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Author*The author of this computation has been verified*
R Software Modulerwasp_structuraltimeseries.wasp
Title produced by softwareStructural Time Series Models
Date of computationWed, 14 Dec 2016 13:04:39 +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/14/t1481717088aayj2i0avgef4by.htm/, Retrieved Fri, 01 Nov 2024 03:46:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299338, Retrieved Fri, 01 Nov 2024 03:46:29 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact103
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Structural Time Series Models] [] [2016-12-14 12:04:39] [349958aef20b862f8399a5ba04d6f6e3] [Current]
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Dataseries X:
6830
6827
6841
6754
6869
6809
6836
6766
6759
6719
6702
6627
6630
6606
6512
6550
6578
6499
6371
6332
6291
6307
6252
6250
6164
6213
6174
6154
6091
6096
6046
6001
5979
5921
5863
5818
5758
5786
5734
5678
5610
5578
5589
5553
5533
5521
5464
5419
5346
5296
5255
5235
5164
5164
5172
5093
5070
5108
5051
5021
5001
4918
4886




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time3 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299338&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]3 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=299338&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299338&T=0

As an alternative you can also use a QR Code:  

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

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







Structural Time Series Model -- Interpolation
tObservedLevelSlopeSeasonalStand. Residuals
168306830000
268276828.14262412599-0.175340225970156-0.141325617580829-0.0687142908903438
368416835.408688478630.5589755834813860.1742882338810750.334922655219353
467546789.50563181395-4.94809043871471-0.927525129429141-2.1129429560422
568696833.849898264051.91430651110568-0.2484237170938512.17946471502743
668096820.14497546919-0.514248623841277-0.379584963837982-0.669841056742302
768366829.64604760231.15636502500694-0.3257502290911660.419349204215593
867666791.85101656993-5.62862616474782-0.465958487583332-1.60396546035966
967596769.9508210914-8.53849545279546-0.506715172376971-0.66275710141301
1067196735.82070187259-13.1879877195213-0.552699196728958-1.03516090245142
1167026710.33758568399-15.442948897126-0.568913259580155-0.495176559163348
1266276653.60271127103-23.0585562238346-0.609537410417997-1.65853571318496
1366306627.52876663758-23.56703046206224.23868480311027-0.141912107846474
1466066605.56234581626-23.2725053175618-0.3391164220292420.0543978109262097
1565126539.02161623997-31.2335824958785-0.896005165157451-1.69486063690857
1665506534.24053881723-26.3366854807757-0.7674133715259391.0582269450891
1765786551.44249046026-18.253159077123-0.7150837770531241.74292764580284
1864996512.59280125186-22.0803503262042-0.708065769811096-0.823375277424617
1963716417.36383721484-35.6734244510956-0.642661101575362-2.92199581362031
2063326351.4866682552-41.2855466686729-0.612316640704187-1.20628584001977
2162916298.75494255269-43.4121895416014-0.601644635906486-0.457176131700109
2263076287.51658333545-37.4345367253266-0.6273191542289731.28528291564262
2362526251.6488211947-37.1434331447137-0.6283455114595770.0626007324200324
2462506236.73811419937-33.0124175284441-0.6400219907546160.888451057743577
2561646180.68623547711-37.1631929418037-2.90633634738567-1.00645069832184
2662136188.08884431858-28.96482773157371.117886296578681.60888408497352
2761746167.6160237137-27.39775638398611.188379105853760.335198117737598
2861546147.95345505669-25.96333167288111.211644446172610.309363537907145
2960916102.1926954493-29.6420559126041.1994061031703-0.791985072943227
3060966086.24272491715-27.09668562564521.194331631484960.547243683340085
3160466050.31779220175-28.73773004916581.20058358210107-0.352687839045449
3260016008.17059881198-31.22995724732881.21073494891747-0.535669106856689
3359795977.46306064443-31.13287315668761.210374845270740.0208711641345774
3459215929.99370038618-34.16863916477071.21992271803776-0.652754134298059
3558635874.87203673382-38.06228561949761.22992343000967-0.837335224535448
3658185824.47766497032-40.35398326017741.2346279724784-0.49288062652102
3757585777.52209699161-41.5560214037331-15.5164531623845-0.28102025743691
3857865766.91830416162-35.84854094220611.858158568810111.14732964955936
3957345731.73091474958-35.72632040716211.862275164276570.0261826525056042
4056785683.79732813842-37.99137047222151.83480790297335-0.488193989471354
4156105622.66136244916-42.29243173263051.8242072771885-0.925766948222865
4255785577.78881332982-42.77206700908651.82493791046869-0.103131783713285
4355895567.12036027444-36.80448316058821.807739561739991.2828051087011
4455535543.1659365305-34.41613881166671.800394438477260.51343947575568
4555335522.56746013476-31.84816516324011.793208251555170.552142329619669
4655215508.251409533-28.58998213039361.785480213077540.700646073484241
4754645468.9250701733-30.58523594980091.78934414690744-0.42910932862816
4854195425.33858454232-33.0014449401941.7930834694873-0.519679734788413
4953465377.8203765345-35.6581519303945-22.9454491144128-0.6093064716508
5052965311.65772357001-41.29193425730321.73151007305323-1.14837920454192
5152555259.82722236083-43.24223557920941.67897566722777-0.418149958842694
5252355226.87077144794-41.3330339522341.697499133870590.411334238463326
5351645171.24965790012-43.98838499578011.6922629352353-0.571470237871405
5451645148.82473653353-39.97987271370221.687369700169260.861983255925734
5551725146.67395248129-32.94803384913691.671136045176861.51178153657747
5650935099.94161064456-35.51007264890631.67744726777163-0.550845760900875
5750705066.82614673126-35.0650249111741.676449748592180.0956985857599992
5851085077.64479068407-26.5375920639931.660250075296671.83386552092824
5950515050.01964255921-26.73971324960261.66056356928931-0.0434708703457974
6050215020.85540497567-27.19031543830821.66112208093402-0.0969181269050432
6150015007.94949767631-24.5681065931557-15.72233618531950.594232252930764
6249184941.33289655531-32.34215941377331.02094518349261-1.59923169389682
6348864894.19524080607-35.08227322426910.959442463419203-0.587810872695126

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Interpolation \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 6830 & 6830 & 0 & 0 & 0 \tabularnewline
2 & 6827 & 6828.14262412599 & -0.175340225970156 & -0.141325617580829 & -0.0687142908903438 \tabularnewline
3 & 6841 & 6835.40868847863 & 0.558975583481386 & 0.174288233881075 & 0.334922655219353 \tabularnewline
4 & 6754 & 6789.50563181395 & -4.94809043871471 & -0.927525129429141 & -2.1129429560422 \tabularnewline
5 & 6869 & 6833.84989826405 & 1.91430651110568 & -0.248423717093851 & 2.17946471502743 \tabularnewline
6 & 6809 & 6820.14497546919 & -0.514248623841277 & -0.379584963837982 & -0.669841056742302 \tabularnewline
7 & 6836 & 6829.6460476023 & 1.15636502500694 & -0.325750229091166 & 0.419349204215593 \tabularnewline
8 & 6766 & 6791.85101656993 & -5.62862616474782 & -0.465958487583332 & -1.60396546035966 \tabularnewline
9 & 6759 & 6769.9508210914 & -8.53849545279546 & -0.506715172376971 & -0.66275710141301 \tabularnewline
10 & 6719 & 6735.82070187259 & -13.1879877195213 & -0.552699196728958 & -1.03516090245142 \tabularnewline
11 & 6702 & 6710.33758568399 & -15.442948897126 & -0.568913259580155 & -0.495176559163348 \tabularnewline
12 & 6627 & 6653.60271127103 & -23.0585562238346 & -0.609537410417997 & -1.65853571318496 \tabularnewline
13 & 6630 & 6627.52876663758 & -23.5670304620622 & 4.23868480311027 & -0.141912107846474 \tabularnewline
14 & 6606 & 6605.56234581626 & -23.2725053175618 & -0.339116422029242 & 0.0543978109262097 \tabularnewline
15 & 6512 & 6539.02161623997 & -31.2335824958785 & -0.896005165157451 & -1.69486063690857 \tabularnewline
16 & 6550 & 6534.24053881723 & -26.3366854807757 & -0.767413371525939 & 1.0582269450891 \tabularnewline
17 & 6578 & 6551.44249046026 & -18.253159077123 & -0.715083777053124 & 1.74292764580284 \tabularnewline
18 & 6499 & 6512.59280125186 & -22.0803503262042 & -0.708065769811096 & -0.823375277424617 \tabularnewline
19 & 6371 & 6417.36383721484 & -35.6734244510956 & -0.642661101575362 & -2.92199581362031 \tabularnewline
20 & 6332 & 6351.4866682552 & -41.2855466686729 & -0.612316640704187 & -1.20628584001977 \tabularnewline
21 & 6291 & 6298.75494255269 & -43.4121895416014 & -0.601644635906486 & -0.457176131700109 \tabularnewline
22 & 6307 & 6287.51658333545 & -37.4345367253266 & -0.627319154228973 & 1.28528291564262 \tabularnewline
23 & 6252 & 6251.6488211947 & -37.1434331447137 & -0.628345511459577 & 0.0626007324200324 \tabularnewline
24 & 6250 & 6236.73811419937 & -33.0124175284441 & -0.640021990754616 & 0.888451057743577 \tabularnewline
25 & 6164 & 6180.68623547711 & -37.1631929418037 & -2.90633634738567 & -1.00645069832184 \tabularnewline
26 & 6213 & 6188.08884431858 & -28.9648277315737 & 1.11788629657868 & 1.60888408497352 \tabularnewline
27 & 6174 & 6167.6160237137 & -27.3977563839861 & 1.18837910585376 & 0.335198117737598 \tabularnewline
28 & 6154 & 6147.95345505669 & -25.9633316728811 & 1.21164444617261 & 0.309363537907145 \tabularnewline
29 & 6091 & 6102.1926954493 & -29.642055912604 & 1.1994061031703 & -0.791985072943227 \tabularnewline
30 & 6096 & 6086.24272491715 & -27.0966856256452 & 1.19433163148496 & 0.547243683340085 \tabularnewline
31 & 6046 & 6050.31779220175 & -28.7377300491658 & 1.20058358210107 & -0.352687839045449 \tabularnewline
32 & 6001 & 6008.17059881198 & -31.2299572473288 & 1.21073494891747 & -0.535669106856689 \tabularnewline
33 & 5979 & 5977.46306064443 & -31.1328731566876 & 1.21037484527074 & 0.0208711641345774 \tabularnewline
34 & 5921 & 5929.99370038618 & -34.1686391647707 & 1.21992271803776 & -0.652754134298059 \tabularnewline
35 & 5863 & 5874.87203673382 & -38.0622856194976 & 1.22992343000967 & -0.837335224535448 \tabularnewline
36 & 5818 & 5824.47766497032 & -40.3539832601774 & 1.2346279724784 & -0.49288062652102 \tabularnewline
37 & 5758 & 5777.52209699161 & -41.5560214037331 & -15.5164531623845 & -0.28102025743691 \tabularnewline
38 & 5786 & 5766.91830416162 & -35.8485409422061 & 1.85815856881011 & 1.14732964955936 \tabularnewline
39 & 5734 & 5731.73091474958 & -35.7263204071621 & 1.86227516427657 & 0.0261826525056042 \tabularnewline
40 & 5678 & 5683.79732813842 & -37.9913704722215 & 1.83480790297335 & -0.488193989471354 \tabularnewline
41 & 5610 & 5622.66136244916 & -42.2924317326305 & 1.8242072771885 & -0.925766948222865 \tabularnewline
42 & 5578 & 5577.78881332982 & -42.7720670090865 & 1.82493791046869 & -0.103131783713285 \tabularnewline
43 & 5589 & 5567.12036027444 & -36.8044831605882 & 1.80773956173999 & 1.2828051087011 \tabularnewline
44 & 5553 & 5543.1659365305 & -34.4161388116667 & 1.80039443847726 & 0.51343947575568 \tabularnewline
45 & 5533 & 5522.56746013476 & -31.8481651632401 & 1.79320825155517 & 0.552142329619669 \tabularnewline
46 & 5521 & 5508.251409533 & -28.5899821303936 & 1.78548021307754 & 0.700646073484241 \tabularnewline
47 & 5464 & 5468.9250701733 & -30.5852359498009 & 1.78934414690744 & -0.42910932862816 \tabularnewline
48 & 5419 & 5425.33858454232 & -33.001444940194 & 1.7930834694873 & -0.519679734788413 \tabularnewline
49 & 5346 & 5377.8203765345 & -35.6581519303945 & -22.9454491144128 & -0.6093064716508 \tabularnewline
50 & 5296 & 5311.65772357001 & -41.2919342573032 & 1.73151007305323 & -1.14837920454192 \tabularnewline
51 & 5255 & 5259.82722236083 & -43.2422355792094 & 1.67897566722777 & -0.418149958842694 \tabularnewline
52 & 5235 & 5226.87077144794 & -41.333033952234 & 1.69749913387059 & 0.411334238463326 \tabularnewline
53 & 5164 & 5171.24965790012 & -43.9883849957801 & 1.6922629352353 & -0.571470237871405 \tabularnewline
54 & 5164 & 5148.82473653353 & -39.9798727137022 & 1.68736970016926 & 0.861983255925734 \tabularnewline
55 & 5172 & 5146.67395248129 & -32.9480338491369 & 1.67113604517686 & 1.51178153657747 \tabularnewline
56 & 5093 & 5099.94161064456 & -35.5100726489063 & 1.67744726777163 & -0.550845760900875 \tabularnewline
57 & 5070 & 5066.82614673126 & -35.065024911174 & 1.67644974859218 & 0.0956985857599992 \tabularnewline
58 & 5108 & 5077.64479068407 & -26.537592063993 & 1.66025007529667 & 1.83386552092824 \tabularnewline
59 & 5051 & 5050.01964255921 & -26.7397132496026 & 1.66056356928931 & -0.0434708703457974 \tabularnewline
60 & 5021 & 5020.85540497567 & -27.1903154383082 & 1.66112208093402 & -0.0969181269050432 \tabularnewline
61 & 5001 & 5007.94949767631 & -24.5681065931557 & -15.7223361853195 & 0.594232252930764 \tabularnewline
62 & 4918 & 4941.33289655531 & -32.3421594137733 & 1.02094518349261 & -1.59923169389682 \tabularnewline
63 & 4886 & 4894.19524080607 & -35.0822732242691 & 0.959442463419203 & -0.587810872695126 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299338&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]6830[/C][C]6830[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]6827[/C][C]6828.14262412599[/C][C]-0.175340225970156[/C][C]-0.141325617580829[/C][C]-0.0687142908903438[/C][/ROW]
[ROW][C]3[/C][C]6841[/C][C]6835.40868847863[/C][C]0.558975583481386[/C][C]0.174288233881075[/C][C]0.334922655219353[/C][/ROW]
[ROW][C]4[/C][C]6754[/C][C]6789.50563181395[/C][C]-4.94809043871471[/C][C]-0.927525129429141[/C][C]-2.1129429560422[/C][/ROW]
[ROW][C]5[/C][C]6869[/C][C]6833.84989826405[/C][C]1.91430651110568[/C][C]-0.248423717093851[/C][C]2.17946471502743[/C][/ROW]
[ROW][C]6[/C][C]6809[/C][C]6820.14497546919[/C][C]-0.514248623841277[/C][C]-0.379584963837982[/C][C]-0.669841056742302[/C][/ROW]
[ROW][C]7[/C][C]6836[/C][C]6829.6460476023[/C][C]1.15636502500694[/C][C]-0.325750229091166[/C][C]0.419349204215593[/C][/ROW]
[ROW][C]8[/C][C]6766[/C][C]6791.85101656993[/C][C]-5.62862616474782[/C][C]-0.465958487583332[/C][C]-1.60396546035966[/C][/ROW]
[ROW][C]9[/C][C]6759[/C][C]6769.9508210914[/C][C]-8.53849545279546[/C][C]-0.506715172376971[/C][C]-0.66275710141301[/C][/ROW]
[ROW][C]10[/C][C]6719[/C][C]6735.82070187259[/C][C]-13.1879877195213[/C][C]-0.552699196728958[/C][C]-1.03516090245142[/C][/ROW]
[ROW][C]11[/C][C]6702[/C][C]6710.33758568399[/C][C]-15.442948897126[/C][C]-0.568913259580155[/C][C]-0.495176559163348[/C][/ROW]
[ROW][C]12[/C][C]6627[/C][C]6653.60271127103[/C][C]-23.0585562238346[/C][C]-0.609537410417997[/C][C]-1.65853571318496[/C][/ROW]
[ROW][C]13[/C][C]6630[/C][C]6627.52876663758[/C][C]-23.5670304620622[/C][C]4.23868480311027[/C][C]-0.141912107846474[/C][/ROW]
[ROW][C]14[/C][C]6606[/C][C]6605.56234581626[/C][C]-23.2725053175618[/C][C]-0.339116422029242[/C][C]0.0543978109262097[/C][/ROW]
[ROW][C]15[/C][C]6512[/C][C]6539.02161623997[/C][C]-31.2335824958785[/C][C]-0.896005165157451[/C][C]-1.69486063690857[/C][/ROW]
[ROW][C]16[/C][C]6550[/C][C]6534.24053881723[/C][C]-26.3366854807757[/C][C]-0.767413371525939[/C][C]1.0582269450891[/C][/ROW]
[ROW][C]17[/C][C]6578[/C][C]6551.44249046026[/C][C]-18.253159077123[/C][C]-0.715083777053124[/C][C]1.74292764580284[/C][/ROW]
[ROW][C]18[/C][C]6499[/C][C]6512.59280125186[/C][C]-22.0803503262042[/C][C]-0.708065769811096[/C][C]-0.823375277424617[/C][/ROW]
[ROW][C]19[/C][C]6371[/C][C]6417.36383721484[/C][C]-35.6734244510956[/C][C]-0.642661101575362[/C][C]-2.92199581362031[/C][/ROW]
[ROW][C]20[/C][C]6332[/C][C]6351.4866682552[/C][C]-41.2855466686729[/C][C]-0.612316640704187[/C][C]-1.20628584001977[/C][/ROW]
[ROW][C]21[/C][C]6291[/C][C]6298.75494255269[/C][C]-43.4121895416014[/C][C]-0.601644635906486[/C][C]-0.457176131700109[/C][/ROW]
[ROW][C]22[/C][C]6307[/C][C]6287.51658333545[/C][C]-37.4345367253266[/C][C]-0.627319154228973[/C][C]1.28528291564262[/C][/ROW]
[ROW][C]23[/C][C]6252[/C][C]6251.6488211947[/C][C]-37.1434331447137[/C][C]-0.628345511459577[/C][C]0.0626007324200324[/C][/ROW]
[ROW][C]24[/C][C]6250[/C][C]6236.73811419937[/C][C]-33.0124175284441[/C][C]-0.640021990754616[/C][C]0.888451057743577[/C][/ROW]
[ROW][C]25[/C][C]6164[/C][C]6180.68623547711[/C][C]-37.1631929418037[/C][C]-2.90633634738567[/C][C]-1.00645069832184[/C][/ROW]
[ROW][C]26[/C][C]6213[/C][C]6188.08884431858[/C][C]-28.9648277315737[/C][C]1.11788629657868[/C][C]1.60888408497352[/C][/ROW]
[ROW][C]27[/C][C]6174[/C][C]6167.6160237137[/C][C]-27.3977563839861[/C][C]1.18837910585376[/C][C]0.335198117737598[/C][/ROW]
[ROW][C]28[/C][C]6154[/C][C]6147.95345505669[/C][C]-25.9633316728811[/C][C]1.21164444617261[/C][C]0.309363537907145[/C][/ROW]
[ROW][C]29[/C][C]6091[/C][C]6102.1926954493[/C][C]-29.642055912604[/C][C]1.1994061031703[/C][C]-0.791985072943227[/C][/ROW]
[ROW][C]30[/C][C]6096[/C][C]6086.24272491715[/C][C]-27.0966856256452[/C][C]1.19433163148496[/C][C]0.547243683340085[/C][/ROW]
[ROW][C]31[/C][C]6046[/C][C]6050.31779220175[/C][C]-28.7377300491658[/C][C]1.20058358210107[/C][C]-0.352687839045449[/C][/ROW]
[ROW][C]32[/C][C]6001[/C][C]6008.17059881198[/C][C]-31.2299572473288[/C][C]1.21073494891747[/C][C]-0.535669106856689[/C][/ROW]
[ROW][C]33[/C][C]5979[/C][C]5977.46306064443[/C][C]-31.1328731566876[/C][C]1.21037484527074[/C][C]0.0208711641345774[/C][/ROW]
[ROW][C]34[/C][C]5921[/C][C]5929.99370038618[/C][C]-34.1686391647707[/C][C]1.21992271803776[/C][C]-0.652754134298059[/C][/ROW]
[ROW][C]35[/C][C]5863[/C][C]5874.87203673382[/C][C]-38.0622856194976[/C][C]1.22992343000967[/C][C]-0.837335224535448[/C][/ROW]
[ROW][C]36[/C][C]5818[/C][C]5824.47766497032[/C][C]-40.3539832601774[/C][C]1.2346279724784[/C][C]-0.49288062652102[/C][/ROW]
[ROW][C]37[/C][C]5758[/C][C]5777.52209699161[/C][C]-41.5560214037331[/C][C]-15.5164531623845[/C][C]-0.28102025743691[/C][/ROW]
[ROW][C]38[/C][C]5786[/C][C]5766.91830416162[/C][C]-35.8485409422061[/C][C]1.85815856881011[/C][C]1.14732964955936[/C][/ROW]
[ROW][C]39[/C][C]5734[/C][C]5731.73091474958[/C][C]-35.7263204071621[/C][C]1.86227516427657[/C][C]0.0261826525056042[/C][/ROW]
[ROW][C]40[/C][C]5678[/C][C]5683.79732813842[/C][C]-37.9913704722215[/C][C]1.83480790297335[/C][C]-0.488193989471354[/C][/ROW]
[ROW][C]41[/C][C]5610[/C][C]5622.66136244916[/C][C]-42.2924317326305[/C][C]1.8242072771885[/C][C]-0.925766948222865[/C][/ROW]
[ROW][C]42[/C][C]5578[/C][C]5577.78881332982[/C][C]-42.7720670090865[/C][C]1.82493791046869[/C][C]-0.103131783713285[/C][/ROW]
[ROW][C]43[/C][C]5589[/C][C]5567.12036027444[/C][C]-36.8044831605882[/C][C]1.80773956173999[/C][C]1.2828051087011[/C][/ROW]
[ROW][C]44[/C][C]5553[/C][C]5543.1659365305[/C][C]-34.4161388116667[/C][C]1.80039443847726[/C][C]0.51343947575568[/C][/ROW]
[ROW][C]45[/C][C]5533[/C][C]5522.56746013476[/C][C]-31.8481651632401[/C][C]1.79320825155517[/C][C]0.552142329619669[/C][/ROW]
[ROW][C]46[/C][C]5521[/C][C]5508.251409533[/C][C]-28.5899821303936[/C][C]1.78548021307754[/C][C]0.700646073484241[/C][/ROW]
[ROW][C]47[/C][C]5464[/C][C]5468.9250701733[/C][C]-30.5852359498009[/C][C]1.78934414690744[/C][C]-0.42910932862816[/C][/ROW]
[ROW][C]48[/C][C]5419[/C][C]5425.33858454232[/C][C]-33.001444940194[/C][C]1.7930834694873[/C][C]-0.519679734788413[/C][/ROW]
[ROW][C]49[/C][C]5346[/C][C]5377.8203765345[/C][C]-35.6581519303945[/C][C]-22.9454491144128[/C][C]-0.6093064716508[/C][/ROW]
[ROW][C]50[/C][C]5296[/C][C]5311.65772357001[/C][C]-41.2919342573032[/C][C]1.73151007305323[/C][C]-1.14837920454192[/C][/ROW]
[ROW][C]51[/C][C]5255[/C][C]5259.82722236083[/C][C]-43.2422355792094[/C][C]1.67897566722777[/C][C]-0.418149958842694[/C][/ROW]
[ROW][C]52[/C][C]5235[/C][C]5226.87077144794[/C][C]-41.333033952234[/C][C]1.69749913387059[/C][C]0.411334238463326[/C][/ROW]
[ROW][C]53[/C][C]5164[/C][C]5171.24965790012[/C][C]-43.9883849957801[/C][C]1.6922629352353[/C][C]-0.571470237871405[/C][/ROW]
[ROW][C]54[/C][C]5164[/C][C]5148.82473653353[/C][C]-39.9798727137022[/C][C]1.68736970016926[/C][C]0.861983255925734[/C][/ROW]
[ROW][C]55[/C][C]5172[/C][C]5146.67395248129[/C][C]-32.9480338491369[/C][C]1.67113604517686[/C][C]1.51178153657747[/C][/ROW]
[ROW][C]56[/C][C]5093[/C][C]5099.94161064456[/C][C]-35.5100726489063[/C][C]1.67744726777163[/C][C]-0.550845760900875[/C][/ROW]
[ROW][C]57[/C][C]5070[/C][C]5066.82614673126[/C][C]-35.065024911174[/C][C]1.67644974859218[/C][C]0.0956985857599992[/C][/ROW]
[ROW][C]58[/C][C]5108[/C][C]5077.64479068407[/C][C]-26.537592063993[/C][C]1.66025007529667[/C][C]1.83386552092824[/C][/ROW]
[ROW][C]59[/C][C]5051[/C][C]5050.01964255921[/C][C]-26.7397132496026[/C][C]1.66056356928931[/C][C]-0.0434708703457974[/C][/ROW]
[ROW][C]60[/C][C]5021[/C][C]5020.85540497567[/C][C]-27.1903154383082[/C][C]1.66112208093402[/C][C]-0.0969181269050432[/C][/ROW]
[ROW][C]61[/C][C]5001[/C][C]5007.94949767631[/C][C]-24.5681065931557[/C][C]-15.7223361853195[/C][C]0.594232252930764[/C][/ROW]
[ROW][C]62[/C][C]4918[/C][C]4941.33289655531[/C][C]-32.3421594137733[/C][C]1.02094518349261[/C][C]-1.59923169389682[/C][/ROW]
[ROW][C]63[/C][C]4886[/C][C]4894.19524080607[/C][C]-35.0822732242691[/C][C]0.959442463419203[/C][C]-0.587810872695126[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299338&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299338&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
168306830000
268276828.14262412599-0.175340225970156-0.141325617580829-0.0687142908903438
368416835.408688478630.5589755834813860.1742882338810750.334922655219353
467546789.50563181395-4.94809043871471-0.927525129429141-2.1129429560422
568696833.849898264051.91430651110568-0.2484237170938512.17946471502743
668096820.14497546919-0.514248623841277-0.379584963837982-0.669841056742302
768366829.64604760231.15636502500694-0.3257502290911660.419349204215593
867666791.85101656993-5.62862616474782-0.465958487583332-1.60396546035966
967596769.9508210914-8.53849545279546-0.506715172376971-0.66275710141301
1067196735.82070187259-13.1879877195213-0.552699196728958-1.03516090245142
1167026710.33758568399-15.442948897126-0.568913259580155-0.495176559163348
1266276653.60271127103-23.0585562238346-0.609537410417997-1.65853571318496
1366306627.52876663758-23.56703046206224.23868480311027-0.141912107846474
1466066605.56234581626-23.2725053175618-0.3391164220292420.0543978109262097
1565126539.02161623997-31.2335824958785-0.896005165157451-1.69486063690857
1665506534.24053881723-26.3366854807757-0.7674133715259391.0582269450891
1765786551.44249046026-18.253159077123-0.7150837770531241.74292764580284
1864996512.59280125186-22.0803503262042-0.708065769811096-0.823375277424617
1963716417.36383721484-35.6734244510956-0.642661101575362-2.92199581362031
2063326351.4866682552-41.2855466686729-0.612316640704187-1.20628584001977
2162916298.75494255269-43.4121895416014-0.601644635906486-0.457176131700109
2263076287.51658333545-37.4345367253266-0.6273191542289731.28528291564262
2362526251.6488211947-37.1434331447137-0.6283455114595770.0626007324200324
2462506236.73811419937-33.0124175284441-0.6400219907546160.888451057743577
2561646180.68623547711-37.1631929418037-2.90633634738567-1.00645069832184
2662136188.08884431858-28.96482773157371.117886296578681.60888408497352
2761746167.6160237137-27.39775638398611.188379105853760.335198117737598
2861546147.95345505669-25.96333167288111.211644446172610.309363537907145
2960916102.1926954493-29.6420559126041.1994061031703-0.791985072943227
3060966086.24272491715-27.09668562564521.194331631484960.547243683340085
3160466050.31779220175-28.73773004916581.20058358210107-0.352687839045449
3260016008.17059881198-31.22995724732881.21073494891747-0.535669106856689
3359795977.46306064443-31.13287315668761.210374845270740.0208711641345774
3459215929.99370038618-34.16863916477071.21992271803776-0.652754134298059
3558635874.87203673382-38.06228561949761.22992343000967-0.837335224535448
3658185824.47766497032-40.35398326017741.2346279724784-0.49288062652102
3757585777.52209699161-41.5560214037331-15.5164531623845-0.28102025743691
3857865766.91830416162-35.84854094220611.858158568810111.14732964955936
3957345731.73091474958-35.72632040716211.862275164276570.0261826525056042
4056785683.79732813842-37.99137047222151.83480790297335-0.488193989471354
4156105622.66136244916-42.29243173263051.8242072771885-0.925766948222865
4255785577.78881332982-42.77206700908651.82493791046869-0.103131783713285
4355895567.12036027444-36.80448316058821.807739561739991.2828051087011
4455535543.1659365305-34.41613881166671.800394438477260.51343947575568
4555335522.56746013476-31.84816516324011.793208251555170.552142329619669
4655215508.251409533-28.58998213039361.785480213077540.700646073484241
4754645468.9250701733-30.58523594980091.78934414690744-0.42910932862816
4854195425.33858454232-33.0014449401941.7930834694873-0.519679734788413
4953465377.8203765345-35.6581519303945-22.9454491144128-0.6093064716508
5052965311.65772357001-41.29193425730321.73151007305323-1.14837920454192
5152555259.82722236083-43.24223557920941.67897566722777-0.418149958842694
5252355226.87077144794-41.3330339522341.697499133870590.411334238463326
5351645171.24965790012-43.98838499578011.6922629352353-0.571470237871405
5451645148.82473653353-39.97987271370221.687369700169260.861983255925734
5551725146.67395248129-32.94803384913691.671136045176861.51178153657747
5650935099.94161064456-35.51007264890631.67744726777163-0.550845760900875
5750705066.82614673126-35.0650249111741.676449748592180.0956985857599992
5851085077.64479068407-26.5375920639931.660250075296671.83386552092824
5950515050.01964255921-26.73971324960261.66056356928931-0.0434708703457974
6050215020.85540497567-27.19031543830821.66112208093402-0.0969181269050432
6150015007.94949767631-24.5681065931557-15.72233618531950.594232252930764
6249184941.33289655531-32.34215941377331.02094518349261-1.59923169389682
6348864894.19524080607-35.08227322426910.959442463419203-0.587810872695126







Structural Time Series Model -- Extrapolation
tObservedLevelSeasonal
14840.766867551324849.41552493473-8.64865738341656
24815.502167837054806.293610037459.20855779959928
34769.405509200024763.171695140166.23381405985666
44730.676888665634720.0497802428810.6271084227586
54665.116310610044676.92786534559-11.8115547355555
64631.323764557644633.80595044831-2.48218589066298
74609.499253994954590.6840355510218.8152184439306
84550.642787445064547.562120653743.08066679132055
94501.75435615174504.44020575645-2.68584960475389
104446.011328784154461.31829085917-15.30696207502
114419.537326424854418.196375961881.3409504629664
124366.703354773574375.0744610646-8.37110629102312
134323.303888783894331.95254616731-8.64865738341656
144298.039189069634288.830631270039.20855779959927
154251.94253043264245.708716372746.23381405985667
164213.213909898214202.5868014754610.6271084227586
174147.653331842624159.46488657817-11.8115547355555
184113.860785790224116.34297168089-2.48218589066298

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Extrapolation \tabularnewline
t & Observed & Level & Seasonal \tabularnewline
1 & 4840.76686755132 & 4849.41552493473 & -8.64865738341656 \tabularnewline
2 & 4815.50216783705 & 4806.29361003745 & 9.20855779959928 \tabularnewline
3 & 4769.40550920002 & 4763.17169514016 & 6.23381405985666 \tabularnewline
4 & 4730.67688866563 & 4720.04978024288 & 10.6271084227586 \tabularnewline
5 & 4665.11631061004 & 4676.92786534559 & -11.8115547355555 \tabularnewline
6 & 4631.32376455764 & 4633.80595044831 & -2.48218589066298 \tabularnewline
7 & 4609.49925399495 & 4590.68403555102 & 18.8152184439306 \tabularnewline
8 & 4550.64278744506 & 4547.56212065374 & 3.08066679132055 \tabularnewline
9 & 4501.7543561517 & 4504.44020575645 & -2.68584960475389 \tabularnewline
10 & 4446.01132878415 & 4461.31829085917 & -15.30696207502 \tabularnewline
11 & 4419.53732642485 & 4418.19637596188 & 1.3409504629664 \tabularnewline
12 & 4366.70335477357 & 4375.0744610646 & -8.37110629102312 \tabularnewline
13 & 4323.30388878389 & 4331.95254616731 & -8.64865738341656 \tabularnewline
14 & 4298.03918906963 & 4288.83063127003 & 9.20855779959927 \tabularnewline
15 & 4251.9425304326 & 4245.70871637274 & 6.23381405985667 \tabularnewline
16 & 4213.21390989821 & 4202.58680147546 & 10.6271084227586 \tabularnewline
17 & 4147.65333184262 & 4159.46488657817 & -11.8115547355555 \tabularnewline
18 & 4113.86078579022 & 4116.34297168089 & -2.48218589066298 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299338&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]4840.76686755132[/C][C]4849.41552493473[/C][C]-8.64865738341656[/C][/ROW]
[ROW][C]2[/C][C]4815.50216783705[/C][C]4806.29361003745[/C][C]9.20855779959928[/C][/ROW]
[ROW][C]3[/C][C]4769.40550920002[/C][C]4763.17169514016[/C][C]6.23381405985666[/C][/ROW]
[ROW][C]4[/C][C]4730.67688866563[/C][C]4720.04978024288[/C][C]10.6271084227586[/C][/ROW]
[ROW][C]5[/C][C]4665.11631061004[/C][C]4676.92786534559[/C][C]-11.8115547355555[/C][/ROW]
[ROW][C]6[/C][C]4631.32376455764[/C][C]4633.80595044831[/C][C]-2.48218589066298[/C][/ROW]
[ROW][C]7[/C][C]4609.49925399495[/C][C]4590.68403555102[/C][C]18.8152184439306[/C][/ROW]
[ROW][C]8[/C][C]4550.64278744506[/C][C]4547.56212065374[/C][C]3.08066679132055[/C][/ROW]
[ROW][C]9[/C][C]4501.7543561517[/C][C]4504.44020575645[/C][C]-2.68584960475389[/C][/ROW]
[ROW][C]10[/C][C]4446.01132878415[/C][C]4461.31829085917[/C][C]-15.30696207502[/C][/ROW]
[ROW][C]11[/C][C]4419.53732642485[/C][C]4418.19637596188[/C][C]1.3409504629664[/C][/ROW]
[ROW][C]12[/C][C]4366.70335477357[/C][C]4375.0744610646[/C][C]-8.37110629102312[/C][/ROW]
[ROW][C]13[/C][C]4323.30388878389[/C][C]4331.95254616731[/C][C]-8.64865738341656[/C][/ROW]
[ROW][C]14[/C][C]4298.03918906963[/C][C]4288.83063127003[/C][C]9.20855779959927[/C][/ROW]
[ROW][C]15[/C][C]4251.9425304326[/C][C]4245.70871637274[/C][C]6.23381405985667[/C][/ROW]
[ROW][C]16[/C][C]4213.21390989821[/C][C]4202.58680147546[/C][C]10.6271084227586[/C][/ROW]
[ROW][C]17[/C][C]4147.65333184262[/C][C]4159.46488657817[/C][C]-11.8115547355555[/C][/ROW]
[ROW][C]18[/C][C]4113.86078579022[/C][C]4116.34297168089[/C][C]-2.48218589066298[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299338&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299338&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
14840.766867551324849.41552493473-8.64865738341656
24815.502167837054806.293610037459.20855779959928
34769.405509200024763.171695140166.23381405985666
44730.676888665634720.0497802428810.6271084227586
54665.116310610044676.92786534559-11.8115547355555
64631.323764557644633.80595044831-2.48218589066298
74609.499253994954590.6840355510218.8152184439306
84550.642787445064547.562120653743.08066679132055
94501.75435615174504.44020575645-2.68584960475389
104446.011328784154461.31829085917-15.30696207502
114419.537326424854418.196375961881.3409504629664
124366.703354773574375.0744610646-8.37110629102312
134323.303888783894331.95254616731-8.64865738341656
144298.039189069634288.830631270039.20855779959927
154251.94253043264245.708716372746.23381405985667
164213.213909898214202.5868014754610.6271084227586
174147.653331842624159.46488657817-11.8115547355555
184113.860785790224116.34297168089-2.48218589066298



Parameters (Session):
par1 = 12 ; par2 = 18 ; par3 = BFGS ;
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')