline
57 & 8498 & 8499.32914891724 & 25.7652883402069 & 0.731502261427332 & -0.303320632562613 \tabularnewline
58 & 8527 & 8526.09940391695 & 25.9566785573406 & 0.731390465604162 & 0.0249063819985957 \tabularnewline
59 & 8519 & 8523.13550584619 & 20.4488975888296 & 0.733968478756268 & -0.716765208745451 \tabularnewline
60 & 8537 & 8537.32031621943 & 19.2559260376688 & 0.734415896131432 & -0.155251692848206 \tabularnewline
61 & 8526 & 8538.88405898815 & 15.9108773603426 & -9.93532016595321 & -0.455139881200011 \tabularnewline
62 & 8549 & 8549.02716461226 & 14.8224969185777 & 0.856823391901911 & -0.135974870811678 \tabularnewline
63 & 8594 & 8588.90015562066 & 19.5878054300489 & 0.884769802167256 & 0.620935404902812 \tabularnewline
64 & 8767 & 8743.40735922899 & 45.2852954216193 & 0.875240628773003 & 3.34389791799696 \tabularnewline
65 & 8690 & 8703.45410238782 & 29.0496588432851 & 0.894836570732049 & -2.11216372054679 \tabularnewline
66 & 8657 & 8667.10113240968 & 16.5930362143835 & 0.908922174958669 & -1.62067320228254 \tabularnewline
67 & 8680 & 8679.75375493253 & 15.842575652241 & 0.909624233509276 & -0.097648079483688 \tabularnewline
68 & 8714 & 8710.57132032566 & 18.6945330864148 & 0.907471334384042 & 0.371114147492799 \tabularnewline
69 & 8746 & 8742.81315985762 & 21.2745692666956 & 0.905908320838856 & 0.335744586514037 \tabularnewline
70 & 8671 & 8683.63304651356 & 5.95227482184528 & 0.913348503638678 & -1.99397228397239 \tabularnewline
71 & 8654 & 8658.34455794771 & 0.00256928791258826 & 0.915663536278134 & -0.774280916109927 \tabularnewline
72 & 8677 & 8673.5289286968 & 2.89391009017836 & 0.914762100643658 & 0.376276726794295 \tabularnewline
73 & 8765 & 8755.06116109377 & 17.7802466926281 & -3.19038633875174 & 2.01095852254534 \tabularnewline
74 & 8760 & 8761.54384490469 & 15.6455397797207 & 0.212244614354223 & -0.268341372350793 \tabularnewline
75 & 8812 & 8806.77996635032 & 21.275474146449 & 0.240484003351067 & 0.733467554650225 \tabularnewline
76 & 8822 & 8822.66656614171 & 20.2490870895427 & 0.24080965520026 & -0.133561525979471 \tabularnewline
77 & 8837 & 8837.64538322147 & 19.2452563856476 & 0.241846337768138 & -0.130599542431184 \tabularnewline
78 & 8997 & 8976.62327319817 & 42.0495201333424 & 0.219782650312651 & 2.96707685280601 \tabularnewline
79 & 8875 & 8895.49878916068 & 18.5906937109539 & 0.238560066602611 & -3.05248708902154 \tabularnewline
80 & 8905 & 8906.10480262101 & 17.0700180993542 & 0.239542265152621 & -0.197883069894946 \tabularnewline
81 & 8927 & 8926.2439993806 & 17.6545363636924 & 0.239239283896828 & 0.0760652309875495 \tabularnewline
82 & 8950 & 8948.91629054392 & 18.6101559449887 & 0.238842252629668 & 0.124360794425303 \tabularnewline
83 & 9010 & 9003.67653860064 & 25.4948742275076 & 0.236550186550802 & 0.895965463612855 \tabularnewline
84 & 9086 & 9077.60978878981 & 34.7199124234015 & 0.234089351138927 & 1.20054249543735 \tabularnewline
85 & 9161 & 9153.58919103001 & 42.5372150187533 & 0.513766239760161 & 1.05054932408264 \tabularnewline
86 & 9248 & 9240.76642946527 & 50.9805134583178 & 0.22202646314836 & 1.06618712113575 \tabularnewline
87 & 9285 & 9285.78612636048 & 49.846255809459 & 0.217051396172911 & -0.147751236249862 \tabularnewline
88 & 9335 & 9334.90533162818 & 49.7077795520145 & 0.217089788117069 & -0.0180198607366465 \tabularnewline
89 & 9354 & 9358.22145542905 & 44.6809978646627 & 0.221626168286903 & -0.654015955628227 \tabularnewline
90 & 9267 & 9286.37719764778 & 22.4876714443314 & 0.24038982586176 & -2.88767490081837 \tabularnewline
91 & 9403 & 9389.23843999858 & 37.7950688881534 & 0.229682970734962 & 1.99185480152133 \tabularnewline
92 & 9469 & 9462.75908777036 & 44.5990050384924 & 0.225842783116186 & 0.885396825720449 \tabularnewline
93 & 9464 & 9470.05225938795 & 37.4941542487246 & 0.229060895046048 & -0.924584721489595 \tabularnewline
94 & 9630 & 9612.16308333698 & 57.4182598146962 & 0.221827430321531 & 2.59286332540615 \tabularnewline
95 & 9724 & 9715.9698324215 & 66.2529065133756 & 0.219257285494814 & 1.14972979596327 \tabularnewline
96 & 9764 & 9766.43792901867 & 63.246692353426 & 0.219958032894122 & -0.391228285395051 \tabularnewline
97 & 9806 & 9812.43510927982 & 59.9763441663596 & -3.54898046890897 & -0.43777341133578 \tabularnewline
98 & 9869 & 9869.20259098803 & 59.3689428319707 & 0.30547936576458 & -0.0769683960879275 \tabularnewline
99 & 9907 & 9909.85798493233 & 55.8076666567473 & 0.291618585258371 & -0.463852539153868 \tabularnewline
100 & 9914 & 9921.19444631187 & 47.3375818699532 & 0.293703771591952 & -1.10222042356786 \tabularnewline
101 & 9922 & 9928.44848769859 & 39.7029836868483 & 0.299821738065744 & -0.993339722758893 \tabularnewline
102 & 9950 & 9952.35705021185 & 36.6947945914332 & 0.302080138326844 & -0.391418401336358 \tabularnewline
103 & 9982 & 9982.75700828954 & 35.4959214609522 & 0.30282475523976 & -0.15600421980329 \tabularnewline
104 & 9981 & 9986.10661892757 & 29.3736360588714 & 0.305893096891951 & -0.796701627041405 \tabularnewline
105 & 10045 & 10040.4857135679 & 34.1359149190363 & 0.30397770271445 & 0.619739823708681 \tabularnewline
106 & 10067 & 10067.8378510925 & 32.843948142048 & 0.304394203223489 & -0.168133384317733 \tabularnewline
107 & 10080 & 10082.7192785602 & 29.4229885916407 & 0.305277919154801 & -0.445200564590337 \tabularnewline
108 & 10051 & 10059.548560874 & 19.4064917721823 & 0.307351178182198 & -1.30354772825866 \tabularnewline
109 & 9962 & 9986.28822832845 & 1.82878810951457 & -8.77244631005813 & -2.34576592779511 \tabularnewline
110 & 9896 & 9908.30411709871 & -13.2882510159991 & 0.413602805535598 & -1.92089857344148 \tabularnewline
111 & 9849 & 9855.29795329796 & -20.8473611526173 & 0.387150848510304 & -0.984484615891793 \tabularnewline
112 & 9854 & 9850.85184983692 & -17.7235517578482 & 0.386459303406898 & 0.406507799705957 \tabularnewline
113 & 9847 & 9844.67168497451 & -15.5249288666298 & 0.384874929480311 & 0.286070439205617 \tabularnewline
114 & 9845 & 9842.38757604747 & -13.0031002759129 & 0.383172391807394 & 0.328140489975303 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298198&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]6788[/C][C]6788[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]6783[/C][C]6783.63380667356[/C][C]-0.321907213784065[/C][C]-0.251405098497128[/C][C]-0.0772685672841303[/C][/ROW]
[ROW][C]3[/C][C]6795[/C][C]6793.20133691136[/C][C]0.519652235911834[/C][C]-0.122543447835118[/C][C]0.267632112996357[/C][/ROW]
[ROW][C]4[/C][C]6835[/C][C]6828.39623056194[/C][C]4.44968239390185[/C][C]0.0277678264238551[/C][C]0.922034772041571[/C][/ROW]
[ROW][C]5[/C][C]6889[/C][C]6880.18608415387[/C][C]10.9488241039906[/C][C]0.145018877980347[/C][C]1.2326030069995[/C][/ROW]
[ROW][C]6[/C][C]6926[/C][C]6920.55411608136[/C][C]15.5032297634979[/C][C]0.199672803964702[/C][C]0.754173410785821[/C][/ROW]
[ROW][C]7[/C][C]6957[/C][C]6953.6884868636[/C][C]18.4468034569817[/C][C]0.226011602894073[/C][C]0.447050405341169[/C][/ROW]
[ROW][C]8[/C][C]6984[/C][C]6982.04926463785[/C][C]20.1830024438763[/C][C]0.238035759721204[/C][C]0.249488665940831[/C][/ROW]
[ROW][C]9[/C][C]7159[/C][C]7135.76237246444[/C][C]44.2893511848128[/C][C]0.369223625940893[/C][C]3.34329209050907[/C][/ROW]
[ROW][C]10[/C][C]7121[/C][C]7129.31086861774[/C][C]34.9497771224072[/C][C]0.328977883295168[/C][C]-1.26613734930941[/C][/ROW]
[ROW][C]11[/C][C]7165[/C][C]7164.61131508796[/C][C]35.0151264346528[/C][C]0.329201848886579[/C][C]0.00873063555989765[/C][/ROW]
[ROW][C]12[/C][C]7208[/C][C]7206.50361962866[/C][C]36.3068989420332[/C][C]0.332732447074862[/C][C]0.170967861202134[/C][/ROW]
[ROW][C]13[/C][C]7217[/C][C]7229.73401780019[/C][C]33.9977460946878[/C][C]-10.622378925111[/C][C]-0.382172311214925[/C][/ROW]
[ROW][C]14[/C][C]7250[/C][C]7250.91015619899[/C][C]31.6132769918541[/C][C]0.647746508037618[/C][C]-0.267392355585926[/C][/ROW]
[ROW][C]15[/C][C]7281[/C][C]7280.67051765289[/C][C]31.2626672109623[/C][C]0.640962638740705[/C][C]-0.0459537485076501[/C][/ROW]
[ROW][C]16[/C][C]7298[/C][C]7299.46030324782[/C][C]28.8929603448066[/C][C]0.641492947617775[/C][C]-0.309275061793948[/C][/ROW]
[ROW][C]17[/C][C]7310[/C][C]7312.08759191045[/C][C]25.7996917650031[/C][C]0.650723915524036[/C][C]-0.403010772665712[/C][/ROW]
[ROW][C]18[/C][C]7362[/C][C]7357.97849080713[/C][C]29.6221462782739[/C][C]0.639659662863188[/C][C]0.497757263812632[/C][/ROW]
[ROW][C]19[/C][C]7387[/C][C]7386.53862180317[/C][C]29.4200347626909[/C][C]0.640146671557412[/C][C]-0.0263127531303979[/C][/ROW]
[ROW][C]20[/C][C]7414[/C][C]7413.73359247068[/C][C]28.9964990116768[/C][C]0.64097123194966[/C][C]-0.0551324846880421[/C][/ROW]
[ROW][C]21[/C][C]7449[/C][C]7447.54918266112[/C][C]29.9139338059557[/C][C]0.639537496985728[/C][C]0.119414363687561[/C][/ROW]
[ROW][C]22[/C][C]7473[/C][C]7473.09484044555[/C][C]29.0822362494191[/C][C]0.640579320533524[/C][C]-0.108248959176606[/C][/ROW]
[ROW][C]23[/C][C]7513[/C][C]7510.89356777966[/C][C]30.7419386577723[/C][C]0.638913392223077[/C][C]0.216009944057723[/C][/ROW]
[ROW][C]24[/C][C]7522[/C][C]7524.28044251309[/C][C]27.4371831423123[/C][C]0.641571261088412[/C][C]-0.430103887882354[/C][/ROW]
[ROW][C]25[/C][C]7588[/C][C]7582.06436718065[/C][C]33.1054657748185[/C][C]0.955486537316623[/C][C]0.820959671355896[/C][/ROW]
[ROW][C]26[/C][C]7602[/C][C]7603.8334547604[/C][C]30.9855386344985[/C][C]-0.27087441506386[/C][C]-0.252657621570641[/C][/ROW]
[ROW][C]27[/C][C]7643[/C][C]7642.04034786758[/C][C]32.3575899939408[/C][C]-0.254466827385922[/C][C]0.17900508702984[/C][/ROW]
[ROW][C]28[/C][C]7651[/C][C]7654.58724444877[/C][C]28.5842164668218[/C][C]-0.251791000609647[/C][C]-0.490964069849694[/C][/ROW]
[ROW][C]29[/C][C]7661[/C][C]7664.40185951215[/C][C]25.0088480645454[/C][C]-0.243172352490002[/C][C]-0.464973640896671[/C][/ROW]
[ROW][C]30[/C][C]7688[/C][C]7688.41098919092[/C][C]24.8184382943353[/C][C]-0.242741458867861[/C][C]-0.0247666705193028[/C][/ROW]
[ROW][C]31[/C][C]7728[/C][C]7726.08375243781[/C][C]27.2665107649664[/C][C]-0.247326635379039[/C][C]0.318480027100886[/C][/ROW]
[ROW][C]32[/C][C]7750[/C][C]7750.69373978569[/C][C]26.7606038973335[/C][C]-0.246561944243131[/C][C]-0.0658240511694493[/C][/ROW]
[ROW][C]33[/C][C]7759[/C][C]7761.86701339287[/C][C]23.7922067360138[/C][C]-0.242961049129781[/C][C]-0.38625382002359[/C][/ROW]
[ROW][C]34[/C][C]7760[/C][C]7763.90189338622[/C][C]19.6488195982451[/C][C]-0.238932262066665[/C][C]-0.539175302125059[/C][/ROW]
[ROW][C]35[/C][C]7806[/C][C]7802.97198944449[/C][C]23.3473632390009[/C][C]-0.241814006536355[/C][C]0.481305087844675[/C][/ROW]
[ROW][C]36[/C][C]7864[/C][C]7858.78026379146[/C][C]29.5292088441012[/C][C]-0.245673400552614[/C][C]0.804484420022479[/C][/ROW]
[ROW][C]37[/C][C]7859[/C][C]7864.43722184575[/C][C]25.0381290884232[/C][C]-1.48601739543939[/C][C]-0.628461024984163[/C][/ROW]
[ROW][C]38[/C][C]7926[/C][C]7920.90747998173[/C][C]30.9416003720203[/C][C]0.515903175382311[/C][C]0.721138473523295[/C][/ROW]
[ROW][C]39[/C][C]7978[/C][C]7973.76153532243[/C][C]35.107429391457[/C][C]0.552837645668223[/C][C]0.543163438901915[/C][/ROW]
[ROW][C]40[/C][C]7999[/C][C]7999.94821075697[/C][C]33.4082902262565[/C][C]0.55378506620236[/C][C]-0.221087302145651[/C][/ROW]
[ROW][C]41[/C][C]8056[/C][C]8052.26948629706[/C][C]37.0108652148076[/C][C]0.547228469475866[/C][C]0.468587656861943[/C][/ROW]
[ROW][C]42[/C][C]8104[/C][C]8101.41434031585[/C][C]39.3219406950004[/C][C]0.543287319994373[/C][C]0.300640504309245[/C][/ROW]
[ROW][C]43[/C][C]8146[/C][C]8144.77752285381[/C][C]40.0915967662177[/C][C]0.54220140327054[/C][C]0.100136261087256[/C][/ROW]
[ROW][C]44[/C][C]8171[/C][C]8172.53202754647[/C][C]37.7420705580916[/C][C]0.544876409512039[/C][C]-0.30571596878861[/C][/ROW]
[ROW][C]45[/C][C]8199[/C][C]8200.15669243193[/C][C]35.8152949249456[/C][C]0.546636914158954[/C][C]-0.250724765457788[/C][/ROW]
[ROW][C]46[/C][C]8212[/C][C]8214.98404852708[/C][C]31.8183217279111[/C][C]0.549564187444266[/C][C]-0.520134360935204[/C][/ROW]
[ROW][C]47[/C][C]8242[/C][C]8242.22124669966[/C][C]30.9458818557714[/C][C]0.550076189088343[/C][C]-0.113535459842938[/C][/ROW]
[ROW][C]48[/C][C]8269[/C][C]8269.12941021664[/C][C]30.1769236103826[/C][C]0.550437776792762[/C][C]-0.10007055181791[/C][/ROW]
[ROW][C]49[/C][C]8279[/C][C]8288.32313128414[/C][C]28.1041708594633[/C][C]-7.49732570592677[/C][C]-0.285046562665964[/C][/ROW]
[ROW][C]50[/C][C]8323[/C][C]8321.50639920853[/C][C]29.0607985330678[/C][C]0.730681150085671[/C][C]0.118466715831756[/C][/ROW]
[ROW][C]51[/C][C]8350[/C][C]8349.45750360931[/C][C]28.8497548266772[/C][C]0.729188203485359[/C][C]-0.0275066198714499[/C][/ROW]
[ROW][C]52[/C][C]8372[/C][C]8372.2843985919[/C][C]27.7025959787562[/C][C]0.729699835457174[/C][C]-0.149270770703015[/C][/ROW]
[ROW][C]53[/C][C]8403[/C][C]8401.94179333342[/C][C]28.074939019504[/C][C]0.729159243472644[/C][C]0.0484361135422353[/C][/ROW]
[ROW][C]54[/C][C]8412[/C][C]8413.96818268432[/C][C]25.0183073242701[/C][C]0.733316948277596[/C][C]-0.397661483444413[/C][/ROW]
[ROW][C]55[/C][C]8460[/C][C]8456.34772737178[/C][C]28.3247811203499[/C][C]0.729596027143463[/C][C]0.430213906695405[/C][/ROW]
[ROW][C]56[/C][C]8484[/C][C]8483.4722639313[/C][C]28.0961987817971[/C][C]0.72980359792786[/C][C]-0.0297438019993816[/C][/ROW]
[ROW][C]57[/C][C]8498[/C][C]8499.32914891724[/C][C]25.7652883402069[/C][C]0.731502261427332[/C][C]-0.303320632562613[/C][/ROW]
[ROW][C]58[/C][C]8527[/C][C]8526.09940391695[/C][C]25.9566785573406[/C][C]0.731390465604162[/C][C]0.0249063819985957[/C][/ROW]
[ROW][C]59[/C][C]8519[/C][C]8523.13550584619[/C][C]20.4488975888296[/C][C]0.733968478756268[/C][C]-0.716765208745451[/C][/ROW]
[ROW][C]60[/C][C]8537[/C][C]8537.32031621943[/C][C]19.2559260376688[/C][C]0.734415896131432[/C][C]-0.155251692848206[/C][/ROW]
[ROW][C]61[/C][C]8526[/C][C]8538.88405898815[/C][C]15.9108773603426[/C][C]-9.93532016595321[/C][C]-0.455139881200011[/C][/ROW]
[ROW][C]62[/C][C]8549[/C][C]8549.02716461226[/C][C]14.8224969185777[/C][C]0.856823391901911[/C][C]-0.135974870811678[/C][/ROW]
[ROW][C]63[/C][C]8594[/C][C]8588.90015562066[/C][C]19.5878054300489[/C][C]0.884769802167256[/C][C]0.620935404902812[/C][/ROW]
[ROW][C]64[/C][C]8767[/C][C]8743.40735922899[/C][C]45.2852954216193[/C][C]0.875240628773003[/C][C]3.34389791799696[/C][/ROW]
[ROW][C]65[/C][C]8690[/C][C]8703.45410238782[/C][C]29.0496588432851[/C][C]0.894836570732049[/C][C]-2.11216372054679[/C][/ROW]
[ROW][C]66[/C][C]8657[/C][C]8667.10113240968[/C][C]16.5930362143835[/C][C]0.908922174958669[/C][C]-1.62067320228254[/C][/ROW]
[ROW][C]67[/C][C]8680[/C][C]8679.75375493253[/C][C]15.842575652241[/C][C]0.909624233509276[/C][C]-0.097648079483688[/C][/ROW]
[ROW][C]68[/C][C]8714[/C][C]8710.57132032566[/C][C]18.6945330864148[/C][C]0.907471334384042[/C][C]0.371114147492799[/C][/ROW]
[ROW][C]69[/C][C]8746[/C][C]8742.81315985762[/C][C]21.2745692666956[/C][C]0.905908320838856[/C][C]0.335744586514037[/C][/ROW]
[ROW][C]70[/C][C]8671[/C][C]8683.63304651356[/C][C]5.95227482184528[/C][C]0.913348503638678[/C][C]-1.99397228397239[/C][/ROW]
[ROW][C]71[/C][C]8654[/C][C]8658.34455794771[/C][C]0.00256928791258826[/C][C]0.915663536278134[/C][C]-0.774280916109927[/C][/ROW]
[ROW][C]72[/C][C]8677[/C][C]8673.5289286968[/C][C]2.89391009017836[/C][C]0.914762100643658[/C][C]0.376276726794295[/C][/ROW]
[ROW][C]73[/C][C]8765[/C][C]8755.06116109377[/C][C]17.7802466926281[/C][C]-3.19038633875174[/C][C]2.01095852254534[/C][/ROW]
[ROW][C]74[/C][C]8760[/C][C]8761.54384490469[/C][C]15.6455397797207[/C][C]0.212244614354223[/C][C]-0.268341372350793[/C][/ROW]
[ROW][C]75[/C][C]8812[/C][C]8806.77996635032[/C][C]21.275474146449[/C][C]0.240484003351067[/C][C]0.733467554650225[/C][/ROW]
[ROW][C]76[/C][C]8822[/C][C]8822.66656614171[/C][C]20.2490870895427[/C][C]0.24080965520026[/C][C]-0.133561525979471[/C][/ROW]
[ROW][C]77[/C][C]8837[/C][C]8837.64538322147[/C][C]19.2452563856476[/C][C]0.241846337768138[/C][C]-0.130599542431184[/C][/ROW]
[ROW][C]78[/C][C]8997[/C][C]8976.62327319817[/C][C]42.0495201333424[/C][C]0.219782650312651[/C][C]2.96707685280601[/C][/ROW]
[ROW][C]79[/C][C]8875[/C][C]8895.49878916068[/C][C]18.5906937109539[/C][C]0.238560066602611[/C][C]-3.05248708902154[/C][/ROW]
[ROW][C]80[/C][C]8905[/C][C]8906.10480262101[/C][C]17.0700180993542[/C][C]0.239542265152621[/C][C]-0.197883069894946[/C][/ROW]
[ROW][C]81[/C][C]8927[/C][C]8926.2439993806[/C][C]17.6545363636924[/C][C]0.239239283896828[/C][C]0.0760652309875495[/C][/ROW]
[ROW][C]82[/C][C]8950[/C][C]8948.91629054392[/C][C]18.6101559449887[/C][C]0.238842252629668[/C][C]0.124360794425303[/C][/ROW]
[ROW][C]83[/C][C]9010[/C][C]9003.67653860064[/C][C]25.4948742275076[/C][C]0.236550186550802[/C][C]0.895965463612855[/C][/ROW]
[ROW][C]84[/C][C]9086[/C][C]9077.60978878981[/C][C]34.7199124234015[/C][C]0.234089351138927[/C][C]1.20054249543735[/C][/ROW]
[ROW][C]85[/C][C]9161[/C][C]9153.58919103001[/C][C]42.5372150187533[/C][C]0.513766239760161[/C][C]1.05054932408264[/C][/ROW]
[ROW][C]86[/C][C]9248[/C][C]9240.76642946527[/C][C]50.9805134583178[/C][C]0.22202646314836[/C][C]1.06618712113575[/C][/ROW]
[ROW][C]87[/C][C]9285[/C][C]9285.78612636048[/C][C]49.846255809459[/C][C]0.217051396172911[/C][C]-0.147751236249862[/C][/ROW]
[ROW][C]88[/C][C]9335[/C][C]9334.90533162818[/C][C]49.7077795520145[/C][C]0.217089788117069[/C][C]-0.0180198607366465[/C][/ROW]
[ROW][C]89[/C][C]9354[/C][C]9358.22145542905[/C][C]44.6809978646627[/C][C]0.221626168286903[/C][C]-0.654015955628227[/C][/ROW]
[ROW][C]90[/C][C]9267[/C][C]9286.37719764778[/C][C]22.4876714443314[/C][C]0.24038982586176[/C][C]-2.88767490081837[/C][/ROW]
[ROW][C]91[/C][C]9403[/C][C]9389.23843999858[/C][C]37.7950688881534[/C][C]0.229682970734962[/C][C]1.99185480152133[/C][/ROW]
[ROW][C]92[/C][C]9469[/C][C]9462.75908777036[/C][C]44.5990050384924[/C][C]0.225842783116186[/C][C]0.885396825720449[/C][/ROW]
[ROW][C]93[/C][C]9464[/C][C]9470.05225938795[/C][C]37.4941542487246[/C][C]0.229060895046048[/C][C]-0.924584721489595[/C][/ROW]
[ROW][C]94[/C][C]9630[/C][C]9612.16308333698[/C][C]57.4182598146962[/C][C]0.221827430321531[/C][C]2.59286332540615[/C][/ROW]
[ROW][C]95[/C][C]9724[/C][C]9715.9698324215[/C][C]66.2529065133756[/C][C]0.219257285494814[/C][C]1.14972979596327[/C][/ROW]
[ROW][C]96[/C][C]9764[/C][C]9766.43792901867[/C][C]63.246692353426[/C][C]0.219958032894122[/C][C]-0.391228285395051[/C][/ROW]
[ROW][C]97[/C][C]9806[/C][C]9812.43510927982[/C][C]59.9763441663596[/C][C]-3.54898046890897[/C][C]-0.43777341133578[/C][/ROW]
[ROW][C]98[/C][C]9869[/C][C]9869.20259098803[/C][C]59.3689428319707[/C][C]0.30547936576458[/C][C]-0.0769683960879275[/C][/ROW]
[ROW][C]99[/C][C]9907[/C][C]9909.85798493233[/C][C]55.8076666567473[/C][C]0.291618585258371[/C][C]-0.463852539153868[/C][/ROW]
[ROW][C]100[/C][C]9914[/C][C]9921.19444631187[/C][C]47.3375818699532[/C][C]0.293703771591952[/C][C]-1.10222042356786[/C][/ROW]
[ROW][C]101[/C][C]9922[/C][C]9928.44848769859[/C][C]39.7029836868483[/C][C]0.299821738065744[/C][C]-0.993339722758893[/C][/ROW]
[ROW][C]102[/C][C]9950[/C][C]9952.35705021185[/C][C]36.6947945914332[/C][C]0.302080138326844[/C][C]-0.391418401336358[/C][/ROW]
[ROW][C]103[/C][C]9982[/C][C]9982.75700828954[/C][C]35.4959214609522[/C][C]0.30282475523976[/C][C]-0.15600421980329[/C][/ROW]
[ROW][C]104[/C][C]9981[/C][C]9986.10661892757[/C][C]29.3736360588714[/C][C]0.305893096891951[/C][C]-0.796701627041405[/C][/ROW]
[ROW][C]105[/C][C]10045[/C][C]10040.4857135679[/C][C]34.1359149190363[/C][C]0.30397770271445[/C][C]0.619739823708681[/C][/ROW]
[ROW][C]106[/C][C]10067[/C][C]10067.8378510925[/C][C]32.843948142048[/C][C]0.304394203223489[/C][C]-0.168133384317733[/C][/ROW]
[ROW][C]107[/C][C]10080[/C][C]10082.7192785602[/C][C]29.4229885916407[/C][C]0.305277919154801[/C][C]-0.445200564590337[/C][/ROW]
[ROW][C]108[/C][C]10051[/C][C]10059.548560874[/C][C]19.4064917721823[/C][C]0.307351178182198[/C][C]-1.30354772825866[/C][/ROW]
[ROW][C]109[/C][C]9962[/C][C]9986.28822832845[/C][C]1.82878810951457[/C][C]-8.77244631005813[/C][C]-2.34576592779511[/C][/ROW]
[ROW][C]110[/C][C]9896[/C][C]9908.30411709871[/C][C]-13.2882510159991[/C][C]0.413602805535598[/C][C]-1.92089857344148[/C][/ROW]
[ROW][C]111[/C][C]9849[/C][C]9855.29795329796[/C][C]-20.8473611526173[/C][C]0.387150848510304[/C][C]-0.984484615891793[/C][/ROW]
[ROW][C]112[/C][C]9854[/C][C]9850.85184983692[/C][C]-17.7235517578482[/C][C]0.386459303406898[/C][C]0.406507799705957[/C][/ROW]
[ROW][C]113[/C][C]9847[/C][C]9844.67168497451[/C][C]-15.5249288666298[/C][C]0.384874929480311[/C][C]0.286070439205617[/C][/ROW]
[ROW][C]114[/C][C]9845[/C][C]9842.38757604747[/C][C]-13.0031002759129[/C][C]0.383172391807394[/C][C]0.328140489975303[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298198&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298198&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
167886788000
267836783.63380667356-0.321907213784065-0.251405098497128-0.0772685672841303
367956793.201336911360.519652235911834-0.1225434478351180.267632112996357
468356828.396230561944.449682393901850.02776782642385510.922034772041571
568896880.1860841538710.94882410399060.1450188779803471.2326030069995
669266920.5541160813615.50322976349790.1996728039647020.754173410785821
769576953.688486863618.44680345698170.2260116028940730.447050405341169
869846982.0492646378520.18300244387630.2380357597212040.249488665940831
971597135.7623724644444.28935118481280.3692236259408933.34329209050907
1071217129.3108686177434.94977712240720.328977883295168-1.26613734930941
1171657164.6113150879635.01512643465280.3292018488865790.00873063555989765
1272087206.5036196286636.30689894203320.3327324470748620.170967861202134
1372177229.7340178001933.9977460946878-10.622378925111-0.382172311214925
1472507250.9101561989931.61327699185410.647746508037618-0.267392355585926
1572817280.6705176528931.26266721096230.640962638740705-0.0459537485076501
1672987299.4603032478228.89296034480660.641492947617775-0.309275061793948
1773107312.0875919104525.79969176500310.650723915524036-0.403010772665712
1873627357.9784908071329.62214627827390.6396596628631880.497757263812632
1973877386.5386218031729.42003476269090.640146671557412-0.0263127531303979
2074147413.7335924706828.99649901167680.64097123194966-0.0551324846880421
2174497447.5491826611229.91393380595570.6395374969857280.119414363687561
2274737473.0948404455529.08223624941910.640579320533524-0.108248959176606
2375137510.8935677796630.74193865777230.6389133922230770.216009944057723
2475227524.2804425130927.43718314231230.641571261088412-0.430103887882354
2575887582.0643671806533.10546577481850.9554865373166230.820959671355896
2676027603.833454760430.9855386344985-0.27087441506386-0.252657621570641
2776437642.0403478675832.3575899939408-0.2544668273859220.17900508702984
2876517654.5872444487728.5842164668218-0.251791000609647-0.490964069849694
2976617664.4018595121525.0088480645454-0.243172352490002-0.464973640896671
3076887688.4109891909224.8184382943353-0.242741458867861-0.0247666705193028
3177287726.0837524378127.2665107649664-0.2473266353790390.318480027100886
3277507750.6937397856926.7606038973335-0.246561944243131-0.0658240511694493
3377597761.8670133928723.7922067360138-0.242961049129781-0.38625382002359
3477607763.9018933862219.6488195982451-0.238932262066665-0.539175302125059
3578067802.9719894444923.3473632390009-0.2418140065363550.481305087844675
3678647858.7802637914629.5292088441012-0.2456734005526140.804484420022479
3778597864.4372218457525.0381290884232-1.48601739543939-0.628461024984163
3879267920.9074799817330.94160037202030.5159031753823110.721138473523295
3979787973.7615353224335.1074293914570.5528376456682230.543163438901915
4079997999.9482107569733.40829022625650.55378506620236-0.221087302145651
4180568052.2694862970637.01086521480760.5472284694758660.468587656861943
4281048101.4143403158539.32194069500040.5432873199943730.300640504309245
4381468144.7775228538140.09159676621770.542201403270540.100136261087256
4481718172.5320275464737.74207055809160.544876409512039-0.30571596878861
4581998200.1566924319335.81529492494560.546636914158954-0.250724765457788
4682128214.9840485270831.81832172791110.549564187444266-0.520134360935204
4782428242.2212466996630.94588185577140.550076189088343-0.113535459842938
4882698269.1294102166430.17692361038260.550437776792762-0.10007055181791
4982798288.3231312841428.1041708594633-7.49732570592677-0.285046562665964
5083238321.5063992085329.06079853306780.7306811500856710.118466715831756
5183508349.4575036093128.84975482667720.729188203485359-0.0275066198714499
5283728372.284398591927.70259597875620.729699835457174-0.149270770703015
5384038401.9417933334228.0749390195040.7291592434726440.0484361135422353
5484128413.9681826843225.01830732427010.733316948277596-0.397661483444413
5584608456.3477273717828.32478112034990.7295960271434630.430213906695405
5684848483.472263931328.09619878179710.72980359792786-0.0297438019993816
5784988499.3291489172425.76528834020690.731502261427332-0.303320632562613
5885278526.0994039169525.95667855734060.7313904656041620.0249063819985957
5985198523.1355058461920.44889758882960.733968478756268-0.716765208745451
6085378537.3203162194319.25592603766880.734415896131432-0.155251692848206
6185268538.8840589881515.9108773603426-9.93532016595321-0.455139881200011
6285498549.0271646122614.82249691857770.856823391901911-0.135974870811678
6385948588.9001556206619.58780543004890.8847698021672560.620935404902812
6487678743.4073592289945.28529542161930.8752406287730033.34389791799696
6586908703.4541023878229.04965884328510.894836570732049-2.11216372054679
6686578667.1011324096816.59303621438350.908922174958669-1.62067320228254
6786808679.7537549325315.8425756522410.909624233509276-0.097648079483688
6887148710.5713203256618.69453308641480.9074713343840420.371114147492799
6987468742.8131598576221.27456926669560.9059083208388560.335744586514037
7086718683.633046513565.952274821845280.913348503638678-1.99397228397239
7186548658.344557947710.002569287912588260.915663536278134-0.774280916109927
7286778673.52892869682.893910090178360.9147621006436580.376276726794295
7387658755.0611610937717.7802466926281-3.190386338751742.01095852254534
7487608761.5438449046915.64553977972070.212244614354223-0.268341372350793
7588128806.7799663503221.2754741464490.2404840033510670.733467554650225
7688228822.6665661417120.24908708954270.24080965520026-0.133561525979471
7788378837.6453832214719.24525638564760.241846337768138-0.130599542431184
7889978976.6232731981742.04952013334240.2197826503126512.96707685280601
7988758895.4987891606818.59069371095390.238560066602611-3.05248708902154
8089058906.1048026210117.07001809935420.239542265152621-0.197883069894946
8189278926.243999380617.65453636369240.2392392838968280.0760652309875495
8289508948.9162905439218.61015594498870.2388422526296680.124360794425303
8390109003.6765386006425.49487422750760.2365501865508020.895965463612855
8490869077.6097887898134.71991242340150.2340893511389271.20054249543735
8591619153.5891910300142.53721501875330.5137662397601611.05054932408264
8692489240.7664294652750.98051345831780.222026463148361.06618712113575
8792859285.7861263604849.8462558094590.217051396172911-0.147751236249862
8893359334.9053316281849.70777955201450.217089788117069-0.0180198607366465
8993549358.2214554290544.68099786466270.221626168286903-0.654015955628227
9092679286.3771976477822.48767144433140.24038982586176-2.88767490081837
9194039389.2384399985837.79506888815340.2296829707349621.99185480152133
9294699462.7590877703644.59900503849240.2258427831161860.885396825720449
9394649470.0522593879537.49415424872460.229060895046048-0.924584721489595
9496309612.1630833369857.41825981469620.2218274303215312.59286332540615
9597249715.969832421566.25290651337560.2192572854948141.14972979596327
9697649766.4379290186763.2466923534260.219958032894122-0.391228285395051
9798069812.4351092798259.9763441663596-3.54898046890897-0.43777341133578
9898699869.2025909880359.36894283197070.30547936576458-0.0769683960879275
9999079909.8579849323355.80766665674730.291618585258371-0.463852539153868
10099149921.1944463118747.33758186995320.293703771591952-1.10222042356786
10199229928.4484876985939.70298368684830.299821738065744-0.993339722758893
10299509952.3570502118536.69479459143320.302080138326844-0.391418401336358
10399829982.7570082895435.49592146095220.30282475523976-0.15600421980329
10499819986.1066189275729.37363605887140.305893096891951-0.796701627041405
1051004510040.485713567934.13591491903630.303977702714450.619739823708681
1061006710067.837851092532.8439481420480.304394203223489-0.168133384317733
1071008010082.719278560229.42298859164070.305277919154801-0.445200564590337
1081005110059.54856087419.40649177218230.307351178182198-1.30354772825866
10999629986.288228328451.82878810951457-8.77244631005813-2.34576592779511
11098969908.30411709871-13.28825101599910.413602805535598-1.92089857344148
11198499855.29795329796-20.84736115261730.387150848510304-0.984484615891793
11298549850.85184983692-17.72355175784820.3864593034068980.406507799705957
11398479844.67168497451-15.52492886662980.3848749294803110.286070439205617
11498459842.38757604747-13.00310027591290.3831723918073940.328140489975303







Structural Time Series Model -- Extrapolation
tObservedLevelSeasonal
19820.273455682419826.10776888223-5.83431319981905
29804.8743574139811.3608705223-6.48651310929734
39803.162926357019796.613972162376.54895419464037
49778.583610443799781.86707380243-3.28346335864283
59769.58085126789767.12017544252.46067582530265
69756.821317441129752.373277082564.44804035855209
79736.835393081329737.62637872263-0.790985641308745
89721.162794375519722.8794803627-1.71668598718986
99709.109097330529708.132582002760.976515327754463
109703.874301882049693.3856836428310.4886182392131
119675.858410213079678.6387852829-2.78037506982345
129659.861419343589663.89188692296-4.03046757938137

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Extrapolation \tabularnewline
t & Observed & Level & Seasonal \tabularnewline
1 & 9820.27345568241 & 9826.10776888223 & -5.83431319981905 \tabularnewline
2 & 9804.874357413 & 9811.3608705223 & -6.48651310929734 \tabularnewline
3 & 9803.16292635701 & 9796.61397216237 & 6.54895419464037 \tabularnewline
4 & 9778.58361044379 & 9781.86707380243 & -3.28346335864283 \tabularnewline
5 & 9769.5808512678 & 9767.1201754425 & 2.46067582530265 \tabularnewline
6 & 9756.82131744112 & 9752.37327708256 & 4.44804035855209 \tabularnewline
7 & 9736.83539308132 & 9737.62637872263 & -0.790985641308745 \tabularnewline
8 & 9721.16279437551 & 9722.8794803627 & -1.71668598718986 \tabularnewline
9 & 9709.10909733052 & 9708.13258200276 & 0.976515327754463 \tabularnewline
10 & 9703.87430188204 & 9693.38568364283 & 10.4886182392131 \tabularnewline
11 & 9675.85841021307 & 9678.6387852829 & -2.78037506982345 \tabularnewline
12 & 9659.86141934358 & 9663.89188692296 & -4.03046757938137 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298198&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]9820.27345568241[/C][C]9826.10776888223[/C][C]-5.83431319981905[/C][/ROW]
[ROW][C]2[/C][C]9804.874357413[/C][C]9811.3608705223[/C][C]-6.48651310929734[/C][/ROW]
[ROW][C]3[/C][C]9803.16292635701[/C][C]9796.61397216237[/C][C]6.54895419464037[/C][/ROW]
[ROW][C]4[/C][C]9778.58361044379[/C][C]9781.86707380243[/C][C]-3.28346335864283[/C][/ROW]
[ROW][C]5[/C][C]9769.5808512678[/C][C]9767.1201754425[/C][C]2.46067582530265[/C][/ROW]
[ROW][C]6[/C][C]9756.82131744112[/C][C]9752.37327708256[/C][C]4.44804035855209[/C][/ROW]
[ROW][C]7[/C][C]9736.83539308132[/C][C]9737.62637872263[/C][C]-0.790985641308745[/C][/ROW]
[ROW][C]8[/C][C]9721.16279437551[/C][C]9722.8794803627[/C][C]-1.71668598718986[/C][/ROW]
[ROW][C]9[/C][C]9709.10909733052[/C][C]9708.13258200276[/C][C]0.976515327754463[/C][/ROW]
[ROW][C]10[/C][C]9703.87430188204[/C][C]9693.38568364283[/C][C]10.4886182392131[/C][/ROW]
[ROW][C]11[/C][C]9675.85841021307[/C][C]9678.6387852829[/C][C]-2.78037506982345[/C][/ROW]
[ROW][C]12[/C][C]9659.86141934358[/C][C]9663.89188692296[/C][C]-4.03046757938137[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298198&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298198&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
19820.273455682419826.10776888223-5.83431319981905
29804.8743574139811.3608705223-6.48651310929734
39803.162926357019796.613972162376.54895419464037
49778.583610443799781.86707380243-3.28346335864283
59769.58085126789767.12017544252.46067582530265
69756.821317441129752.373277082564.44804035855209
79736.835393081329737.62637872263-0.790985641308745
89721.162794375519722.8794803627-1.71668598718986
99709.109097330529708.132582002760.976515327754463
109703.874301882049693.3856836428310.4886182392131
119675.858410213079678.6387852829-2.78037506982345
129659.861419343589663.89188692296-4.03046757938137



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')