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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 computationMon, 28 Nov 2011 09:22:27 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/28/t1322491366t1px4jm0jmb3dhs.htm/, Retrieved Fri, 01 May 2026 18:10:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=147770, Retrieved Fri, 01 May 2026 18:10:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact391

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Structural Time Series Models] [] [2011-11-28 14:22:27] [2be7aedefc35278abdba659ba29c8de8] [Current]
- R       [Structural Time Series Models] [] [2011-11-28 17:07:37] [aefb5c2d4042694c5b6b82f93ac1885a]
-  M        [Structural Time Series Models] [] [2011-11-28 17:09:42] [aefb5c2d4042694c5b6b82f93ac1885a]
-  M        [Structural Time Series Models] [] [2011-11-28 17:11:42] [aefb5c2d4042694c5b6b82f93ac1885a]
- R       [Structural Time Series Models] [] [2011-11-28 20:12:29] [aefb5c2d4042694c5b6b82f93ac1885a]
-  M        [Structural Time Series Models] [] [2011-11-28 20:13:17] [aefb5c2d4042694c5b6b82f93ac1885a]
- R       [Structural Time Series Models] [] [2011-11-28 22:46:30] [74be16979710d4c4e7c6647856088456]
- R       [Structural Time Series Models] [] [2011-11-28 22:47:29] [74be16979710d4c4e7c6647856088456]
- R       [Structural Time Series Models] [] [2011-11-28 22:48:02] [74be16979710d4c4e7c6647856088456]
- R       [Structural Time Series Models] [] [2011-11-28 22:48:33] [74be16979710d4c4e7c6647856088456]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
9700
9081
9084
9743
8587
9731
9563
9998
9437
10038
9918
9252
9737
9035
9133
9487
8700
9627
8947
9283
8829
9947
9628
9318
9605
8640
9214
9567
8547
9185
9470
9123
9278
10170
9434
9655
9429
8739
9552
9687
9019
9672
9206
9069
9788
10312
10105
9863
9656
9295
9946
9701
9049
10190
9706
9765
9893
9994
10433
10073
10112
9266
9820
10097
9115
10411
9678
10408
10153
10368
10581
10597
10680
9738
9556

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147770&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147770&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147770&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 time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net






Structural Time Series Model
tObservedLevelSlopeSeasonalStand. Residuals
197009700000
290819420.74876983189-4.57366027258277-334.803448964206-1.94834264125015
390849148.23386410293-22.2230341314185-61.4737147400464-1.35938514876797
497439343.34222928466-8.81354308532632396.8020471873131.35795496412481
585879095.71670401453-19.3897234367873-504.931078054266-1.70069468175497
697319271.8115669484-13.6789574588719455.8742268908631.44996900849938
795639434.34498941604-10.0336633661858125.6103383672761.31903815630069
899989698.057665009-5.32892304644793295.1918418130312.05149160604926
994379674.89483448955-5.62008630303203-237.585415498712-0.133535063101566
10100389807.96170146545-3.34244046637231227.6354054165551.03724496156112
1199189889.11319101532-1.9367840394971127.42455848313150.63142261575917
1292529667.91926929961-5.59596808609243-412.126898276972-1.63792541267238
1397379552.09346520033-3.60321825359209186.870444126881-0.867991128955308
1490359409.60053648043-2.67830097623638-372.142520524378-1.07958030968515
1591339311.86409925472-4.16419357407604-177.360706417732-0.672654981836742
1694879154.70182524022-8.33677975478718334.586912119477-1.05064354962543
1787009193.58165472528-6.97686101606697-494.3051148333820.333390996185739
1896279253.45699318369-5.30634135990324372.4772477922090.487322267446532
1989479171.22183771209-6.84902720301295-222.963862753513-0.570817054401088
2092839097.54333298203-7.92773975652946186.562788810834-0.499534007121835
2188299104.99946190603-7.72014666099224-276.2553742005410.115264994351102
2299479330.40502674057-5.08078861559478612.7092384949021.74691902012461
2396289424.01076845902-4.23387532981186202.3423796679220.739021637104409
2493189518.23584335688-3.76387411801166-201.8833090193670.738226066304609
2596059459.67901215977-3.82824221490463146.242938514042-0.41299927393743
2686409244.05181693482-4.56158951631669-600.51921073796-1.58336341056381
2792149214.62460786303-4.81030747245246-0.222171178363598-0.181363817381967
2895679224.5152588269-4.57409510505649342.2529624686660.105418963881337
2985479155.49210322739-5.80547880389003-607.478854336245-0.463545967786301
3091858982.94086052249-8.98976466669212204.717139594042-1.21612196637376
3194709195.95126348248-5.17620808386451270.4521289368871.64060386180114
3291239183.67815616814-5.27929635280281-60.5618446083347-0.0528713661577582
3392789382.20014572002-2.87336903490704-107.5617572299771.52368500476979
34101709524.09839580382-1.54047710518845643.5063644348691.08334468835021
3594349459.83211001621-1.967145386125-24.7927357315284-0.469412703827005
3696559554.21363594272-1.4918875946930799.18835733355060.721118803353077
3794299426.43988373316-2.041550983637774.65231585190786-0.943920679048537
3887399354.04326894093-2.44752304155232-613.885897199703-0.522581909811403
3995529400.49008229663-2.02056832730934150.7162063960680.359348877235232
4096879364.46769468858-2.42479727891175323.077525490935-0.247868668824745
4190199439.23969303499-1.34123315353324-421.4727502209150.562507597657474
4296729526.3117944858-0.0429565669624922144.2690507285410.64814873561941
4392069354.36766716141-2.44571076081891-145.583941856492-1.27010850628161
4490699291.78693459228-3.18994179233633-221.805171187696-0.447026313045732
4597889527.27200153755-0.715975227978509256.8098278756771.78025952002197
46103129624.424340844410.100075150472991685.964041645120.731000413630024
47101059836.125685143331.50181437147834265.3846158713711.58105415816898
4898639824.445255638421.4286013482271138.7721854398756-0.0984553656677268
4996569747.286541988571.00246121879073-89.9926634288087-0.585819712707743
5092959801.813325327321.34074610908583-507.6902501322240.397301065018393
5199469816.201904895941.44461879246933129.5858603380510.0963073674180238
5297019677.00034974660.071305462293779726.2725501974939-1.03366376752918
5390499569.03474889489-1.13218532463277-518.29346785566-0.793451126625965
54101909686.252917868460.255496739724403501.835889651690.871673983985699
5597069795.083860988081.49955474935747-90.84559749443080.80325982935323
5697659964.851129745623.26793916612037-202.5956815009231.24994658683419
5798939928.379909689912.90343374384707-34.7290747071367-0.295993912664426
5899949736.87248022491.3930406672218260.319853988471-1.45005328321816
59104339841.171779247492.07200420221525590.1362448903650.767875715674426
60100739924.925903213792.55416915188507146.7310422036240.609240092225543
611011210052.80273704453.2848661592940357.13976165103760.933296632597031
6292669964.623469568592.70195651533584-697.126642945911-0.679282808379915
6398209805.680854925151.514803640431816.9533344473324-1.19659266892572
64100979863.911197796511.99292659556327232.1679902923310.418815651594879
6591159841.339417241321.76440911339012-725.941272815947-0.181297827175938
66104119901.660092508412.33404241141764508.3900472950410.432789884150497
6796789895.094958540412.24839983386813-216.950218273923-0.065942989884464
681040810131.52099042364.36899456875364272.6578211782891.73980299717976
691015310180.00649167494.73050981782183-27.72842124311140.328406731705262
701036810200.93972974154.84815277078179166.7945950845330.120753615482844
711058110156.26812951154.52773784564386425.544693753418-0.369205392526939
721059710266.98140726685.16424053378995328.275566305770.791445739642711
731068010388.57955370055.85367871601794289.5111680427450.866899132578154
74973810404.40049283885.91583858105568-666.563602963270.0740812251511718
75955610104.99051379453.83303815407537-544.006734509468-2.26488583771179

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 9700 & 9700 & 0 & 0 & 0 \tabularnewline
2 & 9081 & 9420.74876983189 & -4.57366027258277 & -334.803448964206 & -1.94834264125015 \tabularnewline
3 & 9084 & 9148.23386410293 & -22.2230341314185 & -61.4737147400464 & -1.35938514876797 \tabularnewline
4 & 9743 & 9343.34222928466 & -8.81354308532632 & 396.802047187313 & 1.35795496412481 \tabularnewline
5 & 8587 & 9095.71670401453 & -19.3897234367873 & -504.931078054266 & -1.70069468175497 \tabularnewline
6 & 9731 & 9271.8115669484 & -13.6789574588719 & 455.874226890863 & 1.44996900849938 \tabularnewline
7 & 9563 & 9434.34498941604 & -10.0336633661858 & 125.610338367276 & 1.31903815630069 \tabularnewline
8 & 9998 & 9698.057665009 & -5.32892304644793 & 295.191841813031 & 2.05149160604926 \tabularnewline
9 & 9437 & 9674.89483448955 & -5.62008630303203 & -237.585415498712 & -0.133535063101566 \tabularnewline
10 & 10038 & 9807.96170146545 & -3.34244046637231 & 227.635405416555 & 1.03724496156112 \tabularnewline
11 & 9918 & 9889.11319101532 & -1.93678403949711 & 27.4245584831315 & 0.63142261575917 \tabularnewline
12 & 9252 & 9667.91926929961 & -5.59596808609243 & -412.126898276972 & -1.63792541267238 \tabularnewline
13 & 9737 & 9552.09346520033 & -3.60321825359209 & 186.870444126881 & -0.867991128955308 \tabularnewline
14 & 9035 & 9409.60053648043 & -2.67830097623638 & -372.142520524378 & -1.07958030968515 \tabularnewline
15 & 9133 & 9311.86409925472 & -4.16419357407604 & -177.360706417732 & -0.672654981836742 \tabularnewline
16 & 9487 & 9154.70182524022 & -8.33677975478718 & 334.586912119477 & -1.05064354962543 \tabularnewline
17 & 8700 & 9193.58165472528 & -6.97686101606697 & -494.305114833382 & 0.333390996185739 \tabularnewline
18 & 9627 & 9253.45699318369 & -5.30634135990324 & 372.477247792209 & 0.487322267446532 \tabularnewline
19 & 8947 & 9171.22183771209 & -6.84902720301295 & -222.963862753513 & -0.570817054401088 \tabularnewline
20 & 9283 & 9097.54333298203 & -7.92773975652946 & 186.562788810834 & -0.499534007121835 \tabularnewline
21 & 8829 & 9104.99946190603 & -7.72014666099224 & -276.255374200541 & 0.115264994351102 \tabularnewline
22 & 9947 & 9330.40502674057 & -5.08078861559478 & 612.709238494902 & 1.74691902012461 \tabularnewline
23 & 9628 & 9424.01076845902 & -4.23387532981186 & 202.342379667922 & 0.739021637104409 \tabularnewline
24 & 9318 & 9518.23584335688 & -3.76387411801166 & -201.883309019367 & 0.738226066304609 \tabularnewline
25 & 9605 & 9459.67901215977 & -3.82824221490463 & 146.242938514042 & -0.41299927393743 \tabularnewline
26 & 8640 & 9244.05181693482 & -4.56158951631669 & -600.51921073796 & -1.58336341056381 \tabularnewline
27 & 9214 & 9214.62460786303 & -4.81030747245246 & -0.222171178363598 & -0.181363817381967 \tabularnewline
28 & 9567 & 9224.5152588269 & -4.57409510505649 & 342.252962468666 & 0.105418963881337 \tabularnewline
29 & 8547 & 9155.49210322739 & -5.80547880389003 & -607.478854336245 & -0.463545967786301 \tabularnewline
30 & 9185 & 8982.94086052249 & -8.98976466669212 & 204.717139594042 & -1.21612196637376 \tabularnewline
31 & 9470 & 9195.95126348248 & -5.17620808386451 & 270.452128936887 & 1.64060386180114 \tabularnewline
32 & 9123 & 9183.67815616814 & -5.27929635280281 & -60.5618446083347 & -0.0528713661577582 \tabularnewline
33 & 9278 & 9382.20014572002 & -2.87336903490704 & -107.561757229977 & 1.52368500476979 \tabularnewline
34 & 10170 & 9524.09839580382 & -1.54047710518845 & 643.506364434869 & 1.08334468835021 \tabularnewline
35 & 9434 & 9459.83211001621 & -1.967145386125 & -24.7927357315284 & -0.469412703827005 \tabularnewline
36 & 9655 & 9554.21363594272 & -1.49188759469307 & 99.1883573335506 & 0.721118803353077 \tabularnewline
37 & 9429 & 9426.43988373316 & -2.04155098363777 & 4.65231585190786 & -0.943920679048537 \tabularnewline
38 & 8739 & 9354.04326894093 & -2.44752304155232 & -613.885897199703 & -0.522581909811403 \tabularnewline
39 & 9552 & 9400.49008229663 & -2.02056832730934 & 150.716206396068 & 0.359348877235232 \tabularnewline
40 & 9687 & 9364.46769468858 & -2.42479727891175 & 323.077525490935 & -0.247868668824745 \tabularnewline
41 & 9019 & 9439.23969303499 & -1.34123315353324 & -421.472750220915 & 0.562507597657474 \tabularnewline
42 & 9672 & 9526.3117944858 & -0.0429565669624922 & 144.269050728541 & 0.64814873561941 \tabularnewline
43 & 9206 & 9354.36766716141 & -2.44571076081891 & -145.583941856492 & -1.27010850628161 \tabularnewline
44 & 9069 & 9291.78693459228 & -3.18994179233633 & -221.805171187696 & -0.447026313045732 \tabularnewline
45 & 9788 & 9527.27200153755 & -0.715975227978509 & 256.809827875677 & 1.78025952002197 \tabularnewline
46 & 10312 & 9624.42434084441 & 0.100075150472991 & 685.96404164512 & 0.731000413630024 \tabularnewline
47 & 10105 & 9836.12568514333 & 1.50181437147834 & 265.384615871371 & 1.58105415816898 \tabularnewline
48 & 9863 & 9824.44525563842 & 1.42860134822711 & 38.7721854398756 & -0.0984553656677268 \tabularnewline
49 & 9656 & 9747.28654198857 & 1.00246121879073 & -89.9926634288087 & -0.585819712707743 \tabularnewline
50 & 9295 & 9801.81332532732 & 1.34074610908583 & -507.690250132224 & 0.397301065018393 \tabularnewline
51 & 9946 & 9816.20190489594 & 1.44461879246933 & 129.585860338051 & 0.0963073674180238 \tabularnewline
52 & 9701 & 9677.0003497466 & 0.0713054622937797 & 26.2725501974939 & -1.03366376752918 \tabularnewline
53 & 9049 & 9569.03474889489 & -1.13218532463277 & -518.29346785566 & -0.793451126625965 \tabularnewline
54 & 10190 & 9686.25291786846 & 0.255496739724403 & 501.83588965169 & 0.871673983985699 \tabularnewline
55 & 9706 & 9795.08386098808 & 1.49955474935747 & -90.8455974944308 & 0.80325982935323 \tabularnewline
56 & 9765 & 9964.85112974562 & 3.26793916612037 & -202.595681500923 & 1.24994658683419 \tabularnewline
57 & 9893 & 9928.37990968991 & 2.90343374384707 & -34.7290747071367 & -0.295993912664426 \tabularnewline
58 & 9994 & 9736.8724802249 & 1.3930406672218 & 260.319853988471 & -1.45005328321816 \tabularnewline
59 & 10433 & 9841.17177924749 & 2.07200420221525 & 590.136244890365 & 0.767875715674426 \tabularnewline
60 & 10073 & 9924.92590321379 & 2.55416915188507 & 146.731042203624 & 0.609240092225543 \tabularnewline
61 & 10112 & 10052.8027370445 & 3.28486615929403 & 57.1397616510376 & 0.933296632597031 \tabularnewline
62 & 9266 & 9964.62346956859 & 2.70195651533584 & -697.126642945911 & -0.679282808379915 \tabularnewline
63 & 9820 & 9805.68085492515 & 1.5148036404318 & 16.9533344473324 & -1.19659266892572 \tabularnewline
64 & 10097 & 9863.91119779651 & 1.99292659556327 & 232.167990292331 & 0.418815651594879 \tabularnewline
65 & 9115 & 9841.33941724132 & 1.76440911339012 & -725.941272815947 & -0.181297827175938 \tabularnewline
66 & 10411 & 9901.66009250841 & 2.33404241141764 & 508.390047295041 & 0.432789884150497 \tabularnewline
67 & 9678 & 9895.09495854041 & 2.24839983386813 & -216.950218273923 & -0.065942989884464 \tabularnewline
68 & 10408 & 10131.5209904236 & 4.36899456875364 & 272.657821178289 & 1.73980299717976 \tabularnewline
69 & 10153 & 10180.0064916749 & 4.73050981782183 & -27.7284212431114 & 0.328406731705262 \tabularnewline
70 & 10368 & 10200.9397297415 & 4.84815277078179 & 166.794595084533 & 0.120753615482844 \tabularnewline
71 & 10581 & 10156.2681295115 & 4.52773784564386 & 425.544693753418 & -0.369205392526939 \tabularnewline
72 & 10597 & 10266.9814072668 & 5.16424053378995 & 328.27556630577 & 0.791445739642711 \tabularnewline
73 & 10680 & 10388.5795537005 & 5.85367871601794 & 289.511168042745 & 0.866899132578154 \tabularnewline
74 & 9738 & 10404.4004928388 & 5.91583858105568 & -666.56360296327 & 0.0740812251511718 \tabularnewline
75 & 9556 & 10104.9905137945 & 3.83303815407537 & -544.006734509468 & -2.26488583771179 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147770&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]9700[/C][C]9700[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]9081[/C][C]9420.74876983189[/C][C]-4.57366027258277[/C][C]-334.803448964206[/C][C]-1.94834264125015[/C][/ROW]
[ROW][C]3[/C][C]9084[/C][C]9148.23386410293[/C][C]-22.2230341314185[/C][C]-61.4737147400464[/C][C]-1.35938514876797[/C][/ROW]
[ROW][C]4[/C][C]9743[/C][C]9343.34222928466[/C][C]-8.81354308532632[/C][C]396.802047187313[/C][C]1.35795496412481[/C][/ROW]
[ROW][C]5[/C][C]8587[/C][C]9095.71670401453[/C][C]-19.3897234367873[/C][C]-504.931078054266[/C][C]-1.70069468175497[/C][/ROW]
[ROW][C]6[/C][C]9731[/C][C]9271.8115669484[/C][C]-13.6789574588719[/C][C]455.874226890863[/C][C]1.44996900849938[/C][/ROW]
[ROW][C]7[/C][C]9563[/C][C]9434.34498941604[/C][C]-10.0336633661858[/C][C]125.610338367276[/C][C]1.31903815630069[/C][/ROW]
[ROW][C]8[/C][C]9998[/C][C]9698.057665009[/C][C]-5.32892304644793[/C][C]295.191841813031[/C][C]2.05149160604926[/C][/ROW]
[ROW][C]9[/C][C]9437[/C][C]9674.89483448955[/C][C]-5.62008630303203[/C][C]-237.585415498712[/C][C]-0.133535063101566[/C][/ROW]
[ROW][C]10[/C][C]10038[/C][C]9807.96170146545[/C][C]-3.34244046637231[/C][C]227.635405416555[/C][C]1.03724496156112[/C][/ROW]
[ROW][C]11[/C][C]9918[/C][C]9889.11319101532[/C][C]-1.93678403949711[/C][C]27.4245584831315[/C][C]0.63142261575917[/C][/ROW]
[ROW][C]12[/C][C]9252[/C][C]9667.91926929961[/C][C]-5.59596808609243[/C][C]-412.126898276972[/C][C]-1.63792541267238[/C][/ROW]
[ROW][C]13[/C][C]9737[/C][C]9552.09346520033[/C][C]-3.60321825359209[/C][C]186.870444126881[/C][C]-0.867991128955308[/C][/ROW]
[ROW][C]14[/C][C]9035[/C][C]9409.60053648043[/C][C]-2.67830097623638[/C][C]-372.142520524378[/C][C]-1.07958030968515[/C][/ROW]
[ROW][C]15[/C][C]9133[/C][C]9311.86409925472[/C][C]-4.16419357407604[/C][C]-177.360706417732[/C][C]-0.672654981836742[/C][/ROW]
[ROW][C]16[/C][C]9487[/C][C]9154.70182524022[/C][C]-8.33677975478718[/C][C]334.586912119477[/C][C]-1.05064354962543[/C][/ROW]
[ROW][C]17[/C][C]8700[/C][C]9193.58165472528[/C][C]-6.97686101606697[/C][C]-494.305114833382[/C][C]0.333390996185739[/C][/ROW]
[ROW][C]18[/C][C]9627[/C][C]9253.45699318369[/C][C]-5.30634135990324[/C][C]372.477247792209[/C][C]0.487322267446532[/C][/ROW]
[ROW][C]19[/C][C]8947[/C][C]9171.22183771209[/C][C]-6.84902720301295[/C][C]-222.963862753513[/C][C]-0.570817054401088[/C][/ROW]
[ROW][C]20[/C][C]9283[/C][C]9097.54333298203[/C][C]-7.92773975652946[/C][C]186.562788810834[/C][C]-0.499534007121835[/C][/ROW]
[ROW][C]21[/C][C]8829[/C][C]9104.99946190603[/C][C]-7.72014666099224[/C][C]-276.255374200541[/C][C]0.115264994351102[/C][/ROW]
[ROW][C]22[/C][C]9947[/C][C]9330.40502674057[/C][C]-5.08078861559478[/C][C]612.709238494902[/C][C]1.74691902012461[/C][/ROW]
[ROW][C]23[/C][C]9628[/C][C]9424.01076845902[/C][C]-4.23387532981186[/C][C]202.342379667922[/C][C]0.739021637104409[/C][/ROW]
[ROW][C]24[/C][C]9318[/C][C]9518.23584335688[/C][C]-3.76387411801166[/C][C]-201.883309019367[/C][C]0.738226066304609[/C][/ROW]
[ROW][C]25[/C][C]9605[/C][C]9459.67901215977[/C][C]-3.82824221490463[/C][C]146.242938514042[/C][C]-0.41299927393743[/C][/ROW]
[ROW][C]26[/C][C]8640[/C][C]9244.05181693482[/C][C]-4.56158951631669[/C][C]-600.51921073796[/C][C]-1.58336341056381[/C][/ROW]
[ROW][C]27[/C][C]9214[/C][C]9214.62460786303[/C][C]-4.81030747245246[/C][C]-0.222171178363598[/C][C]-0.181363817381967[/C][/ROW]
[ROW][C]28[/C][C]9567[/C][C]9224.5152588269[/C][C]-4.57409510505649[/C][C]342.252962468666[/C][C]0.105418963881337[/C][/ROW]
[ROW][C]29[/C][C]8547[/C][C]9155.49210322739[/C][C]-5.80547880389003[/C][C]-607.478854336245[/C][C]-0.463545967786301[/C][/ROW]
[ROW][C]30[/C][C]9185[/C][C]8982.94086052249[/C][C]-8.98976466669212[/C][C]204.717139594042[/C][C]-1.21612196637376[/C][/ROW]
[ROW][C]31[/C][C]9470[/C][C]9195.95126348248[/C][C]-5.17620808386451[/C][C]270.452128936887[/C][C]1.64060386180114[/C][/ROW]
[ROW][C]32[/C][C]9123[/C][C]9183.67815616814[/C][C]-5.27929635280281[/C][C]-60.5618446083347[/C][C]-0.0528713661577582[/C][/ROW]
[ROW][C]33[/C][C]9278[/C][C]9382.20014572002[/C][C]-2.87336903490704[/C][C]-107.561757229977[/C][C]1.52368500476979[/C][/ROW]
[ROW][C]34[/C][C]10170[/C][C]9524.09839580382[/C][C]-1.54047710518845[/C][C]643.506364434869[/C][C]1.08334468835021[/C][/ROW]
[ROW][C]35[/C][C]9434[/C][C]9459.83211001621[/C][C]-1.967145386125[/C][C]-24.7927357315284[/C][C]-0.469412703827005[/C][/ROW]
[ROW][C]36[/C][C]9655[/C][C]9554.21363594272[/C][C]-1.49188759469307[/C][C]99.1883573335506[/C][C]0.721118803353077[/C][/ROW]
[ROW][C]37[/C][C]9429[/C][C]9426.43988373316[/C][C]-2.04155098363777[/C][C]4.65231585190786[/C][C]-0.943920679048537[/C][/ROW]
[ROW][C]38[/C][C]8739[/C][C]9354.04326894093[/C][C]-2.44752304155232[/C][C]-613.885897199703[/C][C]-0.522581909811403[/C][/ROW]
[ROW][C]39[/C][C]9552[/C][C]9400.49008229663[/C][C]-2.02056832730934[/C][C]150.716206396068[/C][C]0.359348877235232[/C][/ROW]
[ROW][C]40[/C][C]9687[/C][C]9364.46769468858[/C][C]-2.42479727891175[/C][C]323.077525490935[/C][C]-0.247868668824745[/C][/ROW]
[ROW][C]41[/C][C]9019[/C][C]9439.23969303499[/C][C]-1.34123315353324[/C][C]-421.472750220915[/C][C]0.562507597657474[/C][/ROW]
[ROW][C]42[/C][C]9672[/C][C]9526.3117944858[/C][C]-0.0429565669624922[/C][C]144.269050728541[/C][C]0.64814873561941[/C][/ROW]
[ROW][C]43[/C][C]9206[/C][C]9354.36766716141[/C][C]-2.44571076081891[/C][C]-145.583941856492[/C][C]-1.27010850628161[/C][/ROW]
[ROW][C]44[/C][C]9069[/C][C]9291.78693459228[/C][C]-3.18994179233633[/C][C]-221.805171187696[/C][C]-0.447026313045732[/C][/ROW]
[ROW][C]45[/C][C]9788[/C][C]9527.27200153755[/C][C]-0.715975227978509[/C][C]256.809827875677[/C][C]1.78025952002197[/C][/ROW]
[ROW][C]46[/C][C]10312[/C][C]9624.42434084441[/C][C]0.100075150472991[/C][C]685.96404164512[/C][C]0.731000413630024[/C][/ROW]
[ROW][C]47[/C][C]10105[/C][C]9836.12568514333[/C][C]1.50181437147834[/C][C]265.384615871371[/C][C]1.58105415816898[/C][/ROW]
[ROW][C]48[/C][C]9863[/C][C]9824.44525563842[/C][C]1.42860134822711[/C][C]38.7721854398756[/C][C]-0.0984553656677268[/C][/ROW]
[ROW][C]49[/C][C]9656[/C][C]9747.28654198857[/C][C]1.00246121879073[/C][C]-89.9926634288087[/C][C]-0.585819712707743[/C][/ROW]
[ROW][C]50[/C][C]9295[/C][C]9801.81332532732[/C][C]1.34074610908583[/C][C]-507.690250132224[/C][C]0.397301065018393[/C][/ROW]
[ROW][C]51[/C][C]9946[/C][C]9816.20190489594[/C][C]1.44461879246933[/C][C]129.585860338051[/C][C]0.0963073674180238[/C][/ROW]
[ROW][C]52[/C][C]9701[/C][C]9677.0003497466[/C][C]0.0713054622937797[/C][C]26.2725501974939[/C][C]-1.03366376752918[/C][/ROW]
[ROW][C]53[/C][C]9049[/C][C]9569.03474889489[/C][C]-1.13218532463277[/C][C]-518.29346785566[/C][C]-0.793451126625965[/C][/ROW]
[ROW][C]54[/C][C]10190[/C][C]9686.25291786846[/C][C]0.255496739724403[/C][C]501.83588965169[/C][C]0.871673983985699[/C][/ROW]
[ROW][C]55[/C][C]9706[/C][C]9795.08386098808[/C][C]1.49955474935747[/C][C]-90.8455974944308[/C][C]0.80325982935323[/C][/ROW]
[ROW][C]56[/C][C]9765[/C][C]9964.85112974562[/C][C]3.26793916612037[/C][C]-202.595681500923[/C][C]1.24994658683419[/C][/ROW]
[ROW][C]57[/C][C]9893[/C][C]9928.37990968991[/C][C]2.90343374384707[/C][C]-34.7290747071367[/C][C]-0.295993912664426[/C][/ROW]
[ROW][C]58[/C][C]9994[/C][C]9736.8724802249[/C][C]1.3930406672218[/C][C]260.319853988471[/C][C]-1.45005328321816[/C][/ROW]
[ROW][C]59[/C][C]10433[/C][C]9841.17177924749[/C][C]2.07200420221525[/C][C]590.136244890365[/C][C]0.767875715674426[/C][/ROW]
[ROW][C]60[/C][C]10073[/C][C]9924.92590321379[/C][C]2.55416915188507[/C][C]146.731042203624[/C][C]0.609240092225543[/C][/ROW]
[ROW][C]61[/C][C]10112[/C][C]10052.8027370445[/C][C]3.28486615929403[/C][C]57.1397616510376[/C][C]0.933296632597031[/C][/ROW]
[ROW][C]62[/C][C]9266[/C][C]9964.62346956859[/C][C]2.70195651533584[/C][C]-697.126642945911[/C][C]-0.679282808379915[/C][/ROW]
[ROW][C]63[/C][C]9820[/C][C]9805.68085492515[/C][C]1.5148036404318[/C][C]16.9533344473324[/C][C]-1.19659266892572[/C][/ROW]
[ROW][C]64[/C][C]10097[/C][C]9863.91119779651[/C][C]1.99292659556327[/C][C]232.167990292331[/C][C]0.418815651594879[/C][/ROW]
[ROW][C]65[/C][C]9115[/C][C]9841.33941724132[/C][C]1.76440911339012[/C][C]-725.941272815947[/C][C]-0.181297827175938[/C][/ROW]
[ROW][C]66[/C][C]10411[/C][C]9901.66009250841[/C][C]2.33404241141764[/C][C]508.390047295041[/C][C]0.432789884150497[/C][/ROW]
[ROW][C]67[/C][C]9678[/C][C]9895.09495854041[/C][C]2.24839983386813[/C][C]-216.950218273923[/C][C]-0.065942989884464[/C][/ROW]
[ROW][C]68[/C][C]10408[/C][C]10131.5209904236[/C][C]4.36899456875364[/C][C]272.657821178289[/C][C]1.73980299717976[/C][/ROW]
[ROW][C]69[/C][C]10153[/C][C]10180.0064916749[/C][C]4.73050981782183[/C][C]-27.7284212431114[/C][C]0.328406731705262[/C][/ROW]
[ROW][C]70[/C][C]10368[/C][C]10200.9397297415[/C][C]4.84815277078179[/C][C]166.794595084533[/C][C]0.120753615482844[/C][/ROW]
[ROW][C]71[/C][C]10581[/C][C]10156.2681295115[/C][C]4.52773784564386[/C][C]425.544693753418[/C][C]-0.369205392526939[/C][/ROW]
[ROW][C]72[/C][C]10597[/C][C]10266.9814072668[/C][C]5.16424053378995[/C][C]328.27556630577[/C][C]0.791445739642711[/C][/ROW]
[ROW][C]73[/C][C]10680[/C][C]10388.5795537005[/C][C]5.85367871601794[/C][C]289.511168042745[/C][C]0.866899132578154[/C][/ROW]
[ROW][C]74[/C][C]9738[/C][C]10404.4004928388[/C][C]5.91583858105568[/C][C]-666.56360296327[/C][C]0.0740812251511718[/C][/ROW]
[ROW][C]75[/C][C]9556[/C][C]10104.9905137945[/C][C]3.83303815407537[/C][C]-544.006734509468[/C][C]-2.26488583771179[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147770&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147770&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
197009700000
290819420.74876983189-4.57366027258277-334.803448964206-1.94834264125015
390849148.23386410293-22.2230341314185-61.4737147400464-1.35938514876797
497439343.34222928466-8.81354308532632396.8020471873131.35795496412481
585879095.71670401453-19.3897234367873-504.931078054266-1.70069468175497
697319271.8115669484-13.6789574588719455.8742268908631.44996900849938
795639434.34498941604-10.0336633661858125.6103383672761.31903815630069
899989698.057665009-5.32892304644793295.1918418130312.05149160604926
994379674.89483448955-5.62008630303203-237.585415498712-0.133535063101566
10100389807.96170146545-3.34244046637231227.6354054165551.03724496156112
1199189889.11319101532-1.9367840394971127.42455848313150.63142261575917
1292529667.91926929961-5.59596808609243-412.126898276972-1.63792541267238
1397379552.09346520033-3.60321825359209186.870444126881-0.867991128955308
1490359409.60053648043-2.67830097623638-372.142520524378-1.07958030968515
1591339311.86409925472-4.16419357407604-177.360706417732-0.672654981836742
1694879154.70182524022-8.33677975478718334.586912119477-1.05064354962543
1787009193.58165472528-6.97686101606697-494.3051148333820.333390996185739
1896279253.45699318369-5.30634135990324372.4772477922090.487322267446532
1989479171.22183771209-6.84902720301295-222.963862753513-0.570817054401088
2092839097.54333298203-7.92773975652946186.562788810834-0.499534007121835
2188299104.99946190603-7.72014666099224-276.2553742005410.115264994351102
2299479330.40502674057-5.08078861559478612.7092384949021.74691902012461
2396289424.01076845902-4.23387532981186202.3423796679220.739021637104409
2493189518.23584335688-3.76387411801166-201.8833090193670.738226066304609
2596059459.67901215977-3.82824221490463146.242938514042-0.41299927393743
2686409244.05181693482-4.56158951631669-600.51921073796-1.58336341056381
2792149214.62460786303-4.81030747245246-0.222171178363598-0.181363817381967
2895679224.5152588269-4.57409510505649342.2529624686660.105418963881337
2985479155.49210322739-5.80547880389003-607.478854336245-0.463545967786301
3091858982.94086052249-8.98976466669212204.717139594042-1.21612196637376
3194709195.95126348248-5.17620808386451270.4521289368871.64060386180114
3291239183.67815616814-5.27929635280281-60.5618446083347-0.0528713661577582
3392789382.20014572002-2.87336903490704-107.5617572299771.52368500476979
34101709524.09839580382-1.54047710518845643.5063644348691.08334468835021
3594349459.83211001621-1.967145386125-24.7927357315284-0.469412703827005
3696559554.21363594272-1.4918875946930799.18835733355060.721118803353077
3794299426.43988373316-2.041550983637774.65231585190786-0.943920679048537
3887399354.04326894093-2.44752304155232-613.885897199703-0.522581909811403
3995529400.49008229663-2.02056832730934150.7162063960680.359348877235232
4096879364.46769468858-2.42479727891175323.077525490935-0.247868668824745
4190199439.23969303499-1.34123315353324-421.4727502209150.562507597657474
4296729526.3117944858-0.0429565669624922144.2690507285410.64814873561941
4392069354.36766716141-2.44571076081891-145.583941856492-1.27010850628161
4490699291.78693459228-3.18994179233633-221.805171187696-0.447026313045732
4597889527.27200153755-0.715975227978509256.8098278756771.78025952002197
46103129624.424340844410.100075150472991685.964041645120.731000413630024
47101059836.125685143331.50181437147834265.3846158713711.58105415816898
4898639824.445255638421.4286013482271138.7721854398756-0.0984553656677268
4996569747.286541988571.00246121879073-89.9926634288087-0.585819712707743
5092959801.813325327321.34074610908583-507.6902501322240.397301065018393
5199469816.201904895941.44461879246933129.5858603380510.0963073674180238
5297019677.00034974660.071305462293779726.2725501974939-1.03366376752918
5390499569.03474889489-1.13218532463277-518.29346785566-0.793451126625965
54101909686.252917868460.255496739724403501.835889651690.871673983985699
5597069795.083860988081.49955474935747-90.84559749443080.80325982935323
5697659964.851129745623.26793916612037-202.5956815009231.24994658683419
5798939928.379909689912.90343374384707-34.7290747071367-0.295993912664426
5899949736.87248022491.3930406672218260.319853988471-1.45005328321816
59104339841.171779247492.07200420221525590.1362448903650.767875715674426
60100739924.925903213792.55416915188507146.7310422036240.609240092225543
611011210052.80273704453.2848661592940357.13976165103760.933296632597031
6292669964.623469568592.70195651533584-697.126642945911-0.679282808379915
6398209805.680854925151.514803640431816.9533344473324-1.19659266892572
64100979863.911197796511.99292659556327232.1679902923310.418815651594879
6591159841.339417241321.76440911339012-725.941272815947-0.181297827175938
66104119901.660092508412.33404241141764508.3900472950410.432789884150497
6796789895.094958540412.24839983386813-216.950218273923-0.065942989884464
681040810131.52099042364.36899456875364272.6578211782891.73980299717976
691015310180.00649167494.73050981782183-27.72842124311140.328406731705262
701036810200.93972974154.84815277078179166.7945950845330.120753615482844
711058110156.26812951154.52773784564386425.544693753418-0.369205392526939
721059710266.98140726685.16424053378995328.275566305770.791445739642711
731068010388.57955370055.85367871601794289.5111680427450.866899132578154
74973810404.40049283885.91583858105568-666.563602963270.0740812251511718
75955610104.99051379453.83303815407537-544.006734509468-2.26488583771179


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')