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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 computationSun, 18 Dec 2016 16:18:40 +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/18/t1482074333vh3283te4ghabt5.htm/, Retrieved Thu, 09 May 2024 01:18:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301133, Retrieved Thu, 09 May 2024 01:18:53 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact54
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Structural Time Series Models] [] [2016-12-18 15:18:40] [94ac3c9a028ddd47e8862e80eac9f626] [Current]
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Dataseries X:
3830.8
3732.6
3733.5
3808.5
3860.5
3844.4
3864.5
3803.1
3756.1
3771.1
3754.4
3759.6
3783.5
3886.5
3944.4
4012.1
4089.5
4144
4166.4
4194.2
4221.8
4254.8
4309
4333.5
4390.5
4387.7
4412.6
4427.1
4460
4515.3
4559.3
4625.5
4655.3
4704.8
4734.5
4779.7
4817.6
4839
4839
4856.7
4890.8
4902.7
4882.6
4833.8
4796.7




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=301133&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=301133&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301133&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
13830.83830.8000
23732.63737.16648290901-14.9495221726765-4.56648290900555-1.96467826524488
33733.53738.18173574763-8.63524293686449-4.681735747631790.456928137425495
43808.53813.526641587727.5692375179069-5.026641587703622.34098542009954
53860.53865.5826824548838.4108084118853-5.082682454878910.677234877165529
63844.43849.4135493147314.0382796479509-5.01354931472908-1.50651872804929
73864.53869.5177919196416.754747306958-5.017791919636270.167373388027878
83803.13808.08762156376-18.293402930622-4.98762156375733-2.15736458926796
93756.13761.08151044507-31.1694629474513-4.9815104450718-0.792341996436287
103771.13776.08693026831-10.4592800436391-4.986930268313791.27430816214484
113754.43759.38652629804-13.2587271687332-4.98652629804247-0.172246693797902
123759.63764.5871851666-4.97850673903523-4.987185166595740.509467991879174
133783.53736.41868978367-15.066847322936647.0813102163304-0.728189688735594
143886.53887.2236702848652.3396101524358-0.7236702848625253.7269789676856
153944.43945.1397893381254.8553803170647-0.7397893381154150.152930158479818
164012.14012.8602778191360.6322950803448-0.7602778191336470.354139054804865
174089.54090.2750166453968.1599485916095-0.7750166453941420.462645134729857
1841444144.7683970042162.0308703767303-0.76839700420865-0.376982433047262
194166.44167.1578075283144.2518938301295-0.757807528310551-1.09379350572473
204194.24194.9553835413936.871715396224-0.755383541387527-0.454074017430514
214221.84222.5546302665332.7125680059376-0.754630266529469-0.255901946518255
224254.84255.5546431433732.841504921216-0.7546431433654070.00793321892617359
2343094309.75517076942.4225347753111-0.7551707689969690.589501933875371
244333.54334.2549266306534.3828173168468-0.754926630647856-0.494668315689898
254390.54380.3695349299739.571580140147110.13046507002940.3456058968501
264387.74389.0453745623626.5476035784904-1.34537456236095-0.755829997012713
274412.64413.942284012325.8044009698228-1.34228401230006-0.0453712644318577
284427.14428.4306077784620.7248771220181-1.33060777845529-0.311790704031371
2944604461.3375392950626.1892194482507-1.337539295057740.33596743950124
304515.34516.6466769536939.2498160292586-1.346676953690080.803416833374424
314559.34560.6474991132641.3807615447572-1.347499113262090.131104237328186
324625.54626.8498678153152.5143714510647-1.349867815312480.685015808922636
334655.34656.6486724447442.3250818929511-1.34867244474483-0.626923635234447
344704.84706.1488806538545.5436210767587-1.348880653848460.198030191933138
354734.54735.848627130238.4364643028735-1.34862713020201-0.43728952202098
364779.74781.0486868088841.470461059029-1.348686808876950.18667598890538
374817.64804.5824805656933.497972859945413.0175194343065-0.517127907503195
3848394840.1623712926734.3904754791317-1.162371292674920.0527553922958677
3948394840.1146884442318.9000073716232-1.11468844422868-0.947597829489724
404856.74857.8137719132318.3610329037732-1.11377191323138-0.0331037726064103
414890.84891.9203984482125.4239259221105-1.120398448213590.434333906190577
424902.74903.8172589979819.3566427259595-1.11725899798342-0.373247625443854
434882.64883.712208433371.65650405304634-1.11220843337285-1.0890018437035
444833.84834.90864708396-20.9775876331307-1.10864708396321-1.39261145836413
454796.74797.80801959266-28.2098256156984-1.10801959266372-0.444983745077702

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Interpolation \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 3830.8 & 3830.8 & 0 & 0 & 0 \tabularnewline
2 & 3732.6 & 3737.16648290901 & -14.9495221726765 & -4.56648290900555 & -1.96467826524488 \tabularnewline
3 & 3733.5 & 3738.18173574763 & -8.63524293686449 & -4.68173574763179 & 0.456928137425495 \tabularnewline
4 & 3808.5 & 3813.5266415877 & 27.5692375179069 & -5.02664158770362 & 2.34098542009954 \tabularnewline
5 & 3860.5 & 3865.58268245488 & 38.4108084118853 & -5.08268245487891 & 0.677234877165529 \tabularnewline
6 & 3844.4 & 3849.41354931473 & 14.0382796479509 & -5.01354931472908 & -1.50651872804929 \tabularnewline
7 & 3864.5 & 3869.51779191964 & 16.754747306958 & -5.01779191963627 & 0.167373388027878 \tabularnewline
8 & 3803.1 & 3808.08762156376 & -18.293402930622 & -4.98762156375733 & -2.15736458926796 \tabularnewline
9 & 3756.1 & 3761.08151044507 & -31.1694629474513 & -4.9815104450718 & -0.792341996436287 \tabularnewline
10 & 3771.1 & 3776.08693026831 & -10.4592800436391 & -4.98693026831379 & 1.27430816214484 \tabularnewline
11 & 3754.4 & 3759.38652629804 & -13.2587271687332 & -4.98652629804247 & -0.172246693797902 \tabularnewline
12 & 3759.6 & 3764.5871851666 & -4.97850673903523 & -4.98718516659574 & 0.509467991879174 \tabularnewline
13 & 3783.5 & 3736.41868978367 & -15.0668473229366 & 47.0813102163304 & -0.728189688735594 \tabularnewline
14 & 3886.5 & 3887.22367028486 & 52.3396101524358 & -0.723670284862525 & 3.7269789676856 \tabularnewline
15 & 3944.4 & 3945.13978933812 & 54.8553803170647 & -0.739789338115415 & 0.152930158479818 \tabularnewline
16 & 4012.1 & 4012.86027781913 & 60.6322950803448 & -0.760277819133647 & 0.354139054804865 \tabularnewline
17 & 4089.5 & 4090.27501664539 & 68.1599485916095 & -0.775016645394142 & 0.462645134729857 \tabularnewline
18 & 4144 & 4144.76839700421 & 62.0308703767303 & -0.76839700420865 & -0.376982433047262 \tabularnewline
19 & 4166.4 & 4167.15780752831 & 44.2518938301295 & -0.757807528310551 & -1.09379350572473 \tabularnewline
20 & 4194.2 & 4194.95538354139 & 36.871715396224 & -0.755383541387527 & -0.454074017430514 \tabularnewline
21 & 4221.8 & 4222.55463026653 & 32.7125680059376 & -0.754630266529469 & -0.255901946518255 \tabularnewline
22 & 4254.8 & 4255.55464314337 & 32.841504921216 & -0.754643143365407 & 0.00793321892617359 \tabularnewline
23 & 4309 & 4309.755170769 & 42.4225347753111 & -0.755170768996969 & 0.589501933875371 \tabularnewline
24 & 4333.5 & 4334.25492663065 & 34.3828173168468 & -0.754926630647856 & -0.494668315689898 \tabularnewline
25 & 4390.5 & 4380.36953492997 & 39.5715801401471 & 10.1304650700294 & 0.3456058968501 \tabularnewline
26 & 4387.7 & 4389.04537456236 & 26.5476035784904 & -1.34537456236095 & -0.755829997012713 \tabularnewline
27 & 4412.6 & 4413.9422840123 & 25.8044009698228 & -1.34228401230006 & -0.0453712644318577 \tabularnewline
28 & 4427.1 & 4428.43060777846 & 20.7248771220181 & -1.33060777845529 & -0.311790704031371 \tabularnewline
29 & 4460 & 4461.33753929506 & 26.1892194482507 & -1.33753929505774 & 0.33596743950124 \tabularnewline
30 & 4515.3 & 4516.64667695369 & 39.2498160292586 & -1.34667695369008 & 0.803416833374424 \tabularnewline
31 & 4559.3 & 4560.64749911326 & 41.3807615447572 & -1.34749911326209 & 0.131104237328186 \tabularnewline
32 & 4625.5 & 4626.84986781531 & 52.5143714510647 & -1.34986781531248 & 0.685015808922636 \tabularnewline
33 & 4655.3 & 4656.64867244474 & 42.3250818929511 & -1.34867244474483 & -0.626923635234447 \tabularnewline
34 & 4704.8 & 4706.14888065385 & 45.5436210767587 & -1.34888065384846 & 0.198030191933138 \tabularnewline
35 & 4734.5 & 4735.8486271302 & 38.4364643028735 & -1.34862713020201 & -0.43728952202098 \tabularnewline
36 & 4779.7 & 4781.04868680888 & 41.470461059029 & -1.34868680887695 & 0.18667598890538 \tabularnewline
37 & 4817.6 & 4804.58248056569 & 33.4979728599454 & 13.0175194343065 & -0.517127907503195 \tabularnewline
38 & 4839 & 4840.16237129267 & 34.3904754791317 & -1.16237129267492 & 0.0527553922958677 \tabularnewline
39 & 4839 & 4840.11468844423 & 18.9000073716232 & -1.11468844422868 & -0.947597829489724 \tabularnewline
40 & 4856.7 & 4857.81377191323 & 18.3610329037732 & -1.11377191323138 & -0.0331037726064103 \tabularnewline
41 & 4890.8 & 4891.92039844821 & 25.4239259221105 & -1.12039844821359 & 0.434333906190577 \tabularnewline
42 & 4902.7 & 4903.81725899798 & 19.3566427259595 & -1.11725899798342 & -0.373247625443854 \tabularnewline
43 & 4882.6 & 4883.71220843337 & 1.65650405304634 & -1.11220843337285 & -1.0890018437035 \tabularnewline
44 & 4833.8 & 4834.90864708396 & -20.9775876331307 & -1.10864708396321 & -1.39261145836413 \tabularnewline
45 & 4796.7 & 4797.80801959266 & -28.2098256156984 & -1.10801959266372 & -0.444983745077702 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301133&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]3830.8[/C][C]3830.8[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]3732.6[/C][C]3737.16648290901[/C][C]-14.9495221726765[/C][C]-4.56648290900555[/C][C]-1.96467826524488[/C][/ROW]
[ROW][C]3[/C][C]3733.5[/C][C]3738.18173574763[/C][C]-8.63524293686449[/C][C]-4.68173574763179[/C][C]0.456928137425495[/C][/ROW]
[ROW][C]4[/C][C]3808.5[/C][C]3813.5266415877[/C][C]27.5692375179069[/C][C]-5.02664158770362[/C][C]2.34098542009954[/C][/ROW]
[ROW][C]5[/C][C]3860.5[/C][C]3865.58268245488[/C][C]38.4108084118853[/C][C]-5.08268245487891[/C][C]0.677234877165529[/C][/ROW]
[ROW][C]6[/C][C]3844.4[/C][C]3849.41354931473[/C][C]14.0382796479509[/C][C]-5.01354931472908[/C][C]-1.50651872804929[/C][/ROW]
[ROW][C]7[/C][C]3864.5[/C][C]3869.51779191964[/C][C]16.754747306958[/C][C]-5.01779191963627[/C][C]0.167373388027878[/C][/ROW]
[ROW][C]8[/C][C]3803.1[/C][C]3808.08762156376[/C][C]-18.293402930622[/C][C]-4.98762156375733[/C][C]-2.15736458926796[/C][/ROW]
[ROW][C]9[/C][C]3756.1[/C][C]3761.08151044507[/C][C]-31.1694629474513[/C][C]-4.9815104450718[/C][C]-0.792341996436287[/C][/ROW]
[ROW][C]10[/C][C]3771.1[/C][C]3776.08693026831[/C][C]-10.4592800436391[/C][C]-4.98693026831379[/C][C]1.27430816214484[/C][/ROW]
[ROW][C]11[/C][C]3754.4[/C][C]3759.38652629804[/C][C]-13.2587271687332[/C][C]-4.98652629804247[/C][C]-0.172246693797902[/C][/ROW]
[ROW][C]12[/C][C]3759.6[/C][C]3764.5871851666[/C][C]-4.97850673903523[/C][C]-4.98718516659574[/C][C]0.509467991879174[/C][/ROW]
[ROW][C]13[/C][C]3783.5[/C][C]3736.41868978367[/C][C]-15.0668473229366[/C][C]47.0813102163304[/C][C]-0.728189688735594[/C][/ROW]
[ROW][C]14[/C][C]3886.5[/C][C]3887.22367028486[/C][C]52.3396101524358[/C][C]-0.723670284862525[/C][C]3.7269789676856[/C][/ROW]
[ROW][C]15[/C][C]3944.4[/C][C]3945.13978933812[/C][C]54.8553803170647[/C][C]-0.739789338115415[/C][C]0.152930158479818[/C][/ROW]
[ROW][C]16[/C][C]4012.1[/C][C]4012.86027781913[/C][C]60.6322950803448[/C][C]-0.760277819133647[/C][C]0.354139054804865[/C][/ROW]
[ROW][C]17[/C][C]4089.5[/C][C]4090.27501664539[/C][C]68.1599485916095[/C][C]-0.775016645394142[/C][C]0.462645134729857[/C][/ROW]
[ROW][C]18[/C][C]4144[/C][C]4144.76839700421[/C][C]62.0308703767303[/C][C]-0.76839700420865[/C][C]-0.376982433047262[/C][/ROW]
[ROW][C]19[/C][C]4166.4[/C][C]4167.15780752831[/C][C]44.2518938301295[/C][C]-0.757807528310551[/C][C]-1.09379350572473[/C][/ROW]
[ROW][C]20[/C][C]4194.2[/C][C]4194.95538354139[/C][C]36.871715396224[/C][C]-0.755383541387527[/C][C]-0.454074017430514[/C][/ROW]
[ROW][C]21[/C][C]4221.8[/C][C]4222.55463026653[/C][C]32.7125680059376[/C][C]-0.754630266529469[/C][C]-0.255901946518255[/C][/ROW]
[ROW][C]22[/C][C]4254.8[/C][C]4255.55464314337[/C][C]32.841504921216[/C][C]-0.754643143365407[/C][C]0.00793321892617359[/C][/ROW]
[ROW][C]23[/C][C]4309[/C][C]4309.755170769[/C][C]42.4225347753111[/C][C]-0.755170768996969[/C][C]0.589501933875371[/C][/ROW]
[ROW][C]24[/C][C]4333.5[/C][C]4334.25492663065[/C][C]34.3828173168468[/C][C]-0.754926630647856[/C][C]-0.494668315689898[/C][/ROW]
[ROW][C]25[/C][C]4390.5[/C][C]4380.36953492997[/C][C]39.5715801401471[/C][C]10.1304650700294[/C][C]0.3456058968501[/C][/ROW]
[ROW][C]26[/C][C]4387.7[/C][C]4389.04537456236[/C][C]26.5476035784904[/C][C]-1.34537456236095[/C][C]-0.755829997012713[/C][/ROW]
[ROW][C]27[/C][C]4412.6[/C][C]4413.9422840123[/C][C]25.8044009698228[/C][C]-1.34228401230006[/C][C]-0.0453712644318577[/C][/ROW]
[ROW][C]28[/C][C]4427.1[/C][C]4428.43060777846[/C][C]20.7248771220181[/C][C]-1.33060777845529[/C][C]-0.311790704031371[/C][/ROW]
[ROW][C]29[/C][C]4460[/C][C]4461.33753929506[/C][C]26.1892194482507[/C][C]-1.33753929505774[/C][C]0.33596743950124[/C][/ROW]
[ROW][C]30[/C][C]4515.3[/C][C]4516.64667695369[/C][C]39.2498160292586[/C][C]-1.34667695369008[/C][C]0.803416833374424[/C][/ROW]
[ROW][C]31[/C][C]4559.3[/C][C]4560.64749911326[/C][C]41.3807615447572[/C][C]-1.34749911326209[/C][C]0.131104237328186[/C][/ROW]
[ROW][C]32[/C][C]4625.5[/C][C]4626.84986781531[/C][C]52.5143714510647[/C][C]-1.34986781531248[/C][C]0.685015808922636[/C][/ROW]
[ROW][C]33[/C][C]4655.3[/C][C]4656.64867244474[/C][C]42.3250818929511[/C][C]-1.34867244474483[/C][C]-0.626923635234447[/C][/ROW]
[ROW][C]34[/C][C]4704.8[/C][C]4706.14888065385[/C][C]45.5436210767587[/C][C]-1.34888065384846[/C][C]0.198030191933138[/C][/ROW]
[ROW][C]35[/C][C]4734.5[/C][C]4735.8486271302[/C][C]38.4364643028735[/C][C]-1.34862713020201[/C][C]-0.43728952202098[/C][/ROW]
[ROW][C]36[/C][C]4779.7[/C][C]4781.04868680888[/C][C]41.470461059029[/C][C]-1.34868680887695[/C][C]0.18667598890538[/C][/ROW]
[ROW][C]37[/C][C]4817.6[/C][C]4804.58248056569[/C][C]33.4979728599454[/C][C]13.0175194343065[/C][C]-0.517127907503195[/C][/ROW]
[ROW][C]38[/C][C]4839[/C][C]4840.16237129267[/C][C]34.3904754791317[/C][C]-1.16237129267492[/C][C]0.0527553922958677[/C][/ROW]
[ROW][C]39[/C][C]4839[/C][C]4840.11468844423[/C][C]18.9000073716232[/C][C]-1.11468844422868[/C][C]-0.947597829489724[/C][/ROW]
[ROW][C]40[/C][C]4856.7[/C][C]4857.81377191323[/C][C]18.3610329037732[/C][C]-1.11377191323138[/C][C]-0.0331037726064103[/C][/ROW]
[ROW][C]41[/C][C]4890.8[/C][C]4891.92039844821[/C][C]25.4239259221105[/C][C]-1.12039844821359[/C][C]0.434333906190577[/C][/ROW]
[ROW][C]42[/C][C]4902.7[/C][C]4903.81725899798[/C][C]19.3566427259595[/C][C]-1.11725899798342[/C][C]-0.373247625443854[/C][/ROW]
[ROW][C]43[/C][C]4882.6[/C][C]4883.71220843337[/C][C]1.65650405304634[/C][C]-1.11220843337285[/C][C]-1.0890018437035[/C][/ROW]
[ROW][C]44[/C][C]4833.8[/C][C]4834.90864708396[/C][C]-20.9775876331307[/C][C]-1.10864708396321[/C][C]-1.39261145836413[/C][/ROW]
[ROW][C]45[/C][C]4796.7[/C][C]4797.80801959266[/C][C]-28.2098256156984[/C][C]-1.10801959266372[/C][C]-0.444983745077702[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301133&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301133&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
13830.83830.8000
23732.63737.16648290901-14.9495221726765-4.56648290900555-1.96467826524488
33733.53738.18173574763-8.63524293686449-4.681735747631790.456928137425495
43808.53813.526641587727.5692375179069-5.026641587703622.34098542009954
53860.53865.5826824548838.4108084118853-5.082682454878910.677234877165529
63844.43849.4135493147314.0382796479509-5.01354931472908-1.50651872804929
73864.53869.5177919196416.754747306958-5.017791919636270.167373388027878
83803.13808.08762156376-18.293402930622-4.98762156375733-2.15736458926796
93756.13761.08151044507-31.1694629474513-4.9815104450718-0.792341996436287
103771.13776.08693026831-10.4592800436391-4.986930268313791.27430816214484
113754.43759.38652629804-13.2587271687332-4.98652629804247-0.172246693797902
123759.63764.5871851666-4.97850673903523-4.987185166595740.509467991879174
133783.53736.41868978367-15.066847322936647.0813102163304-0.728189688735594
143886.53887.2236702848652.3396101524358-0.7236702848625253.7269789676856
153944.43945.1397893381254.8553803170647-0.7397893381154150.152930158479818
164012.14012.8602778191360.6322950803448-0.7602778191336470.354139054804865
174089.54090.2750166453968.1599485916095-0.7750166453941420.462645134729857
1841444144.7683970042162.0308703767303-0.76839700420865-0.376982433047262
194166.44167.1578075283144.2518938301295-0.757807528310551-1.09379350572473
204194.24194.9553835413936.871715396224-0.755383541387527-0.454074017430514
214221.84222.5546302665332.7125680059376-0.754630266529469-0.255901946518255
224254.84255.5546431433732.841504921216-0.7546431433654070.00793321892617359
2343094309.75517076942.4225347753111-0.7551707689969690.589501933875371
244333.54334.2549266306534.3828173168468-0.754926630647856-0.494668315689898
254390.54380.3695349299739.571580140147110.13046507002940.3456058968501
264387.74389.0453745623626.5476035784904-1.34537456236095-0.755829997012713
274412.64413.942284012325.8044009698228-1.34228401230006-0.0453712644318577
284427.14428.4306077784620.7248771220181-1.33060777845529-0.311790704031371
2944604461.3375392950626.1892194482507-1.337539295057740.33596743950124
304515.34516.6466769536939.2498160292586-1.346676953690080.803416833374424
314559.34560.6474991132641.3807615447572-1.347499113262090.131104237328186
324625.54626.8498678153152.5143714510647-1.349867815312480.685015808922636
334655.34656.6486724447442.3250818929511-1.34867244474483-0.626923635234447
344704.84706.1488806538545.5436210767587-1.348880653848460.198030191933138
354734.54735.848627130238.4364643028735-1.34862713020201-0.43728952202098
364779.74781.0486868088841.470461059029-1.348686808876950.18667598890538
374817.64804.5824805656933.497972859945413.0175194343065-0.517127907503195
3848394840.1623712926734.3904754791317-1.162371292674920.0527553922958677
3948394840.1146884442318.9000073716232-1.11468844422868-0.947597829489724
404856.74857.8137719132318.3610329037732-1.11377191323138-0.0331037726064103
414890.84891.9203984482125.4239259221105-1.120398448213590.434333906190577
424902.74903.8172589979819.3566427259595-1.11725899798342-0.373247625443854
434882.64883.712208433371.65650405304634-1.11220843337285-1.0890018437035
444833.84834.90864708396-20.9775876331307-1.10864708396321-1.39261145836413
454796.74797.80801959266-28.2098256156984-1.10801959266372-0.444983745077702







Structural Time Series Model -- Extrapolation
tObservedLevelSeasonal
14783.347665456084793.74913414872-10.401468692638
24759.523834378684779.08055185929-19.5567174806144
34737.979712243784764.41196956987-26.4322573260896
44736.739915623354749.74338728044-13.003471657095
54709.858797251654735.07480499102-25.21600773937
64697.837460495124720.40622270159-22.5687622064749
74708.400912353524705.737640412162.66327194135654
84724.124168846244691.0690581227433.0551107234985
94716.932248100094676.4004758333140.5317722667817
104699.725153425444661.7318935438937.9932598815577
114661.652884167854647.0633112544614.5895729133878
124620.740426340734632.39472896503-11.6543026243002

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Extrapolation \tabularnewline
t & Observed & Level & Seasonal \tabularnewline
1 & 4783.34766545608 & 4793.74913414872 & -10.401468692638 \tabularnewline
2 & 4759.52383437868 & 4779.08055185929 & -19.5567174806144 \tabularnewline
3 & 4737.97971224378 & 4764.41196956987 & -26.4322573260896 \tabularnewline
4 & 4736.73991562335 & 4749.74338728044 & -13.003471657095 \tabularnewline
5 & 4709.85879725165 & 4735.07480499102 & -25.21600773937 \tabularnewline
6 & 4697.83746049512 & 4720.40622270159 & -22.5687622064749 \tabularnewline
7 & 4708.40091235352 & 4705.73764041216 & 2.66327194135654 \tabularnewline
8 & 4724.12416884624 & 4691.06905812274 & 33.0551107234985 \tabularnewline
9 & 4716.93224810009 & 4676.40047583331 & 40.5317722667817 \tabularnewline
10 & 4699.72515342544 & 4661.73189354389 & 37.9932598815577 \tabularnewline
11 & 4661.65288416785 & 4647.06331125446 & 14.5895729133878 \tabularnewline
12 & 4620.74042634073 & 4632.39472896503 & -11.6543026243002 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301133&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]4783.34766545608[/C][C]4793.74913414872[/C][C]-10.401468692638[/C][/ROW]
[ROW][C]2[/C][C]4759.52383437868[/C][C]4779.08055185929[/C][C]-19.5567174806144[/C][/ROW]
[ROW][C]3[/C][C]4737.97971224378[/C][C]4764.41196956987[/C][C]-26.4322573260896[/C][/ROW]
[ROW][C]4[/C][C]4736.73991562335[/C][C]4749.74338728044[/C][C]-13.003471657095[/C][/ROW]
[ROW][C]5[/C][C]4709.85879725165[/C][C]4735.07480499102[/C][C]-25.21600773937[/C][/ROW]
[ROW][C]6[/C][C]4697.83746049512[/C][C]4720.40622270159[/C][C]-22.5687622064749[/C][/ROW]
[ROW][C]7[/C][C]4708.40091235352[/C][C]4705.73764041216[/C][C]2.66327194135654[/C][/ROW]
[ROW][C]8[/C][C]4724.12416884624[/C][C]4691.06905812274[/C][C]33.0551107234985[/C][/ROW]
[ROW][C]9[/C][C]4716.93224810009[/C][C]4676.40047583331[/C][C]40.5317722667817[/C][/ROW]
[ROW][C]10[/C][C]4699.72515342544[/C][C]4661.73189354389[/C][C]37.9932598815577[/C][/ROW]
[ROW][C]11[/C][C]4661.65288416785[/C][C]4647.06331125446[/C][C]14.5895729133878[/C][/ROW]
[ROW][C]12[/C][C]4620.74042634073[/C][C]4632.39472896503[/C][C]-11.6543026243002[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301133&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301133&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
14783.347665456084793.74913414872-10.401468692638
24759.523834378684779.08055185929-19.5567174806144
34737.979712243784764.41196956987-26.4322573260896
44736.739915623354749.74338728044-13.003471657095
54709.858797251654735.07480499102-25.21600773937
64697.837460495124720.40622270159-22.5687622064749
74708.400912353524705.737640412162.66327194135654
84724.124168846244691.0690581227433.0551107234985
94716.932248100094676.4004758333140.5317722667817
104699.725153425444661.7318935438937.9932598815577
114661.652884167854647.0633112544614.5895729133878
124620.740426340734632.39472896503-11.6543026243002



Parameters (Session):
par1 = 1 ; par2 = 1 ; par3 = 0 ; par4 = 12 ;
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')