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Author*The author of this computation has been verified*
R Software Modulerwasp_structuraltimeseries.wasp
Title produced by softwareStructural Time Series Models
Date of computationFri, 16 Dec 2016 09:53:37 +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/16/t1481878494gn1rf8e1ygoxs4p.htm/, Retrieved Fri, 01 Nov 2024 03:40:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300147, Retrieved Fri, 01 Nov 2024 03:40:38 +0000
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Original text written by user:s=4
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact71
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Structural Time Series Models] [structuaral TSM k...] [2016-12-16 08:53:37] [d92250bd36540c2281a4ec15b45df1dd] [Current]
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Dataseries X:
6173.25
5891.5
6704.15
5967.25
6356.05
6135.7
7315.8
6398.55
6284.6
6175.85
7330.5
6293.95
6405.15
6112.9
7067.6
6262.25
6437.05
6318.2
7850.75
6674.05
7012.85
6814.35
8070.45
7006.5
7246.35
7213.55
8404.85
7428.5
7455.35
7517.45
8790.15
7685.3
7717.35
7946.4
9321.85
7936.65
8314.7
8219.35
9868.6
8356.35
8481.55
8540.1
10163.55
8780.15
8724.6
8818.6
10350.65
8896.9
8838.4
9224.25
10559.3




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=300147&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=300147&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300147&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
16173.256173.25000
25891.55936.81396340674-64.5582228072565-45.3139634067385-0.531104597542968
36704.156315.0487602405438.5372846067192389.1012397594573.11298600720926
45967.256216.4113994127115.7956386605335-249.161399412713-1.42976837501949
56356.056255.51497714416.8516175207444100.5350228560020.265339093004089
66135.76341.3846589843221.8010732162777-205.684658984320.747449232670975
77315.86605.3084435430945.9750779497022710.4915564569092.47864159727307
86398.556707.9281337698551.5697329423396-309.3781337698530.590033277483625
96284.66556.5406482365234.3870039629774-271.94064823652-2.16655889887302
106175.856519.7483587114928.6659614323055-343.898358711489-0.761915622237051
117330.56559.3273556159429.564797046535771.1726443840620.116189307794489
126293.956540.9241388770625.5871504044799-246.974138877065-0.510533236157889
136405.156588.6198046515927.3801625178044-183.4698046515890.236146776085698
146112.96548.5691208285822.0198477177033-435.669120828583-0.721844302688699
157067.66425.2437530127110.5499305617703642.35624698729-1.55659186182866
166262.256435.8703515197410.5559592137298-173.620351519740.000821313478905336
176437.056492.7474793625214.1767645619631-55.69747936251730.496584469708406
186318.26589.9701346730620.6255520289703-271.7701346730640.890959697484241
197850.756896.5934540489142.7254806737365954.1565459510933.06983633406303
206674.056980.1655929241945.8709594704307-306.1155929241940.438585236031581
217012.857101.4564912547951.6613669952939-88.60649125479130.810065890859894
226814.357214.4392734597456.3560860228298-400.0892734597440.658835693028936
238070.457233.2946989488253.4920051808317837.155301051181-0.403007070879189
247006.57314.5300100409355.6067257895456-308.0300100409270.298207212822629
257246.357372.2036574374855.7640191503516-125.8536574374760.0222206178561047
267213.557503.6029393720761.5117918649544-290.0529393720670.813241243972893
278404.857589.6960640871463.3775522636088815.1539359128620.264334845205438
287428.57702.9114968855967.1564720931288-274.4114968855880.535986252685203
297455.357718.7193300231763.2663313191709-263.36933002317-0.552281939507468
307517.457792.9280649910764.0947197602143-275.4780649910660.117700079111652
318790.157918.7447001500768.7644593493869871.4052998499330.663942936973955
327685.37977.0225911925667.9714845257268-291.722591192556-0.112810075244348
337717.358023.0235771253866.3108512244485-305.673577125382-0.23635998303457
347946.48157.1752864996171.4366611735247-210.7752864996110.72986393657201
359321.858336.3256131010979.5725326520437985.5243868989111.15887180333748
367936.658357.7555714232475.1820663862742-421.105571423242-0.62556252982288
378314.78529.9264265757182.5042214137597-215.2264265757071.04353750594688
388219.358574.2262439716679.6205420391004-354.876243971661-0.411063078086825
399868.68741.4266928342386.23001751100561127.173307165770.942338058247857
408356.358844.8453173419187.5270266003852-488.4953173419060.184947746556763
418481.558831.3088450182879.9019241104355-349.758845018282-1.08744641830966
428540.18905.4057958219179.4639903798089-365.305795821909-0.0624623252324555
4310163.559000.859727811880.67018799333011162.69027218820.17205548041109
448780.159141.8816676484785.2224838226857-361.7316676484710.649403550206814
458724.69173.0373866609681.1445072649869-448.437386660959-0.58177871091093
468818.69221.2316449938578.6593676036415-402.631644993848-0.354558905453758
4710350.659253.1807193850975.13658491619791097.46928061491-0.502625135295324
488896.99270.9911442593670.8133368968208-374.091144259362-0.616859248619134
498838.49292.5529133842267.0991492762736-454.15291338422-0.529974116879503
509224.259449.6120796519973.8830870181986-225.3620796519860.968022141635347
5110559.39496.9914449073371.88447043937241062.30855509267-0.28519611829763

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Interpolation \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 6173.25 & 6173.25 & 0 & 0 & 0 \tabularnewline
2 & 5891.5 & 5936.81396340674 & -64.5582228072565 & -45.3139634067385 & -0.531104597542968 \tabularnewline
3 & 6704.15 & 6315.04876024054 & 38.5372846067192 & 389.101239759457 & 3.11298600720926 \tabularnewline
4 & 5967.25 & 6216.41139941271 & 15.7956386605335 & -249.161399412713 & -1.42976837501949 \tabularnewline
5 & 6356.05 & 6255.514977144 & 16.8516175207444 & 100.535022856002 & 0.265339093004089 \tabularnewline
6 & 6135.7 & 6341.38465898432 & 21.8010732162777 & -205.68465898432 & 0.747449232670975 \tabularnewline
7 & 7315.8 & 6605.30844354309 & 45.9750779497022 & 710.491556456909 & 2.47864159727307 \tabularnewline
8 & 6398.55 & 6707.92813376985 & 51.5697329423396 & -309.378133769853 & 0.590033277483625 \tabularnewline
9 & 6284.6 & 6556.54064823652 & 34.3870039629774 & -271.94064823652 & -2.16655889887302 \tabularnewline
10 & 6175.85 & 6519.74835871149 & 28.6659614323055 & -343.898358711489 & -0.761915622237051 \tabularnewline
11 & 7330.5 & 6559.32735561594 & 29.564797046535 & 771.172644384062 & 0.116189307794489 \tabularnewline
12 & 6293.95 & 6540.92413887706 & 25.5871504044799 & -246.974138877065 & -0.510533236157889 \tabularnewline
13 & 6405.15 & 6588.61980465159 & 27.3801625178044 & -183.469804651589 & 0.236146776085698 \tabularnewline
14 & 6112.9 & 6548.56912082858 & 22.0198477177033 & -435.669120828583 & -0.721844302688699 \tabularnewline
15 & 7067.6 & 6425.24375301271 & 10.5499305617703 & 642.35624698729 & -1.55659186182866 \tabularnewline
16 & 6262.25 & 6435.87035151974 & 10.5559592137298 & -173.62035151974 & 0.000821313478905336 \tabularnewline
17 & 6437.05 & 6492.74747936252 & 14.1767645619631 & -55.6974793625173 & 0.496584469708406 \tabularnewline
18 & 6318.2 & 6589.97013467306 & 20.6255520289703 & -271.770134673064 & 0.890959697484241 \tabularnewline
19 & 7850.75 & 6896.59345404891 & 42.7254806737365 & 954.156545951093 & 3.06983633406303 \tabularnewline
20 & 6674.05 & 6980.16559292419 & 45.8709594704307 & -306.115592924194 & 0.438585236031581 \tabularnewline
21 & 7012.85 & 7101.45649125479 & 51.6613669952939 & -88.6064912547913 & 0.810065890859894 \tabularnewline
22 & 6814.35 & 7214.43927345974 & 56.3560860228298 & -400.089273459744 & 0.658835693028936 \tabularnewline
23 & 8070.45 & 7233.29469894882 & 53.4920051808317 & 837.155301051181 & -0.403007070879189 \tabularnewline
24 & 7006.5 & 7314.53001004093 & 55.6067257895456 & -308.030010040927 & 0.298207212822629 \tabularnewline
25 & 7246.35 & 7372.20365743748 & 55.7640191503516 & -125.853657437476 & 0.0222206178561047 \tabularnewline
26 & 7213.55 & 7503.60293937207 & 61.5117918649544 & -290.052939372067 & 0.813241243972893 \tabularnewline
27 & 8404.85 & 7589.69606408714 & 63.3775522636088 & 815.153935912862 & 0.264334845205438 \tabularnewline
28 & 7428.5 & 7702.91149688559 & 67.1564720931288 & -274.411496885588 & 0.535986252685203 \tabularnewline
29 & 7455.35 & 7718.71933002317 & 63.2663313191709 & -263.36933002317 & -0.552281939507468 \tabularnewline
30 & 7517.45 & 7792.92806499107 & 64.0947197602143 & -275.478064991066 & 0.117700079111652 \tabularnewline
31 & 8790.15 & 7918.74470015007 & 68.7644593493869 & 871.405299849933 & 0.663942936973955 \tabularnewline
32 & 7685.3 & 7977.02259119256 & 67.9714845257268 & -291.722591192556 & -0.112810075244348 \tabularnewline
33 & 7717.35 & 8023.02357712538 & 66.3108512244485 & -305.673577125382 & -0.23635998303457 \tabularnewline
34 & 7946.4 & 8157.17528649961 & 71.4366611735247 & -210.775286499611 & 0.72986393657201 \tabularnewline
35 & 9321.85 & 8336.32561310109 & 79.5725326520437 & 985.524386898911 & 1.15887180333748 \tabularnewline
36 & 7936.65 & 8357.75557142324 & 75.1820663862742 & -421.105571423242 & -0.62556252982288 \tabularnewline
37 & 8314.7 & 8529.92642657571 & 82.5042214137597 & -215.226426575707 & 1.04353750594688 \tabularnewline
38 & 8219.35 & 8574.22624397166 & 79.6205420391004 & -354.876243971661 & -0.411063078086825 \tabularnewline
39 & 9868.6 & 8741.42669283423 & 86.2300175110056 & 1127.17330716577 & 0.942338058247857 \tabularnewline
40 & 8356.35 & 8844.84531734191 & 87.5270266003852 & -488.495317341906 & 0.184947746556763 \tabularnewline
41 & 8481.55 & 8831.30884501828 & 79.9019241104355 & -349.758845018282 & -1.08744641830966 \tabularnewline
42 & 8540.1 & 8905.40579582191 & 79.4639903798089 & -365.305795821909 & -0.0624623252324555 \tabularnewline
43 & 10163.55 & 9000.8597278118 & 80.6701879933301 & 1162.6902721882 & 0.17205548041109 \tabularnewline
44 & 8780.15 & 9141.88166764847 & 85.2224838226857 & -361.731667648471 & 0.649403550206814 \tabularnewline
45 & 8724.6 & 9173.03738666096 & 81.1445072649869 & -448.437386660959 & -0.58177871091093 \tabularnewline
46 & 8818.6 & 9221.23164499385 & 78.6593676036415 & -402.631644993848 & -0.354558905453758 \tabularnewline
47 & 10350.65 & 9253.18071938509 & 75.1365849161979 & 1097.46928061491 & -0.502625135295324 \tabularnewline
48 & 8896.9 & 9270.99114425936 & 70.8133368968208 & -374.091144259362 & -0.616859248619134 \tabularnewline
49 & 8838.4 & 9292.55291338422 & 67.0991492762736 & -454.15291338422 & -0.529974116879503 \tabularnewline
50 & 9224.25 & 9449.61207965199 & 73.8830870181986 & -225.362079651986 & 0.968022141635347 \tabularnewline
51 & 10559.3 & 9496.99144490733 & 71.8844704393724 & 1062.30855509267 & -0.28519611829763 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300147&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]6173.25[/C][C]6173.25[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]5891.5[/C][C]5936.81396340674[/C][C]-64.5582228072565[/C][C]-45.3139634067385[/C][C]-0.531104597542968[/C][/ROW]
[ROW][C]3[/C][C]6704.15[/C][C]6315.04876024054[/C][C]38.5372846067192[/C][C]389.101239759457[/C][C]3.11298600720926[/C][/ROW]
[ROW][C]4[/C][C]5967.25[/C][C]6216.41139941271[/C][C]15.7956386605335[/C][C]-249.161399412713[/C][C]-1.42976837501949[/C][/ROW]
[ROW][C]5[/C][C]6356.05[/C][C]6255.514977144[/C][C]16.8516175207444[/C][C]100.535022856002[/C][C]0.265339093004089[/C][/ROW]
[ROW][C]6[/C][C]6135.7[/C][C]6341.38465898432[/C][C]21.8010732162777[/C][C]-205.68465898432[/C][C]0.747449232670975[/C][/ROW]
[ROW][C]7[/C][C]7315.8[/C][C]6605.30844354309[/C][C]45.9750779497022[/C][C]710.491556456909[/C][C]2.47864159727307[/C][/ROW]
[ROW][C]8[/C][C]6398.55[/C][C]6707.92813376985[/C][C]51.5697329423396[/C][C]-309.378133769853[/C][C]0.590033277483625[/C][/ROW]
[ROW][C]9[/C][C]6284.6[/C][C]6556.54064823652[/C][C]34.3870039629774[/C][C]-271.94064823652[/C][C]-2.16655889887302[/C][/ROW]
[ROW][C]10[/C][C]6175.85[/C][C]6519.74835871149[/C][C]28.6659614323055[/C][C]-343.898358711489[/C][C]-0.761915622237051[/C][/ROW]
[ROW][C]11[/C][C]7330.5[/C][C]6559.32735561594[/C][C]29.564797046535[/C][C]771.172644384062[/C][C]0.116189307794489[/C][/ROW]
[ROW][C]12[/C][C]6293.95[/C][C]6540.92413887706[/C][C]25.5871504044799[/C][C]-246.974138877065[/C][C]-0.510533236157889[/C][/ROW]
[ROW][C]13[/C][C]6405.15[/C][C]6588.61980465159[/C][C]27.3801625178044[/C][C]-183.469804651589[/C][C]0.236146776085698[/C][/ROW]
[ROW][C]14[/C][C]6112.9[/C][C]6548.56912082858[/C][C]22.0198477177033[/C][C]-435.669120828583[/C][C]-0.721844302688699[/C][/ROW]
[ROW][C]15[/C][C]7067.6[/C][C]6425.24375301271[/C][C]10.5499305617703[/C][C]642.35624698729[/C][C]-1.55659186182866[/C][/ROW]
[ROW][C]16[/C][C]6262.25[/C][C]6435.87035151974[/C][C]10.5559592137298[/C][C]-173.62035151974[/C][C]0.000821313478905336[/C][/ROW]
[ROW][C]17[/C][C]6437.05[/C][C]6492.74747936252[/C][C]14.1767645619631[/C][C]-55.6974793625173[/C][C]0.496584469708406[/C][/ROW]
[ROW][C]18[/C][C]6318.2[/C][C]6589.97013467306[/C][C]20.6255520289703[/C][C]-271.770134673064[/C][C]0.890959697484241[/C][/ROW]
[ROW][C]19[/C][C]7850.75[/C][C]6896.59345404891[/C][C]42.7254806737365[/C][C]954.156545951093[/C][C]3.06983633406303[/C][/ROW]
[ROW][C]20[/C][C]6674.05[/C][C]6980.16559292419[/C][C]45.8709594704307[/C][C]-306.115592924194[/C][C]0.438585236031581[/C][/ROW]
[ROW][C]21[/C][C]7012.85[/C][C]7101.45649125479[/C][C]51.6613669952939[/C][C]-88.6064912547913[/C][C]0.810065890859894[/C][/ROW]
[ROW][C]22[/C][C]6814.35[/C][C]7214.43927345974[/C][C]56.3560860228298[/C][C]-400.089273459744[/C][C]0.658835693028936[/C][/ROW]
[ROW][C]23[/C][C]8070.45[/C][C]7233.29469894882[/C][C]53.4920051808317[/C][C]837.155301051181[/C][C]-0.403007070879189[/C][/ROW]
[ROW][C]24[/C][C]7006.5[/C][C]7314.53001004093[/C][C]55.6067257895456[/C][C]-308.030010040927[/C][C]0.298207212822629[/C][/ROW]
[ROW][C]25[/C][C]7246.35[/C][C]7372.20365743748[/C][C]55.7640191503516[/C][C]-125.853657437476[/C][C]0.0222206178561047[/C][/ROW]
[ROW][C]26[/C][C]7213.55[/C][C]7503.60293937207[/C][C]61.5117918649544[/C][C]-290.052939372067[/C][C]0.813241243972893[/C][/ROW]
[ROW][C]27[/C][C]8404.85[/C][C]7589.69606408714[/C][C]63.3775522636088[/C][C]815.153935912862[/C][C]0.264334845205438[/C][/ROW]
[ROW][C]28[/C][C]7428.5[/C][C]7702.91149688559[/C][C]67.1564720931288[/C][C]-274.411496885588[/C][C]0.535986252685203[/C][/ROW]
[ROW][C]29[/C][C]7455.35[/C][C]7718.71933002317[/C][C]63.2663313191709[/C][C]-263.36933002317[/C][C]-0.552281939507468[/C][/ROW]
[ROW][C]30[/C][C]7517.45[/C][C]7792.92806499107[/C][C]64.0947197602143[/C][C]-275.478064991066[/C][C]0.117700079111652[/C][/ROW]
[ROW][C]31[/C][C]8790.15[/C][C]7918.74470015007[/C][C]68.7644593493869[/C][C]871.405299849933[/C][C]0.663942936973955[/C][/ROW]
[ROW][C]32[/C][C]7685.3[/C][C]7977.02259119256[/C][C]67.9714845257268[/C][C]-291.722591192556[/C][C]-0.112810075244348[/C][/ROW]
[ROW][C]33[/C][C]7717.35[/C][C]8023.02357712538[/C][C]66.3108512244485[/C][C]-305.673577125382[/C][C]-0.23635998303457[/C][/ROW]
[ROW][C]34[/C][C]7946.4[/C][C]8157.17528649961[/C][C]71.4366611735247[/C][C]-210.775286499611[/C][C]0.72986393657201[/C][/ROW]
[ROW][C]35[/C][C]9321.85[/C][C]8336.32561310109[/C][C]79.5725326520437[/C][C]985.524386898911[/C][C]1.15887180333748[/C][/ROW]
[ROW][C]36[/C][C]7936.65[/C][C]8357.75557142324[/C][C]75.1820663862742[/C][C]-421.105571423242[/C][C]-0.62556252982288[/C][/ROW]
[ROW][C]37[/C][C]8314.7[/C][C]8529.92642657571[/C][C]82.5042214137597[/C][C]-215.226426575707[/C][C]1.04353750594688[/C][/ROW]
[ROW][C]38[/C][C]8219.35[/C][C]8574.22624397166[/C][C]79.6205420391004[/C][C]-354.876243971661[/C][C]-0.411063078086825[/C][/ROW]
[ROW][C]39[/C][C]9868.6[/C][C]8741.42669283423[/C][C]86.2300175110056[/C][C]1127.17330716577[/C][C]0.942338058247857[/C][/ROW]
[ROW][C]40[/C][C]8356.35[/C][C]8844.84531734191[/C][C]87.5270266003852[/C][C]-488.495317341906[/C][C]0.184947746556763[/C][/ROW]
[ROW][C]41[/C][C]8481.55[/C][C]8831.30884501828[/C][C]79.9019241104355[/C][C]-349.758845018282[/C][C]-1.08744641830966[/C][/ROW]
[ROW][C]42[/C][C]8540.1[/C][C]8905.40579582191[/C][C]79.4639903798089[/C][C]-365.305795821909[/C][C]-0.0624623252324555[/C][/ROW]
[ROW][C]43[/C][C]10163.55[/C][C]9000.8597278118[/C][C]80.6701879933301[/C][C]1162.6902721882[/C][C]0.17205548041109[/C][/ROW]
[ROW][C]44[/C][C]8780.15[/C][C]9141.88166764847[/C][C]85.2224838226857[/C][C]-361.731667648471[/C][C]0.649403550206814[/C][/ROW]
[ROW][C]45[/C][C]8724.6[/C][C]9173.03738666096[/C][C]81.1445072649869[/C][C]-448.437386660959[/C][C]-0.58177871091093[/C][/ROW]
[ROW][C]46[/C][C]8818.6[/C][C]9221.23164499385[/C][C]78.6593676036415[/C][C]-402.631644993848[/C][C]-0.354558905453758[/C][/ROW]
[ROW][C]47[/C][C]10350.65[/C][C]9253.18071938509[/C][C]75.1365849161979[/C][C]1097.46928061491[/C][C]-0.502625135295324[/C][/ROW]
[ROW][C]48[/C][C]8896.9[/C][C]9270.99114425936[/C][C]70.8133368968208[/C][C]-374.091144259362[/C][C]-0.616859248619134[/C][/ROW]
[ROW][C]49[/C][C]8838.4[/C][C]9292.55291338422[/C][C]67.0991492762736[/C][C]-454.15291338422[/C][C]-0.529974116879503[/C][/ROW]
[ROW][C]50[/C][C]9224.25[/C][C]9449.61207965199[/C][C]73.8830870181986[/C][C]-225.362079651986[/C][C]0.968022141635347[/C][/ROW]
[ROW][C]51[/C][C]10559.3[/C][C]9496.99144490733[/C][C]71.8844704393724[/C][C]1062.30855509267[/C][C]-0.28519611829763[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300147&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300147&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
16173.256173.25000
25891.55936.81396340674-64.5582228072565-45.3139634067385-0.531104597542968
36704.156315.0487602405438.5372846067192389.1012397594573.11298600720926
45967.256216.4113994127115.7956386605335-249.161399412713-1.42976837501949
56356.056255.51497714416.8516175207444100.5350228560020.265339093004089
66135.76341.3846589843221.8010732162777-205.684658984320.747449232670975
77315.86605.3084435430945.9750779497022710.4915564569092.47864159727307
86398.556707.9281337698551.5697329423396-309.3781337698530.590033277483625
96284.66556.5406482365234.3870039629774-271.94064823652-2.16655889887302
106175.856519.7483587114928.6659614323055-343.898358711489-0.761915622237051
117330.56559.3273556159429.564797046535771.1726443840620.116189307794489
126293.956540.9241388770625.5871504044799-246.974138877065-0.510533236157889
136405.156588.6198046515927.3801625178044-183.4698046515890.236146776085698
146112.96548.5691208285822.0198477177033-435.669120828583-0.721844302688699
157067.66425.2437530127110.5499305617703642.35624698729-1.55659186182866
166262.256435.8703515197410.5559592137298-173.620351519740.000821313478905336
176437.056492.7474793625214.1767645619631-55.69747936251730.496584469708406
186318.26589.9701346730620.6255520289703-271.7701346730640.890959697484241
197850.756896.5934540489142.7254806737365954.1565459510933.06983633406303
206674.056980.1655929241945.8709594704307-306.1155929241940.438585236031581
217012.857101.4564912547951.6613669952939-88.60649125479130.810065890859894
226814.357214.4392734597456.3560860228298-400.0892734597440.658835693028936
238070.457233.2946989488253.4920051808317837.155301051181-0.403007070879189
247006.57314.5300100409355.6067257895456-308.0300100409270.298207212822629
257246.357372.2036574374855.7640191503516-125.8536574374760.0222206178561047
267213.557503.6029393720761.5117918649544-290.0529393720670.813241243972893
278404.857589.6960640871463.3775522636088815.1539359128620.264334845205438
287428.57702.9114968855967.1564720931288-274.4114968855880.535986252685203
297455.357718.7193300231763.2663313191709-263.36933002317-0.552281939507468
307517.457792.9280649910764.0947197602143-275.4780649910660.117700079111652
318790.157918.7447001500768.7644593493869871.4052998499330.663942936973955
327685.37977.0225911925667.9714845257268-291.722591192556-0.112810075244348
337717.358023.0235771253866.3108512244485-305.673577125382-0.23635998303457
347946.48157.1752864996171.4366611735247-210.7752864996110.72986393657201
359321.858336.3256131010979.5725326520437985.5243868989111.15887180333748
367936.658357.7555714232475.1820663862742-421.105571423242-0.62556252982288
378314.78529.9264265757182.5042214137597-215.2264265757071.04353750594688
388219.358574.2262439716679.6205420391004-354.876243971661-0.411063078086825
399868.68741.4266928342386.23001751100561127.173307165770.942338058247857
408356.358844.8453173419187.5270266003852-488.4953173419060.184947746556763
418481.558831.3088450182879.9019241104355-349.758845018282-1.08744641830966
428540.18905.4057958219179.4639903798089-365.305795821909-0.0624623252324555
4310163.559000.859727811880.67018799333011162.69027218820.17205548041109
448780.159141.8816676484785.2224838226857-361.7316676484710.649403550206814
458724.69173.0373866609681.1445072649869-448.437386660959-0.58177871091093
468818.69221.2316449938578.6593676036415-402.631644993848-0.354558905453758
4710350.659253.1807193850975.13658491619791097.46928061491-0.502625135295324
488896.99270.9911442593670.8133368968208-374.091144259362-0.616859248619134
498838.49292.5529133842267.0991492762736-454.15291338422-0.529974116879503
509224.259449.6120796519973.8830870181986-225.3620796519860.968022141635347
5110559.39496.9914449073371.88447043937241062.30855509267-0.28519611829763







Structural Time Series Model -- Extrapolation
tObservedLevelSeasonal
19204.111128032519559.14547430822-355.034346275704
29144.064232809479626.23795388001-482.173721070545
39456.241192676849693.3304334518-237.089240774962
410834.72022114489760.42291302361074.29730812121
59472.481046319689827.51539259539-355.034346275704
69412.434151096649894.60787216718-482.173721070545
79724.611110964019961.70035173897-237.089240774962
811103.09013943210028.79283131081074.29730812121
99740.8509646068610095.8853108826-355.034346275704
109680.8040693838110162.9777904544-482.173721070545
119992.9810292511810230.0702700261-237.089240774962
1211371.460057719210297.16274959791074.29730812121

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Extrapolation \tabularnewline
t & Observed & Level & Seasonal \tabularnewline
1 & 9204.11112803251 & 9559.14547430822 & -355.034346275704 \tabularnewline
2 & 9144.06423280947 & 9626.23795388001 & -482.173721070545 \tabularnewline
3 & 9456.24119267684 & 9693.3304334518 & -237.089240774962 \tabularnewline
4 & 10834.7202211448 & 9760.4229130236 & 1074.29730812121 \tabularnewline
5 & 9472.48104631968 & 9827.51539259539 & -355.034346275704 \tabularnewline
6 & 9412.43415109664 & 9894.60787216718 & -482.173721070545 \tabularnewline
7 & 9724.61111096401 & 9961.70035173897 & -237.089240774962 \tabularnewline
8 & 11103.090139432 & 10028.7928313108 & 1074.29730812121 \tabularnewline
9 & 9740.85096460686 & 10095.8853108826 & -355.034346275704 \tabularnewline
10 & 9680.80406938381 & 10162.9777904544 & -482.173721070545 \tabularnewline
11 & 9992.98102925118 & 10230.0702700261 & -237.089240774962 \tabularnewline
12 & 11371.4600577192 & 10297.1627495979 & 1074.29730812121 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300147&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]9204.11112803251[/C][C]9559.14547430822[/C][C]-355.034346275704[/C][/ROW]
[ROW][C]2[/C][C]9144.06423280947[/C][C]9626.23795388001[/C][C]-482.173721070545[/C][/ROW]
[ROW][C]3[/C][C]9456.24119267684[/C][C]9693.3304334518[/C][C]-237.089240774962[/C][/ROW]
[ROW][C]4[/C][C]10834.7202211448[/C][C]9760.4229130236[/C][C]1074.29730812121[/C][/ROW]
[ROW][C]5[/C][C]9472.48104631968[/C][C]9827.51539259539[/C][C]-355.034346275704[/C][/ROW]
[ROW][C]6[/C][C]9412.43415109664[/C][C]9894.60787216718[/C][C]-482.173721070545[/C][/ROW]
[ROW][C]7[/C][C]9724.61111096401[/C][C]9961.70035173897[/C][C]-237.089240774962[/C][/ROW]
[ROW][C]8[/C][C]11103.090139432[/C][C]10028.7928313108[/C][C]1074.29730812121[/C][/ROW]
[ROW][C]9[/C][C]9740.85096460686[/C][C]10095.8853108826[/C][C]-355.034346275704[/C][/ROW]
[ROW][C]10[/C][C]9680.80406938381[/C][C]10162.9777904544[/C][C]-482.173721070545[/C][/ROW]
[ROW][C]11[/C][C]9992.98102925118[/C][C]10230.0702700261[/C][C]-237.089240774962[/C][/ROW]
[ROW][C]12[/C][C]11371.4600577192[/C][C]10297.1627495979[/C][C]1074.29730812121[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300147&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300147&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
19204.111128032519559.14547430822-355.034346275704
29144.064232809479626.23795388001-482.173721070545
39456.241192676849693.3304334518-237.089240774962
410834.72022114489760.42291302361074.29730812121
59472.481046319689827.51539259539-355.034346275704
69412.434151096649894.60787216718-482.173721070545
79724.611110964019961.70035173897-237.089240774962
811103.09013943210028.79283131081074.29730812121
99740.8509646068610095.8853108826-355.034346275704
109680.8040693838110162.9777904544-482.173721070545
119992.9810292511810230.0702700261-237.089240774962
1211371.460057719210297.16274959791074.29730812121



Parameters (Session):
par4 = 12 ;
Parameters (R input):
par1 = 4 ; 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')