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Description of Statistical Computation

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 computationSun, 19 Dec 2010 13:19:14 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/19/t129276501049err4azk2i2fh6.htm/, Retrieved Sun, 05 May 2024 06:45:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112365, Retrieved Sun, 05 May 2024 06:45:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact138

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [] [2008-12-08 19:22:39] [d2d412c7f4d35ffbf5ee5ee89db327d4]
- RMPD  [ARIMA Backward Selection] [] [2010-12-14 13:44:15] [42a441ca3193af442aa2201743dfb347]
- RMP     [Classical Decomposition] [] [2010-12-19 12:38:53] [07fa8844ca5618cd0482008937d9acea]
- RMP         [Structural Time Series Models] [] [2010-12-19 13:19:14] [ef8aba939446289dd59b403ac33ef077] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
19876
45335
48674
156392
100837
101605
532850
294189
80763
105995
25045
90474
48481
50730
68694
207716
99132
104012
422632
364974
82687
66834
28408
97073
40284
24421
116346
72120
108751
91738
402216
390070
106045
110070
70668
167841
28607
95371
30605
131063
81214
85451
455196
454570
63114
74287
42350
113375

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112365&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112365&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112365&T=0

As an alternative you can also use a QR Code:  
QR Code


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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ 72.249.76.132






Structural Time Series Model
tObservedLevelSlopeSeasonalStand. Residuals
11987619876000
24533523705.16254620475616.7522027315321629.83745379530.377795414304257
34867449924.222071934417299.1503055579-1250.222071934420.323492544118435
4156392118643.27734350541742.087828667537748.72265649520.789228636195483
5100837137795.31877983230205.5178236298-36958.3187798317-0.367820509206533
6101605126812.8696489009132.46928179208-25207.8696488998-0.613684411245519
7532850350459.558185676115664.421114603182390.4418143243.08504736453304
8294189406741.20027843786369.1058814291-112552.200278437-0.86135391283276
980763255397.689881801-31541.5340120403-174634.689881801-3.47143212212441
10105995118683.916325191-83889.6419868158-12688.9163251907-1.53680028047496
112504511682.2177423321-95400.309773368413362.7822576679-0.337692294788612
12904748578.67816380266-49443.883738307981895.32183619731.34858582023923
134848123850.8408790019-17460.910643838324630.15912099810.944181517057383
145073033836.8548505416-3814.1412204815916893.14514945840.407154962785429
156869463100.136042131612555.24614411095593.863957868440.478278592444982
16207716129052.84112570738285.189125976978663.15887429280.749381345869228
1799132177105.57867499142972.6437995942-77973.57867499070.139758478522345
18104012234895.57115229250175.1171322573-130883.5711522920.214131816162629
19422632227588.39683249522243.2365240479195043.603167505-0.817447379367588
20364974288810.07070324441023.698323716676163.92929675610.54820571136675
2182687258982.1939640137003.77461835468-176295.193964013-0.997398248842642
2266834148865.314897505-49297.108895649-82031.3148975048-1.65389196050231
232840863317.1809415257-66742.2166687941-34909.1809415257-0.512602849346666
249707319313.6236036491-55796.340114621477759.37639635090.321909185348457
25402844584.49418177875-36002.326565502235699.50581822120.582794387586316
26244219726.4336433907-16144.471316055514694.56635660930.58354973095151
2711634682780.067015545126748.607538146133565.93298445491.25454303229922
287212064702.0670171275351.533163592217417.93298287303-0.626322751446359
29108751134511.65198133336051.6728168491-25760.65198133330.904954280000311
3091738202486.60962477351322.9654287587-110748.6096247730.451251783733253
31402216238150.19578686943811.5559866347164065.804213131-0.220837457595763
32390070263383.39434911934925.1282819528126686.605650881-0.260040486045174
33106045245406.3917835669731.43421624283-139361.391783566-0.737320977478277
34110070199958.699285429-16491.9172303027-89888.6992854294-0.769511284026466
3570668139516.721833644-37387.9313008423-68848.7218336444-0.614610367114593
36167841103895.282026581-36546.603861935763945.71797341920.024767245211941
372860743906.6921714098-47729.6669201649-15299.6921714098-0.328866951263245
389537161223.7277646957-16706.291846559834147.27223530430.90989727424474
393060522335.55907111-27253.37102113778269.44092888999-0.308720577161575
4013106389285.719583352517368.770294277341777.28041664751.30787450927381
4181214132342.07234716029524.6514659624-51128.07234715960.357607747375734
4285451181030.37611563038614.2063266881-95579.37611563030.267861474738855
43455196252992.54074851954464.0991427527202203.4592514810.466046312004838
44454570302167.5614541351952.9794877709152402.438545870-0.0735885515555617
4563114245619.143715174606.416079718307-182505.143715174-1.50325370118597
4674287168819.180736287-35933.3515807221-94532.1807362867-1.07172166660501
4742350106500.037859408-48387.3759783597-64150.0378594085-0.366190189097005
4811337545956.1712552038-54134.701471767567418.8287447962-0.169149952581934

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 19876 & 19876 & 0 & 0 & 0 \tabularnewline
2 & 45335 & 23705.1625462047 & 5616.75220273153 & 21629.8374537953 & 0.377795414304257 \tabularnewline
3 & 48674 & 49924.2220719344 & 17299.1503055579 & -1250.22207193442 & 0.323492544118435 \tabularnewline
4 & 156392 & 118643.277343505 & 41742.0878286675 & 37748.7226564952 & 0.789228636195483 \tabularnewline
5 & 100837 & 137795.318779832 & 30205.5178236298 & -36958.3187798317 & -0.367820509206533 \tabularnewline
6 & 101605 & 126812.869648900 & 9132.46928179208 & -25207.8696488998 & -0.613684411245519 \tabularnewline
7 & 532850 & 350459.558185676 & 115664.421114603 & 182390.441814324 & 3.08504736453304 \tabularnewline
8 & 294189 & 406741.200278437 & 86369.1058814291 & -112552.200278437 & -0.86135391283276 \tabularnewline
9 & 80763 & 255397.689881801 & -31541.5340120403 & -174634.689881801 & -3.47143212212441 \tabularnewline
10 & 105995 & 118683.916325191 & -83889.6419868158 & -12688.9163251907 & -1.53680028047496 \tabularnewline
11 & 25045 & 11682.2177423321 & -95400.3097733684 & 13362.7822576679 & -0.337692294788612 \tabularnewline
12 & 90474 & 8578.67816380266 & -49443.8837383079 & 81895.3218361973 & 1.34858582023923 \tabularnewline
13 & 48481 & 23850.8408790019 & -17460.9106438383 & 24630.1591209981 & 0.944181517057383 \tabularnewline
14 & 50730 & 33836.8548505416 & -3814.14122048159 & 16893.1451494584 & 0.407154962785429 \tabularnewline
15 & 68694 & 63100.1360421316 & 12555.2461441109 & 5593.86395786844 & 0.478278592444982 \tabularnewline
16 & 207716 & 129052.841125707 & 38285.1891259769 & 78663.1588742928 & 0.749381345869228 \tabularnewline
17 & 99132 & 177105.578674991 & 42972.6437995942 & -77973.5786749907 & 0.139758478522345 \tabularnewline
18 & 104012 & 234895.571152292 & 50175.1171322573 & -130883.571152292 & 0.214131816162629 \tabularnewline
19 & 422632 & 227588.396832495 & 22243.2365240479 & 195043.603167505 & -0.817447379367588 \tabularnewline
20 & 364974 & 288810.070703244 & 41023.6983237166 & 76163.9292967561 & 0.54820571136675 \tabularnewline
21 & 82687 & 258982.193964013 & 7003.77461835468 & -176295.193964013 & -0.997398248842642 \tabularnewline
22 & 66834 & 148865.314897505 & -49297.108895649 & -82031.3148975048 & -1.65389196050231 \tabularnewline
23 & 28408 & 63317.1809415257 & -66742.2166687941 & -34909.1809415257 & -0.512602849346666 \tabularnewline
24 & 97073 & 19313.6236036491 & -55796.3401146214 & 77759.3763963509 & 0.321909185348457 \tabularnewline
25 & 40284 & 4584.49418177875 & -36002.3265655022 & 35699.5058182212 & 0.582794387586316 \tabularnewline
26 & 24421 & 9726.4336433907 & -16144.4713160555 & 14694.5663566093 & 0.58354973095151 \tabularnewline
27 & 116346 & 82780.0670155451 & 26748.6075381461 & 33565.9329844549 & 1.25454303229922 \tabularnewline
28 & 72120 & 64702.067017127 & 5351.53316359221 & 7417.93298287303 & -0.626322751446359 \tabularnewline
29 & 108751 & 134511.651981333 & 36051.6728168491 & -25760.6519813333 & 0.904954280000311 \tabularnewline
30 & 91738 & 202486.609624773 & 51322.9654287587 & -110748.609624773 & 0.451251783733253 \tabularnewline
31 & 402216 & 238150.195786869 & 43811.5559866347 & 164065.804213131 & -0.220837457595763 \tabularnewline
32 & 390070 & 263383.394349119 & 34925.1282819528 & 126686.605650881 & -0.260040486045174 \tabularnewline
33 & 106045 & 245406.391783566 & 9731.43421624283 & -139361.391783566 & -0.737320977478277 \tabularnewline
34 & 110070 & 199958.699285429 & -16491.9172303027 & -89888.6992854294 & -0.769511284026466 \tabularnewline
35 & 70668 & 139516.721833644 & -37387.9313008423 & -68848.7218336444 & -0.614610367114593 \tabularnewline
36 & 167841 & 103895.282026581 & -36546.6038619357 & 63945.7179734192 & 0.024767245211941 \tabularnewline
37 & 28607 & 43906.6921714098 & -47729.6669201649 & -15299.6921714098 & -0.328866951263245 \tabularnewline
38 & 95371 & 61223.7277646957 & -16706.2918465598 & 34147.2722353043 & 0.90989727424474 \tabularnewline
39 & 30605 & 22335.55907111 & -27253.3710211377 & 8269.44092888999 & -0.308720577161575 \tabularnewline
40 & 131063 & 89285.7195833525 & 17368.7702942773 & 41777.2804166475 & 1.30787450927381 \tabularnewline
41 & 81214 & 132342.072347160 & 29524.6514659624 & -51128.0723471596 & 0.357607747375734 \tabularnewline
42 & 85451 & 181030.376115630 & 38614.2063266881 & -95579.3761156303 & 0.267861474738855 \tabularnewline
43 & 455196 & 252992.540748519 & 54464.0991427527 & 202203.459251481 & 0.466046312004838 \tabularnewline
44 & 454570 & 302167.56145413 & 51952.9794877709 & 152402.438545870 & -0.0735885515555617 \tabularnewline
45 & 63114 & 245619.143715174 & 606.416079718307 & -182505.143715174 & -1.50325370118597 \tabularnewline
46 & 74287 & 168819.180736287 & -35933.3515807221 & -94532.1807362867 & -1.07172166660501 \tabularnewline
47 & 42350 & 106500.037859408 & -48387.3759783597 & -64150.0378594085 & -0.366190189097005 \tabularnewline
48 & 113375 & 45956.1712552038 & -54134.7014717675 & 67418.8287447962 & -0.169149952581934 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112365&T=1

[TABLE]
[ROW][C]Structural Time Series Model[/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]19876[/C][C]19876[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]45335[/C][C]23705.1625462047[/C][C]5616.75220273153[/C][C]21629.8374537953[/C][C]0.377795414304257[/C][/ROW]
[ROW][C]3[/C][C]48674[/C][C]49924.2220719344[/C][C]17299.1503055579[/C][C]-1250.22207193442[/C][C]0.323492544118435[/C][/ROW]
[ROW][C]4[/C][C]156392[/C][C]118643.277343505[/C][C]41742.0878286675[/C][C]37748.7226564952[/C][C]0.789228636195483[/C][/ROW]
[ROW][C]5[/C][C]100837[/C][C]137795.318779832[/C][C]30205.5178236298[/C][C]-36958.3187798317[/C][C]-0.367820509206533[/C][/ROW]
[ROW][C]6[/C][C]101605[/C][C]126812.869648900[/C][C]9132.46928179208[/C][C]-25207.8696488998[/C][C]-0.613684411245519[/C][/ROW]
[ROW][C]7[/C][C]532850[/C][C]350459.558185676[/C][C]115664.421114603[/C][C]182390.441814324[/C][C]3.08504736453304[/C][/ROW]
[ROW][C]8[/C][C]294189[/C][C]406741.200278437[/C][C]86369.1058814291[/C][C]-112552.200278437[/C][C]-0.86135391283276[/C][/ROW]
[ROW][C]9[/C][C]80763[/C][C]255397.689881801[/C][C]-31541.5340120403[/C][C]-174634.689881801[/C][C]-3.47143212212441[/C][/ROW]
[ROW][C]10[/C][C]105995[/C][C]118683.916325191[/C][C]-83889.6419868158[/C][C]-12688.9163251907[/C][C]-1.53680028047496[/C][/ROW]
[ROW][C]11[/C][C]25045[/C][C]11682.2177423321[/C][C]-95400.3097733684[/C][C]13362.7822576679[/C][C]-0.337692294788612[/C][/ROW]
[ROW][C]12[/C][C]90474[/C][C]8578.67816380266[/C][C]-49443.8837383079[/C][C]81895.3218361973[/C][C]1.34858582023923[/C][/ROW]
[ROW][C]13[/C][C]48481[/C][C]23850.8408790019[/C][C]-17460.9106438383[/C][C]24630.1591209981[/C][C]0.944181517057383[/C][/ROW]
[ROW][C]14[/C][C]50730[/C][C]33836.8548505416[/C][C]-3814.14122048159[/C][C]16893.1451494584[/C][C]0.407154962785429[/C][/ROW]
[ROW][C]15[/C][C]68694[/C][C]63100.1360421316[/C][C]12555.2461441109[/C][C]5593.86395786844[/C][C]0.478278592444982[/C][/ROW]
[ROW][C]16[/C][C]207716[/C][C]129052.841125707[/C][C]38285.1891259769[/C][C]78663.1588742928[/C][C]0.749381345869228[/C][/ROW]
[ROW][C]17[/C][C]99132[/C][C]177105.578674991[/C][C]42972.6437995942[/C][C]-77973.5786749907[/C][C]0.139758478522345[/C][/ROW]
[ROW][C]18[/C][C]104012[/C][C]234895.571152292[/C][C]50175.1171322573[/C][C]-130883.571152292[/C][C]0.214131816162629[/C][/ROW]
[ROW][C]19[/C][C]422632[/C][C]227588.396832495[/C][C]22243.2365240479[/C][C]195043.603167505[/C][C]-0.817447379367588[/C][/ROW]
[ROW][C]20[/C][C]364974[/C][C]288810.070703244[/C][C]41023.6983237166[/C][C]76163.9292967561[/C][C]0.54820571136675[/C][/ROW]
[ROW][C]21[/C][C]82687[/C][C]258982.193964013[/C][C]7003.77461835468[/C][C]-176295.193964013[/C][C]-0.997398248842642[/C][/ROW]
[ROW][C]22[/C][C]66834[/C][C]148865.314897505[/C][C]-49297.108895649[/C][C]-82031.3148975048[/C][C]-1.65389196050231[/C][/ROW]
[ROW][C]23[/C][C]28408[/C][C]63317.1809415257[/C][C]-66742.2166687941[/C][C]-34909.1809415257[/C][C]-0.512602849346666[/C][/ROW]
[ROW][C]24[/C][C]97073[/C][C]19313.6236036491[/C][C]-55796.3401146214[/C][C]77759.3763963509[/C][C]0.321909185348457[/C][/ROW]
[ROW][C]25[/C][C]40284[/C][C]4584.49418177875[/C][C]-36002.3265655022[/C][C]35699.5058182212[/C][C]0.582794387586316[/C][/ROW]
[ROW][C]26[/C][C]24421[/C][C]9726.4336433907[/C][C]-16144.4713160555[/C][C]14694.5663566093[/C][C]0.58354973095151[/C][/ROW]
[ROW][C]27[/C][C]116346[/C][C]82780.0670155451[/C][C]26748.6075381461[/C][C]33565.9329844549[/C][C]1.25454303229922[/C][/ROW]
[ROW][C]28[/C][C]72120[/C][C]64702.067017127[/C][C]5351.53316359221[/C][C]7417.93298287303[/C][C]-0.626322751446359[/C][/ROW]
[ROW][C]29[/C][C]108751[/C][C]134511.651981333[/C][C]36051.6728168491[/C][C]-25760.6519813333[/C][C]0.904954280000311[/C][/ROW]
[ROW][C]30[/C][C]91738[/C][C]202486.609624773[/C][C]51322.9654287587[/C][C]-110748.609624773[/C][C]0.451251783733253[/C][/ROW]
[ROW][C]31[/C][C]402216[/C][C]238150.195786869[/C][C]43811.5559866347[/C][C]164065.804213131[/C][C]-0.220837457595763[/C][/ROW]
[ROW][C]32[/C][C]390070[/C][C]263383.394349119[/C][C]34925.1282819528[/C][C]126686.605650881[/C][C]-0.260040486045174[/C][/ROW]
[ROW][C]33[/C][C]106045[/C][C]245406.391783566[/C][C]9731.43421624283[/C][C]-139361.391783566[/C][C]-0.737320977478277[/C][/ROW]
[ROW][C]34[/C][C]110070[/C][C]199958.699285429[/C][C]-16491.9172303027[/C][C]-89888.6992854294[/C][C]-0.769511284026466[/C][/ROW]
[ROW][C]35[/C][C]70668[/C][C]139516.721833644[/C][C]-37387.9313008423[/C][C]-68848.7218336444[/C][C]-0.614610367114593[/C][/ROW]
[ROW][C]36[/C][C]167841[/C][C]103895.282026581[/C][C]-36546.6038619357[/C][C]63945.7179734192[/C][C]0.024767245211941[/C][/ROW]
[ROW][C]37[/C][C]28607[/C][C]43906.6921714098[/C][C]-47729.6669201649[/C][C]-15299.6921714098[/C][C]-0.328866951263245[/C][/ROW]
[ROW][C]38[/C][C]95371[/C][C]61223.7277646957[/C][C]-16706.2918465598[/C][C]34147.2722353043[/C][C]0.90989727424474[/C][/ROW]
[ROW][C]39[/C][C]30605[/C][C]22335.55907111[/C][C]-27253.3710211377[/C][C]8269.44092888999[/C][C]-0.308720577161575[/C][/ROW]
[ROW][C]40[/C][C]131063[/C][C]89285.7195833525[/C][C]17368.7702942773[/C][C]41777.2804166475[/C][C]1.30787450927381[/C][/ROW]
[ROW][C]41[/C][C]81214[/C][C]132342.072347160[/C][C]29524.6514659624[/C][C]-51128.0723471596[/C][C]0.357607747375734[/C][/ROW]
[ROW][C]42[/C][C]85451[/C][C]181030.376115630[/C][C]38614.2063266881[/C][C]-95579.3761156303[/C][C]0.267861474738855[/C][/ROW]
[ROW][C]43[/C][C]455196[/C][C]252992.540748519[/C][C]54464.0991427527[/C][C]202203.459251481[/C][C]0.466046312004838[/C][/ROW]
[ROW][C]44[/C][C]454570[/C][C]302167.56145413[/C][C]51952.9794877709[/C][C]152402.438545870[/C][C]-0.0735885515555617[/C][/ROW]
[ROW][C]45[/C][C]63114[/C][C]245619.143715174[/C][C]606.416079718307[/C][C]-182505.143715174[/C][C]-1.50325370118597[/C][/ROW]
[ROW][C]46[/C][C]74287[/C][C]168819.180736287[/C][C]-35933.3515807221[/C][C]-94532.1807362867[/C][C]-1.07172166660501[/C][/ROW]
[ROW][C]47[/C][C]42350[/C][C]106500.037859408[/C][C]-48387.3759783597[/C][C]-64150.0378594085[/C][C]-0.366190189097005[/C][/ROW]
[ROW][C]48[/C][C]113375[/C][C]45956.1712552038[/C][C]-54134.7014717675[/C][C]67418.8287447962[/C][C]-0.169149952581934[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112365&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112365&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Structural Time Series Model
tObservedLevelSlopeSeasonalStand. Residuals
11987619876000
24533523705.16254620475616.7522027315321629.83745379530.377795414304257
34867449924.222071934417299.1503055579-1250.222071934420.323492544118435
4156392118643.27734350541742.087828667537748.72265649520.789228636195483
5100837137795.31877983230205.5178236298-36958.3187798317-0.367820509206533
6101605126812.8696489009132.46928179208-25207.8696488998-0.613684411245519
7532850350459.558185676115664.421114603182390.4418143243.08504736453304
8294189406741.20027843786369.1058814291-112552.200278437-0.86135391283276
980763255397.689881801-31541.5340120403-174634.689881801-3.47143212212441
10105995118683.916325191-83889.6419868158-12688.9163251907-1.53680028047496
112504511682.2177423321-95400.309773368413362.7822576679-0.337692294788612
12904748578.67816380266-49443.883738307981895.32183619731.34858582023923
134848123850.8408790019-17460.910643838324630.15912099810.944181517057383
145073033836.8548505416-3814.1412204815916893.14514945840.407154962785429
156869463100.136042131612555.24614411095593.863957868440.478278592444982
16207716129052.84112570738285.189125976978663.15887429280.749381345869228
1799132177105.57867499142972.6437995942-77973.57867499070.139758478522345
18104012234895.57115229250175.1171322573-130883.5711522920.214131816162629
19422632227588.39683249522243.2365240479195043.603167505-0.817447379367588
20364974288810.07070324441023.698323716676163.92929675610.54820571136675
2182687258982.1939640137003.77461835468-176295.193964013-0.997398248842642
2266834148865.314897505-49297.108895649-82031.3148975048-1.65389196050231
232840863317.1809415257-66742.2166687941-34909.1809415257-0.512602849346666
249707319313.6236036491-55796.340114621477759.37639635090.321909185348457
25402844584.49418177875-36002.326565502235699.50581822120.582794387586316
26244219726.4336433907-16144.471316055514694.56635660930.58354973095151
2711634682780.067015545126748.607538146133565.93298445491.25454303229922
287212064702.0670171275351.533163592217417.93298287303-0.626322751446359
29108751134511.65198133336051.6728168491-25760.65198133330.904954280000311
3091738202486.60962477351322.9654287587-110748.6096247730.451251783733253
31402216238150.19578686943811.5559866347164065.804213131-0.220837457595763
32390070263383.39434911934925.1282819528126686.605650881-0.260040486045174
33106045245406.3917835669731.43421624283-139361.391783566-0.737320977478277
34110070199958.699285429-16491.9172303027-89888.6992854294-0.769511284026466
3570668139516.721833644-37387.9313008423-68848.7218336444-0.614610367114593
36167841103895.282026581-36546.603861935763945.71797341920.024767245211941
372860743906.6921714098-47729.6669201649-15299.6921714098-0.328866951263245
389537161223.7277646957-16706.291846559834147.27223530430.90989727424474
393060522335.55907111-27253.37102113778269.44092888999-0.308720577161575
4013106389285.719583352517368.770294277341777.28041664751.30787450927381
4181214132342.07234716029524.6514659624-51128.07234715960.357607747375734
4285451181030.37611563038614.2063266881-95579.37611563030.267861474738855
43455196252992.54074851954464.0991427527202203.4592514810.466046312004838
44454570302167.5614541351952.9794877709152402.438545870-0.0735885515555617
4563114245619.143715174606.416079718307-182505.143715174-1.50325370118597
4674287168819.180736287-35933.3515807221-94532.1807362867-1.07172166660501
4742350106500.037859408-48387.3759783597-64150.0378594085-0.366190189097005
4811337545956.1712552038-54134.701471767567418.8287447962-0.169149952581934


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ;
Parameters (R input):
par1 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
nx <- length(x)
x <- ts(x,frequency=par1)
m <- StructTS(x,type='BSM')
m$coef
m$fitted
m$resid
mylevel <- as.numeric(m$fitted[,'level'])
myslope <- as.numeric(m$fitted[,'slope'])
myseas <- as.numeric(m$fitted[,'sea'])
myresid <- as.numeric(m$resid)
myfit <- mylevel+myseas
mylagmax <- nx/2
bitmap(file='test2.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(x),lag.max = mylagmax,main='Observed')
acf(mylevel,na.action=na.pass,lag.max = mylagmax,main='Level')
acf(myseas,na.action=na.pass,lag.max = mylagmax,main='Seasonal')
acf(myresid,na.action=na.pass,lag.max = mylagmax,main='Standardized Residals')
par(op)
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
spectrum(as.numeric(x),main='Observed')
spectrum(mylevel,main='Level')
spectrum(myseas,main='Seasonal')
spectrum(myresid,main='Standardized Residals')
par(op)
dev.off()
bitmap(file='test4.png')
op <- par(mfrow = c(2,2))
cpgram(as.numeric(x),main='Observed')
cpgram(mylevel,main='Level')
cpgram(myseas,main='Seasonal')
cpgram(myresid,main='Standardized Residals')
par(op)
dev.off()
bitmap(file='test1.png')
plot(as.numeric(m$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()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Structural Time Series Model',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')