Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_structuraltimeseries.wasp
Title produced by softwareStructural Time Series Models
Date of computationWed, 07 Dec 2016 16:37:56 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/07/t1481125158x0sgcr3piuaxy9k.htm/, Retrieved Wed, 08 May 2024 01:26:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298207, Retrieved Wed, 08 May 2024 01:26:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact61
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Structural Time Series Models] [Structural Time S...] [2016-12-07 15:37:56] [3b055ff671ad33431c4331443bac114d] [Current]
Feedback Forum

Post a new message
Dataseries X:
9137.8
9009.4
8926.6
9145
9186.2
9152.2
9093.6
9199.2
9310.6
9282
9248.4
9341.6
9478.8
9438
9374.6
9488.8
9631.8
9588.4
9514.6
9623.2
9744.6
9685.8
9598
9703.4
9817.8
9762.6
9669.6
9789.2
9917.4
9864.4
9779.2
9898.8
10048.8
9983.4
9913.4
10031.6
10184.6
10125
10065.4
10188.6
10350.4
10320.6
10232.6
10357.2
10520.2
10473.8
10407
10536
10700.2
10664.2
10606
10716.6
10882.8
10849.4
10794
10907.8




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=298207&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=298207&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298207&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
19137.89137.8000
29009.49048.82524388103-5.10101111849992-39.4252438810283-2.3600858437535
38926.68963.43771514923-12.4140050898602-36.837715149234-2.27847685066989
491459050.46769522786-1.5208750994346294.53230477213743.27641028496022
59186.29145.8069765131610.723031215343340.39302348683953.17596148687193
69152.29173.806827553213.1646198760275-21.60682755319940.551735198383198
79093.69138.653348037415.76177159229154-45.05334803741-1.51694989538618
89199.29169.843432880079.8760946758679229.3565671199320.789964286907983
99310.69261.8821090782623.645238019865948.71789092173572.5346975350691
1092829299.519135581326.0425636743857-17.51913558129980.429583167110932
119248.49285.3189927941119.0504960808183-36.9189927941056-1.23149006605954
129341.69321.4221348830622.039749583511920.17786511694050.520664458999205
139478.89380.9877137768928.375596956891997.81228622310971.2026654511779
1494389435.5487466139932.96504548957062.451253386004310.80248663357497
159374.69472.2303977119833.6131412047352-97.6303977119820.106044433238903
169488.89469.1294284308727.244910464442119.6705715691261-1.08082970381653
179631.89545.2351190603135.766705105342686.56488093968521.47127222103553
189588.49592.8902262779437.8487968657784-4.490226277944440.35694856391116
199514.69604.1015652057233.180974612409-89.5015652057167-0.795638995611695
209623.29630.8157808274432.0481656693777-7.61578082743666-0.192950553524062
219744.69681.298074743135.277300662813763.30192525689950.550442341430526
229685.89702.2562901854632.7690874546634-16.4562901854649-0.427710581256437
2395989683.2606024785323.7117707345913-85.2606024785287-1.54467801652213
249703.49697.4175211103122.04439739569445.98247888968551-0.285679501638498
259817.89724.1715304759322.865660426283293.62846952406650.143017861463867
269762.69753.007858938123.91089172887459.592141061900740.179794646181875
279669.69766.498803571522.0943444033488-96.8988035714986-0.305838460534298
289789.29790.2164236427822.3759270204534-1.016423642780920.0477511943134382
299917.49824.3714911278824.421496269805893.02850887212140.351047446349412
309864.49855.1432967995125.52783888438749.25670320049360.189839243822945
319779.29875.520033452524.6291681901693-96.320033452495-0.153471410451541
329898.89906.8906288090725.8050318734844-8.090628809067240.200265285535186
3310048.89955.5321098156829.785519899526493.26789018431850.677562843748169
349983.49982.2830637466629.25705081479741.11693625334295-0.0899878588568536
359913.410001.972892561727.5929454700765-88.572892561721-0.283866041809377
3610031.610027.729159552627.27372334538553.87084044735551-0.0547218222507281
3710184.610075.231681550630.7935612513554109.3683184494240.606089440729663
381012510111.022064453631.66424301885113.97793554643070.149026268498199
3910065.410155.459935948533.8856920467941-90.05993594848860.376788756530536
4010188.610194.381539588134.7588547866066-5.781539588124950.148342956412294
4110350.410246.658167993837.7951978959884103.7418320061650.5194772602061
4210320.610301.039621569440.675056635387219.56037843055270.493835480772388
4310232.610340.10707000240.3955475969827-107.507070002007-0.0478068925683738
4410357.210377.097345940639.8034209499466-19.8973459405656-0.100955209697748
4510520.210420.020047915340.3454168298378100.1799520847080.092259484208739
4610473.810464.721321425841.10147140140249.078678574232590.128733065582018
471040710501.336269996440.323434040215-94.3362699963913-0.132783225620138
481053610541.218824239340.2469799285354-5.21882423925345-0.0130949646718287
4910700.210588.765715667141.5142106440735111.4342843328910.217350887033404
5010664.210646.171813739344.274972909104318.02818626066970.471731549091218
511060610698.530449818145.6777757857345-92.53044981808720.238566240684973
5210716.610738.922245986244.7621412360011-22.3222459862089-0.155785345253566
5310882.810784.634818079344.926681756592798.16518192065910.0281116648163677
5410849.410829.20754857344.865350170104120.1924514269907-0.0105036658067863
551079410888.659031054847.3954335169413-94.65903105481380.432798340394449
5610907.810934.039801407547.0458957021844-26.239801407536-0.0596331286594309

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Interpolation \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 9137.8 & 9137.8 & 0 & 0 & 0 \tabularnewline
2 & 9009.4 & 9048.82524388103 & -5.10101111849992 & -39.4252438810283 & -2.3600858437535 \tabularnewline
3 & 8926.6 & 8963.43771514923 & -12.4140050898602 & -36.837715149234 & -2.27847685066989 \tabularnewline
4 & 9145 & 9050.46769522786 & -1.52087509943462 & 94.5323047721374 & 3.27641028496022 \tabularnewline
5 & 9186.2 & 9145.80697651316 & 10.7230312153433 & 40.3930234868395 & 3.17596148687193 \tabularnewline
6 & 9152.2 & 9173.8068275532 & 13.1646198760275 & -21.6068275531994 & 0.551735198383198 \tabularnewline
7 & 9093.6 & 9138.65334803741 & 5.76177159229154 & -45.05334803741 & -1.51694989538618 \tabularnewline
8 & 9199.2 & 9169.84343288007 & 9.87609467586792 & 29.356567119932 & 0.789964286907983 \tabularnewline
9 & 9310.6 & 9261.88210907826 & 23.6452380198659 & 48.7178909217357 & 2.5346975350691 \tabularnewline
10 & 9282 & 9299.5191355813 & 26.0425636743857 & -17.5191355812998 & 0.429583167110932 \tabularnewline
11 & 9248.4 & 9285.31899279411 & 19.0504960808183 & -36.9189927941056 & -1.23149006605954 \tabularnewline
12 & 9341.6 & 9321.42213488306 & 22.0397495835119 & 20.1778651169405 & 0.520664458999205 \tabularnewline
13 & 9478.8 & 9380.98771377689 & 28.3755969568919 & 97.8122862231097 & 1.2026654511779 \tabularnewline
14 & 9438 & 9435.54874661399 & 32.9650454895706 & 2.45125338600431 & 0.80248663357497 \tabularnewline
15 & 9374.6 & 9472.23039771198 & 33.6131412047352 & -97.630397711982 & 0.106044433238903 \tabularnewline
16 & 9488.8 & 9469.12942843087 & 27.2449104644421 & 19.6705715691261 & -1.08082970381653 \tabularnewline
17 & 9631.8 & 9545.23511906031 & 35.7667051053426 & 86.5648809396852 & 1.47127222103553 \tabularnewline
18 & 9588.4 & 9592.89022627794 & 37.8487968657784 & -4.49022627794444 & 0.35694856391116 \tabularnewline
19 & 9514.6 & 9604.10156520572 & 33.180974612409 & -89.5015652057167 & -0.795638995611695 \tabularnewline
20 & 9623.2 & 9630.81578082744 & 32.0481656693777 & -7.61578082743666 & -0.192950553524062 \tabularnewline
21 & 9744.6 & 9681.2980747431 & 35.2773006628137 & 63.3019252568995 & 0.550442341430526 \tabularnewline
22 & 9685.8 & 9702.25629018546 & 32.7690874546634 & -16.4562901854649 & -0.427710581256437 \tabularnewline
23 & 9598 & 9683.26060247853 & 23.7117707345913 & -85.2606024785287 & -1.54467801652213 \tabularnewline
24 & 9703.4 & 9697.41752111031 & 22.0443973956944 & 5.98247888968551 & -0.285679501638498 \tabularnewline
25 & 9817.8 & 9724.17153047593 & 22.8656604262832 & 93.6284695240665 & 0.143017861463867 \tabularnewline
26 & 9762.6 & 9753.0078589381 & 23.9108917288745 & 9.59214106190074 & 0.179794646181875 \tabularnewline
27 & 9669.6 & 9766.4988035715 & 22.0943444033488 & -96.8988035714986 & -0.305838460534298 \tabularnewline
28 & 9789.2 & 9790.21642364278 & 22.3759270204534 & -1.01642364278092 & 0.0477511943134382 \tabularnewline
29 & 9917.4 & 9824.37149112788 & 24.4214962698058 & 93.0285088721214 & 0.351047446349412 \tabularnewline
30 & 9864.4 & 9855.14329679951 & 25.5278388843874 & 9.2567032004936 & 0.189839243822945 \tabularnewline
31 & 9779.2 & 9875.5200334525 & 24.6291681901693 & -96.320033452495 & -0.153471410451541 \tabularnewline
32 & 9898.8 & 9906.89062880907 & 25.8050318734844 & -8.09062880906724 & 0.200265285535186 \tabularnewline
33 & 10048.8 & 9955.53210981568 & 29.7855198995264 & 93.2678901843185 & 0.677562843748169 \tabularnewline
34 & 9983.4 & 9982.28306374666 & 29.2570508147974 & 1.11693625334295 & -0.0899878588568536 \tabularnewline
35 & 9913.4 & 10001.9728925617 & 27.5929454700765 & -88.572892561721 & -0.283866041809377 \tabularnewline
36 & 10031.6 & 10027.7291595526 & 27.2737233453855 & 3.87084044735551 & -0.0547218222507281 \tabularnewline
37 & 10184.6 & 10075.2316815506 & 30.7935612513554 & 109.368318449424 & 0.606089440729663 \tabularnewline
38 & 10125 & 10111.0220644536 & 31.664243018851 & 13.9779355464307 & 0.149026268498199 \tabularnewline
39 & 10065.4 & 10155.4599359485 & 33.8856920467941 & -90.0599359484886 & 0.376788756530536 \tabularnewline
40 & 10188.6 & 10194.3815395881 & 34.7588547866066 & -5.78153958812495 & 0.148342956412294 \tabularnewline
41 & 10350.4 & 10246.6581679938 & 37.7951978959884 & 103.741832006165 & 0.5194772602061 \tabularnewline
42 & 10320.6 & 10301.0396215694 & 40.6750566353872 & 19.5603784305527 & 0.493835480772388 \tabularnewline
43 & 10232.6 & 10340.107070002 & 40.3955475969827 & -107.507070002007 & -0.0478068925683738 \tabularnewline
44 & 10357.2 & 10377.0973459406 & 39.8034209499466 & -19.8973459405656 & -0.100955209697748 \tabularnewline
45 & 10520.2 & 10420.0200479153 & 40.3454168298378 & 100.179952084708 & 0.092259484208739 \tabularnewline
46 & 10473.8 & 10464.7213214258 & 41.1014714014024 & 9.07867857423259 & 0.128733065582018 \tabularnewline
47 & 10407 & 10501.3362699964 & 40.323434040215 & -94.3362699963913 & -0.132783225620138 \tabularnewline
48 & 10536 & 10541.2188242393 & 40.2469799285354 & -5.21882423925345 & -0.0130949646718287 \tabularnewline
49 & 10700.2 & 10588.7657156671 & 41.5142106440735 & 111.434284332891 & 0.217350887033404 \tabularnewline
50 & 10664.2 & 10646.1718137393 & 44.2749729091043 & 18.0281862606697 & 0.471731549091218 \tabularnewline
51 & 10606 & 10698.5304498181 & 45.6777757857345 & -92.5304498180872 & 0.238566240684973 \tabularnewline
52 & 10716.6 & 10738.9222459862 & 44.7621412360011 & -22.3222459862089 & -0.155785345253566 \tabularnewline
53 & 10882.8 & 10784.6348180793 & 44.9266817565927 & 98.1651819206591 & 0.0281116648163677 \tabularnewline
54 & 10849.4 & 10829.207548573 & 44.8653501701041 & 20.1924514269907 & -0.0105036658067863 \tabularnewline
55 & 10794 & 10888.6590310548 & 47.3954335169413 & -94.6590310548138 & 0.432798340394449 \tabularnewline
56 & 10907.8 & 10934.0398014075 & 47.0458957021844 & -26.239801407536 & -0.0596331286594309 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298207&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]9137.8[/C][C]9137.8[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]9009.4[/C][C]9048.82524388103[/C][C]-5.10101111849992[/C][C]-39.4252438810283[/C][C]-2.3600858437535[/C][/ROW]
[ROW][C]3[/C][C]8926.6[/C][C]8963.43771514923[/C][C]-12.4140050898602[/C][C]-36.837715149234[/C][C]-2.27847685066989[/C][/ROW]
[ROW][C]4[/C][C]9145[/C][C]9050.46769522786[/C][C]-1.52087509943462[/C][C]94.5323047721374[/C][C]3.27641028496022[/C][/ROW]
[ROW][C]5[/C][C]9186.2[/C][C]9145.80697651316[/C][C]10.7230312153433[/C][C]40.3930234868395[/C][C]3.17596148687193[/C][/ROW]
[ROW][C]6[/C][C]9152.2[/C][C]9173.8068275532[/C][C]13.1646198760275[/C][C]-21.6068275531994[/C][C]0.551735198383198[/C][/ROW]
[ROW][C]7[/C][C]9093.6[/C][C]9138.65334803741[/C][C]5.76177159229154[/C][C]-45.05334803741[/C][C]-1.51694989538618[/C][/ROW]
[ROW][C]8[/C][C]9199.2[/C][C]9169.84343288007[/C][C]9.87609467586792[/C][C]29.356567119932[/C][C]0.789964286907983[/C][/ROW]
[ROW][C]9[/C][C]9310.6[/C][C]9261.88210907826[/C][C]23.6452380198659[/C][C]48.7178909217357[/C][C]2.5346975350691[/C][/ROW]
[ROW][C]10[/C][C]9282[/C][C]9299.5191355813[/C][C]26.0425636743857[/C][C]-17.5191355812998[/C][C]0.429583167110932[/C][/ROW]
[ROW][C]11[/C][C]9248.4[/C][C]9285.31899279411[/C][C]19.0504960808183[/C][C]-36.9189927941056[/C][C]-1.23149006605954[/C][/ROW]
[ROW][C]12[/C][C]9341.6[/C][C]9321.42213488306[/C][C]22.0397495835119[/C][C]20.1778651169405[/C][C]0.520664458999205[/C][/ROW]
[ROW][C]13[/C][C]9478.8[/C][C]9380.98771377689[/C][C]28.3755969568919[/C][C]97.8122862231097[/C][C]1.2026654511779[/C][/ROW]
[ROW][C]14[/C][C]9438[/C][C]9435.54874661399[/C][C]32.9650454895706[/C][C]2.45125338600431[/C][C]0.80248663357497[/C][/ROW]
[ROW][C]15[/C][C]9374.6[/C][C]9472.23039771198[/C][C]33.6131412047352[/C][C]-97.630397711982[/C][C]0.106044433238903[/C][/ROW]
[ROW][C]16[/C][C]9488.8[/C][C]9469.12942843087[/C][C]27.2449104644421[/C][C]19.6705715691261[/C][C]-1.08082970381653[/C][/ROW]
[ROW][C]17[/C][C]9631.8[/C][C]9545.23511906031[/C][C]35.7667051053426[/C][C]86.5648809396852[/C][C]1.47127222103553[/C][/ROW]
[ROW][C]18[/C][C]9588.4[/C][C]9592.89022627794[/C][C]37.8487968657784[/C][C]-4.49022627794444[/C][C]0.35694856391116[/C][/ROW]
[ROW][C]19[/C][C]9514.6[/C][C]9604.10156520572[/C][C]33.180974612409[/C][C]-89.5015652057167[/C][C]-0.795638995611695[/C][/ROW]
[ROW][C]20[/C][C]9623.2[/C][C]9630.81578082744[/C][C]32.0481656693777[/C][C]-7.61578082743666[/C][C]-0.192950553524062[/C][/ROW]
[ROW][C]21[/C][C]9744.6[/C][C]9681.2980747431[/C][C]35.2773006628137[/C][C]63.3019252568995[/C][C]0.550442341430526[/C][/ROW]
[ROW][C]22[/C][C]9685.8[/C][C]9702.25629018546[/C][C]32.7690874546634[/C][C]-16.4562901854649[/C][C]-0.427710581256437[/C][/ROW]
[ROW][C]23[/C][C]9598[/C][C]9683.26060247853[/C][C]23.7117707345913[/C][C]-85.2606024785287[/C][C]-1.54467801652213[/C][/ROW]
[ROW][C]24[/C][C]9703.4[/C][C]9697.41752111031[/C][C]22.0443973956944[/C][C]5.98247888968551[/C][C]-0.285679501638498[/C][/ROW]
[ROW][C]25[/C][C]9817.8[/C][C]9724.17153047593[/C][C]22.8656604262832[/C][C]93.6284695240665[/C][C]0.143017861463867[/C][/ROW]
[ROW][C]26[/C][C]9762.6[/C][C]9753.0078589381[/C][C]23.9108917288745[/C][C]9.59214106190074[/C][C]0.179794646181875[/C][/ROW]
[ROW][C]27[/C][C]9669.6[/C][C]9766.4988035715[/C][C]22.0943444033488[/C][C]-96.8988035714986[/C][C]-0.305838460534298[/C][/ROW]
[ROW][C]28[/C][C]9789.2[/C][C]9790.21642364278[/C][C]22.3759270204534[/C][C]-1.01642364278092[/C][C]0.0477511943134382[/C][/ROW]
[ROW][C]29[/C][C]9917.4[/C][C]9824.37149112788[/C][C]24.4214962698058[/C][C]93.0285088721214[/C][C]0.351047446349412[/C][/ROW]
[ROW][C]30[/C][C]9864.4[/C][C]9855.14329679951[/C][C]25.5278388843874[/C][C]9.2567032004936[/C][C]0.189839243822945[/C][/ROW]
[ROW][C]31[/C][C]9779.2[/C][C]9875.5200334525[/C][C]24.6291681901693[/C][C]-96.320033452495[/C][C]-0.153471410451541[/C][/ROW]
[ROW][C]32[/C][C]9898.8[/C][C]9906.89062880907[/C][C]25.8050318734844[/C][C]-8.09062880906724[/C][C]0.200265285535186[/C][/ROW]
[ROW][C]33[/C][C]10048.8[/C][C]9955.53210981568[/C][C]29.7855198995264[/C][C]93.2678901843185[/C][C]0.677562843748169[/C][/ROW]
[ROW][C]34[/C][C]9983.4[/C][C]9982.28306374666[/C][C]29.2570508147974[/C][C]1.11693625334295[/C][C]-0.0899878588568536[/C][/ROW]
[ROW][C]35[/C][C]9913.4[/C][C]10001.9728925617[/C][C]27.5929454700765[/C][C]-88.572892561721[/C][C]-0.283866041809377[/C][/ROW]
[ROW][C]36[/C][C]10031.6[/C][C]10027.7291595526[/C][C]27.2737233453855[/C][C]3.87084044735551[/C][C]-0.0547218222507281[/C][/ROW]
[ROW][C]37[/C][C]10184.6[/C][C]10075.2316815506[/C][C]30.7935612513554[/C][C]109.368318449424[/C][C]0.606089440729663[/C][/ROW]
[ROW][C]38[/C][C]10125[/C][C]10111.0220644536[/C][C]31.664243018851[/C][C]13.9779355464307[/C][C]0.149026268498199[/C][/ROW]
[ROW][C]39[/C][C]10065.4[/C][C]10155.4599359485[/C][C]33.8856920467941[/C][C]-90.0599359484886[/C][C]0.376788756530536[/C][/ROW]
[ROW][C]40[/C][C]10188.6[/C][C]10194.3815395881[/C][C]34.7588547866066[/C][C]-5.78153958812495[/C][C]0.148342956412294[/C][/ROW]
[ROW][C]41[/C][C]10350.4[/C][C]10246.6581679938[/C][C]37.7951978959884[/C][C]103.741832006165[/C][C]0.5194772602061[/C][/ROW]
[ROW][C]42[/C][C]10320.6[/C][C]10301.0396215694[/C][C]40.6750566353872[/C][C]19.5603784305527[/C][C]0.493835480772388[/C][/ROW]
[ROW][C]43[/C][C]10232.6[/C][C]10340.107070002[/C][C]40.3955475969827[/C][C]-107.507070002007[/C][C]-0.0478068925683738[/C][/ROW]
[ROW][C]44[/C][C]10357.2[/C][C]10377.0973459406[/C][C]39.8034209499466[/C][C]-19.8973459405656[/C][C]-0.100955209697748[/C][/ROW]
[ROW][C]45[/C][C]10520.2[/C][C]10420.0200479153[/C][C]40.3454168298378[/C][C]100.179952084708[/C][C]0.092259484208739[/C][/ROW]
[ROW][C]46[/C][C]10473.8[/C][C]10464.7213214258[/C][C]41.1014714014024[/C][C]9.07867857423259[/C][C]0.128733065582018[/C][/ROW]
[ROW][C]47[/C][C]10407[/C][C]10501.3362699964[/C][C]40.323434040215[/C][C]-94.3362699963913[/C][C]-0.132783225620138[/C][/ROW]
[ROW][C]48[/C][C]10536[/C][C]10541.2188242393[/C][C]40.2469799285354[/C][C]-5.21882423925345[/C][C]-0.0130949646718287[/C][/ROW]
[ROW][C]49[/C][C]10700.2[/C][C]10588.7657156671[/C][C]41.5142106440735[/C][C]111.434284332891[/C][C]0.217350887033404[/C][/ROW]
[ROW][C]50[/C][C]10664.2[/C][C]10646.1718137393[/C][C]44.2749729091043[/C][C]18.0281862606697[/C][C]0.471731549091218[/C][/ROW]
[ROW][C]51[/C][C]10606[/C][C]10698.5304498181[/C][C]45.6777757857345[/C][C]-92.5304498180872[/C][C]0.238566240684973[/C][/ROW]
[ROW][C]52[/C][C]10716.6[/C][C]10738.9222459862[/C][C]44.7621412360011[/C][C]-22.3222459862089[/C][C]-0.155785345253566[/C][/ROW]
[ROW][C]53[/C][C]10882.8[/C][C]10784.6348180793[/C][C]44.9266817565927[/C][C]98.1651819206591[/C][C]0.0281116648163677[/C][/ROW]
[ROW][C]54[/C][C]10849.4[/C][C]10829.207548573[/C][C]44.8653501701041[/C][C]20.1924514269907[/C][C]-0.0105036658067863[/C][/ROW]
[ROW][C]55[/C][C]10794[/C][C]10888.6590310548[/C][C]47.3954335169413[/C][C]-94.6590310548138[/C][C]0.432798340394449[/C][/ROW]
[ROW][C]56[/C][C]10907.8[/C][C]10934.0398014075[/C][C]47.0458957021844[/C][C]-26.239801407536[/C][C]-0.0596331286594309[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298207&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298207&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
19137.89137.8000
29009.49048.82524388103-5.10101111849992-39.4252438810283-2.3600858437535
38926.68963.43771514923-12.4140050898602-36.837715149234-2.27847685066989
491459050.46769522786-1.5208750994346294.53230477213743.27641028496022
59186.29145.8069765131610.723031215343340.39302348683953.17596148687193
69152.29173.806827553213.1646198760275-21.60682755319940.551735198383198
79093.69138.653348037415.76177159229154-45.05334803741-1.51694989538618
89199.29169.843432880079.8760946758679229.3565671199320.789964286907983
99310.69261.8821090782623.645238019865948.71789092173572.5346975350691
1092829299.519135581326.0425636743857-17.51913558129980.429583167110932
119248.49285.3189927941119.0504960808183-36.9189927941056-1.23149006605954
129341.69321.4221348830622.039749583511920.17786511694050.520664458999205
139478.89380.9877137768928.375596956891997.81228622310971.2026654511779
1494389435.5487466139932.96504548957062.451253386004310.80248663357497
159374.69472.2303977119833.6131412047352-97.6303977119820.106044433238903
169488.89469.1294284308727.244910464442119.6705715691261-1.08082970381653
179631.89545.2351190603135.766705105342686.56488093968521.47127222103553
189588.49592.8902262779437.8487968657784-4.490226277944440.35694856391116
199514.69604.1015652057233.180974612409-89.5015652057167-0.795638995611695
209623.29630.8157808274432.0481656693777-7.61578082743666-0.192950553524062
219744.69681.298074743135.277300662813763.30192525689950.550442341430526
229685.89702.2562901854632.7690874546634-16.4562901854649-0.427710581256437
2395989683.2606024785323.7117707345913-85.2606024785287-1.54467801652213
249703.49697.4175211103122.04439739569445.98247888968551-0.285679501638498
259817.89724.1715304759322.865660426283293.62846952406650.143017861463867
269762.69753.007858938123.91089172887459.592141061900740.179794646181875
279669.69766.498803571522.0943444033488-96.8988035714986-0.305838460534298
289789.29790.2164236427822.3759270204534-1.016423642780920.0477511943134382
299917.49824.3714911278824.421496269805893.02850887212140.351047446349412
309864.49855.1432967995125.52783888438749.25670320049360.189839243822945
319779.29875.520033452524.6291681901693-96.320033452495-0.153471410451541
329898.89906.8906288090725.8050318734844-8.090628809067240.200265285535186
3310048.89955.5321098156829.785519899526493.26789018431850.677562843748169
349983.49982.2830637466629.25705081479741.11693625334295-0.0899878588568536
359913.410001.972892561727.5929454700765-88.572892561721-0.283866041809377
3610031.610027.729159552627.27372334538553.87084044735551-0.0547218222507281
3710184.610075.231681550630.7935612513554109.3683184494240.606089440729663
381012510111.022064453631.66424301885113.97793554643070.149026268498199
3910065.410155.459935948533.8856920467941-90.05993594848860.376788756530536
4010188.610194.381539588134.7588547866066-5.781539588124950.148342956412294
4110350.410246.658167993837.7951978959884103.7418320061650.5194772602061
4210320.610301.039621569440.675056635387219.56037843055270.493835480772388
4310232.610340.10707000240.3955475969827-107.507070002007-0.0478068925683738
4410357.210377.097345940639.8034209499466-19.8973459405656-0.100955209697748
4510520.210420.020047915340.3454168298378100.1799520847080.092259484208739
4610473.810464.721321425841.10147140140249.078678574232590.128733065582018
471040710501.336269996440.323434040215-94.3362699963913-0.132783225620138
481053610541.218824239340.2469799285354-5.21882423925345-0.0130949646718287
4910700.210588.765715667141.5142106440735111.4342843328910.217350887033404
5010664.210646.171813739344.274972909104318.02818626066970.471731549091218
511060610698.530449818145.6777757857345-92.53044981808720.238566240684973
5210716.610738.922245986244.7621412360011-22.3222459862089-0.155785345253566
5310882.810784.634818079344.926681756592798.16518192065910.0281116648163677
5410849.410829.20754857344.865350170104120.1924514269907-0.0105036658067863
551079410888.659031054847.3954335169413-94.65903105481380.432798340394449
5610907.810934.039801407547.0458957021844-26.239801407536-0.0596331286594309







Structural Time Series Model -- Extrapolation
tObservedLevelSeasonal
111074.170539482210971.2910444387102.8794950435
211027.638388542411016.015492294211.6228962482273
310963.321116670911060.7399401496-97.4188234787553
411089.859884218911105.4643880051-15.6045037862335
511246.800059281211150.188835860596.6112234206921
611203.365022043511194.9132837168.45173832753275
711145.560199395511239.6377315715-94.0775321759521
811261.730177201411284.3621794269-22.6320022254602
911428.217818977311329.086627282499.1311916949164
1011392.271217449411373.811075137818.460142311537
1111329.878294196511418.5355229933-88.6572287967352
1211444.493374265511463.2599708487-18.7665965832692
1311610.863913747711507.9844187042102.8794950435
1411564.331762807911552.708866559611.6228962482273
1511500.014490936311597.4333144151-97.4188234787553
1611626.553258484311642.1577622705-15.6045037862335
1711783.493433546711686.88221012696.6112234206921
1811740.05839630911731.60665798158.45173832753275

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Extrapolation \tabularnewline
t & Observed & Level & Seasonal \tabularnewline
1 & 11074.1705394822 & 10971.2910444387 & 102.8794950435 \tabularnewline
2 & 11027.6383885424 & 11016.0154922942 & 11.6228962482273 \tabularnewline
3 & 10963.3211166709 & 11060.7399401496 & -97.4188234787553 \tabularnewline
4 & 11089.8598842189 & 11105.4643880051 & -15.6045037862335 \tabularnewline
5 & 11246.8000592812 & 11150.1888358605 & 96.6112234206921 \tabularnewline
6 & 11203.3650220435 & 11194.913283716 & 8.45173832753275 \tabularnewline
7 & 11145.5601993955 & 11239.6377315715 & -94.0775321759521 \tabularnewline
8 & 11261.7301772014 & 11284.3621794269 & -22.6320022254602 \tabularnewline
9 & 11428.2178189773 & 11329.0866272824 & 99.1311916949164 \tabularnewline
10 & 11392.2712174494 & 11373.8110751378 & 18.460142311537 \tabularnewline
11 & 11329.8782941965 & 11418.5355229933 & -88.6572287967352 \tabularnewline
12 & 11444.4933742655 & 11463.2599708487 & -18.7665965832692 \tabularnewline
13 & 11610.8639137477 & 11507.9844187042 & 102.8794950435 \tabularnewline
14 & 11564.3317628079 & 11552.7088665596 & 11.6228962482273 \tabularnewline
15 & 11500.0144909363 & 11597.4333144151 & -97.4188234787553 \tabularnewline
16 & 11626.5532584843 & 11642.1577622705 & -15.6045037862335 \tabularnewline
17 & 11783.4934335467 & 11686.882210126 & 96.6112234206921 \tabularnewline
18 & 11740.058396309 & 11731.6066579815 & 8.45173832753275 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298207&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]11074.1705394822[/C][C]10971.2910444387[/C][C]102.8794950435[/C][/ROW]
[ROW][C]2[/C][C]11027.6383885424[/C][C]11016.0154922942[/C][C]11.6228962482273[/C][/ROW]
[ROW][C]3[/C][C]10963.3211166709[/C][C]11060.7399401496[/C][C]-97.4188234787553[/C][/ROW]
[ROW][C]4[/C][C]11089.8598842189[/C][C]11105.4643880051[/C][C]-15.6045037862335[/C][/ROW]
[ROW][C]5[/C][C]11246.8000592812[/C][C]11150.1888358605[/C][C]96.6112234206921[/C][/ROW]
[ROW][C]6[/C][C]11203.3650220435[/C][C]11194.913283716[/C][C]8.45173832753275[/C][/ROW]
[ROW][C]7[/C][C]11145.5601993955[/C][C]11239.6377315715[/C][C]-94.0775321759521[/C][/ROW]
[ROW][C]8[/C][C]11261.7301772014[/C][C]11284.3621794269[/C][C]-22.6320022254602[/C][/ROW]
[ROW][C]9[/C][C]11428.2178189773[/C][C]11329.0866272824[/C][C]99.1311916949164[/C][/ROW]
[ROW][C]10[/C][C]11392.2712174494[/C][C]11373.8110751378[/C][C]18.460142311537[/C][/ROW]
[ROW][C]11[/C][C]11329.8782941965[/C][C]11418.5355229933[/C][C]-88.6572287967352[/C][/ROW]
[ROW][C]12[/C][C]11444.4933742655[/C][C]11463.2599708487[/C][C]-18.7665965832692[/C][/ROW]
[ROW][C]13[/C][C]11610.8639137477[/C][C]11507.9844187042[/C][C]102.8794950435[/C][/ROW]
[ROW][C]14[/C][C]11564.3317628079[/C][C]11552.7088665596[/C][C]11.6228962482273[/C][/ROW]
[ROW][C]15[/C][C]11500.0144909363[/C][C]11597.4333144151[/C][C]-97.4188234787553[/C][/ROW]
[ROW][C]16[/C][C]11626.5532584843[/C][C]11642.1577622705[/C][C]-15.6045037862335[/C][/ROW]
[ROW][C]17[/C][C]11783.4934335467[/C][C]11686.882210126[/C][C]96.6112234206921[/C][/ROW]
[ROW][C]18[/C][C]11740.058396309[/C][C]11731.6066579815[/C][C]8.45173832753275[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298207&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298207&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
111074.170539482210971.2910444387102.8794950435
211027.638388542411016.015492294211.6228962482273
310963.321116670911060.7399401496-97.4188234787553
411089.859884218911105.4643880051-15.6045037862335
511246.800059281211150.188835860596.6112234206921
611203.365022043511194.9132837168.45173832753275
711145.560199395511239.6377315715-94.0775321759521
811261.730177201411284.3621794269-22.6320022254602
911428.217818977311329.086627282499.1311916949164
1011392.271217449411373.811075137818.460142311537
1111329.878294196511418.5355229933-88.6572287967352
1211444.493374265511463.2599708487-18.7665965832692
1311610.863913747711507.9844187042102.8794950435
1411564.331762807911552.708866559611.6228962482273
1511500.014490936311597.4333144151-97.4188234787553
1611626.553258484311642.1577622705-15.6045037862335
1711783.493433546711686.88221012696.6112234206921
1811740.05839630911731.60665798158.45173832753275



Parameters (Session):
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')