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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, 29 Nov 2010 19:38:40 +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/Nov/29/t1291059407d1pmijtbu2tldus.htm/, Retrieved Thu, 09 Oct 2025 03:31:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=103061, Retrieved Thu, 09 Oct 2025 03:31:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact495

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [HPC Retail Sales] [2008-03-02 15:42:48] [74be16979710d4c4e7c6647856088456]
- RMPD  [Structural Time Series Models] [HPC Retail Sales] [2008-03-06 16:52:55] [74be16979710d4c4e7c6647856088456]
- R  D    [Structural Time Series Models] [HPC Retail Sales] [2008-03-08 11:33:35] [74be16979710d4c4e7c6647856088456]
-  M D        [Structural Time Series Models] [] [2010-11-29 19:38:40] [6b31f806e9ccc1f74a26091056f791cb] [Current]
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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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=103061&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=103061&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=103061&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Structural Time Series Model
tObservedLevelSlopeSeasonalStand. Residuals
197009700000
290819420.73826143724-4.57503397341958-334.787519603489-1.94833334163912
390849148.2321179393-22.2237094197417-61.4690304983253-1.35932643409782
497439343.34784279535-8.81409411905787396.7931526789631.35800127903027
585879095.71560122164-19.3900508950312-504.925703792404-1.70072005826550
697319271.81617651786-13.6794107595607455.8658809054161.44999185241013
795639434.35034089968-10.0342463289384125.6016347264531.31902540905375
899989698.06426815202-5.32959008439349295.1800124719982.05147092821893
994379674.89458065279-5.62085046102419-237.584715886029-0.133579165574056
10100389807.96279120464-3.34319558001558227.6316520735301.03724338622322
1199189889.11386429406-1.9375518131796927.42228045278690.631414668717427
1292529667.91369803597-5.59677101946833-412.117084956487-1.63793928486377
1397379552.08919683104-3.60384830364244186.876824343213-0.86796446389266
1490359409.59461289113-2.67899179874603-372.133903984141-1.07956785129385
1591339311.85888699227-4.16496377652654-177.353888196247-0.67263041852816
1694879154.6991129672-8.33751560952523334.592068482095-1.05060412474450
1787009193.57962658768-6.97757667942651-494.3039001225350.333396634245948
1896279253.45705313334-5.30704495076988372.4759768803360.487335939269192
1989479171.22145721854-6.84965694819369-222.962111985044-0.570806365140045
2092839097.54473044052-7.9282844438071186.562558772713-0.499507926303598
2188299105.00140503028-7.72068337088595-276.2576146389810.115271254865714
2299479330.41241252412-5.08131169335917612.6975153914661.74693468698770
2396289424.01713036317-4.23441714346645202.3342302945730.739005531424524
2493189518.23854501278-3.76445656788943-201.8877551728090.738190425668709
2596059459.6764990432-3.82879668964206146.246535934106-0.413027727127945
2686409244.04419693524-4.56210826835633-600.507662320528-1.58337128262167
2792149214.61938780211-4.81080269738311-0.216560409926335-0.181339244605956
2895679224.51118253601-4.57455968023359342.256760585470.105428869742625
2985479155.4886485682-5.80592525102668-607.47431171241-0.463530804487792
3091858982.93759019902-8.99015439781354204.723302297932-1.21609902294576
3194709195.9541349013-5.17658585074512270.4452240179851.64062702511872
3291239183.67746128691-5.27971708127399-60.5609704574843-0.0528942848586842
3392789382.2031240767-2.87382163726794-107.5684708160541.52369097697964
34101709524.10444499342-1.54094165229579643.4976443162761.08335330561814
3594349459.83617457115-1.96760262952293-24.7956415240818-0.469416342075148
3696559554.21997360096-1.4923627528290199.18023145485960.721127399788619
3794299426.43987264545-2.042007229370824.65470651173262-0.943949209605843
3887399354.03907144591-2.44798555611793-613.880376278443-0.522600930760403
3995529400.48683975417-2.02101862661404150.7185611013000.35935310438646
4096879364.4635244278-2.42525722468452323.0822973172-0.247867870689966
4190199439.23652410943-1.34166618786891-421.4709485891590.562508893296961
4296729526.30772242682-0.0434007403760955144.2715823596330.648134938879188
4392069354.36176555553-2.44614244313665-145.574980077923-1.27009877550764
4490699291.78361543161-3.19031980157339-221.800829933417-0.446996838873957
4597889527.2780010181-0.716325423929073256.7993940516021.78030332470969
46103129624.431802729870.0997096557668707685.9547918212560.731002105273374
47101059836.134640422121.50139418927993265.3718235562221.58104225512828
4898639824.45036443631.4281663446815438.7673703806751-0.0984793462368908
4996569747.2863632081.00202236663603-89.9909935668874-0.585846269053593
5092959801.812029757271.34029273272877-507.6898995470020.397289413220854
5199469816.199045036981.44415573243535129.5885069845190.0962975321299138
5297019676.99358770350.070804316682502326.2818444387936-1.03367139621804
5390499569.02885731826-1.13267721713387-518.285700753553-0.793427719629616
54101909686.25186774630.255068536707771501.83476982350.87169897914784
5597069795.081270759881.49910586267001-90.84491072536070.80323867926703
5697659964.8494480683.26747801761584-202.5970159982921.24993666724777
5798939928.379262275842.90299520624118-34.727741819565-0.295978019126401
5899949736.872303587081.39266123286321260.323497899433-1.45002304740247
59104339841.179603832382.07165022719497590.1264369001060.767925760346507
60100739924.933159087422.55379055226267146.7223250991370.609228534708351
611011210052.80742908423.2844438343052057.13286187135520.933264996691682
6292669964.622617162072.70151742228969-697.124074751948-0.679309531053419
6398209805.676379779831.5143546701226816.9607325809287-1.19659604466942
64100979863.907230440621.99248522598743232.1709386550580.418815616005065
6591159841.332519372441.76394392356767-725.933900660862-0.181313146896724
66104119901.655761164662.33360759523426508.3932939959890.432805119386746
6796789895.092123241382.24798389845139-216.947256592625-0.0659276055973027
681040810131.52545359694.36862516981357272.6490646515751.73983212739908
691015310180.00901380924.7301202823308-27.73170501800630.328389718555463
701036810200.94013384704.84774719815622166.7939295901400.120738774353953
711058110156.26949365054.52735315252525425.544193645666-0.369189195693014
721059710266.98737046255.16385994100877328.2676204111630.791469925792096
731068010388.58681284485.85328339486479289.5017995476800.866897317561849
74973810404.40260996195.9154121077354-666.5658201414970.0740447124641135
75955610104.98216424603.83257015297632-543.992788832738-2.26492225140974

\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 & 9420.73826143724 & -4.57503397341958 & -334.787519603489 & -1.94833334163912 \tabularnewline
3 & 9084 & 9148.2321179393 & -22.2237094197417 & -61.4690304983253 & -1.35932643409782 \tabularnewline
4 & 9743 & 9343.34784279535 & -8.81409411905787 & 396.793152678963 & 1.35800127903027 \tabularnewline
5 & 8587 & 9095.71560122164 & -19.3900508950312 & -504.925703792404 & -1.70072005826550 \tabularnewline
6 & 9731 & 9271.81617651786 & -13.6794107595607 & 455.865880905416 & 1.44999185241013 \tabularnewline
7 & 9563 & 9434.35034089968 & -10.0342463289384 & 125.601634726453 & 1.31902540905375 \tabularnewline
8 & 9998 & 9698.06426815202 & -5.32959008439349 & 295.180012471998 & 2.05147092821893 \tabularnewline
9 & 9437 & 9674.89458065279 & -5.62085046102419 & -237.584715886029 & -0.133579165574056 \tabularnewline
10 & 10038 & 9807.96279120464 & -3.34319558001558 & 227.631652073530 & 1.03724338622322 \tabularnewline
11 & 9918 & 9889.11386429406 & -1.93755181317969 & 27.4222804527869 & 0.631414668717427 \tabularnewline
12 & 9252 & 9667.91369803597 & -5.59677101946833 & -412.117084956487 & -1.63793928486377 \tabularnewline
13 & 9737 & 9552.08919683104 & -3.60384830364244 & 186.876824343213 & -0.86796446389266 \tabularnewline
14 & 9035 & 9409.59461289113 & -2.67899179874603 & -372.133903984141 & -1.07956785129385 \tabularnewline
15 & 9133 & 9311.85888699227 & -4.16496377652654 & -177.353888196247 & -0.67263041852816 \tabularnewline
16 & 9487 & 9154.6991129672 & -8.33751560952523 & 334.592068482095 & -1.05060412474450 \tabularnewline
17 & 8700 & 9193.57962658768 & -6.97757667942651 & -494.303900122535 & 0.333396634245948 \tabularnewline
18 & 9627 & 9253.45705313334 & -5.30704495076988 & 372.475976880336 & 0.487335939269192 \tabularnewline
19 & 8947 & 9171.22145721854 & -6.84965694819369 & -222.962111985044 & -0.570806365140045 \tabularnewline
20 & 9283 & 9097.54473044052 & -7.9282844438071 & 186.562558772713 & -0.499507926303598 \tabularnewline
21 & 8829 & 9105.00140503028 & -7.72068337088595 & -276.257614638981 & 0.115271254865714 \tabularnewline
22 & 9947 & 9330.41241252412 & -5.08131169335917 & 612.697515391466 & 1.74693468698770 \tabularnewline
23 & 9628 & 9424.01713036317 & -4.23441714346645 & 202.334230294573 & 0.739005531424524 \tabularnewline
24 & 9318 & 9518.23854501278 & -3.76445656788943 & -201.887755172809 & 0.738190425668709 \tabularnewline
25 & 9605 & 9459.6764990432 & -3.82879668964206 & 146.246535934106 & -0.413027727127945 \tabularnewline
26 & 8640 & 9244.04419693524 & -4.56210826835633 & -600.507662320528 & -1.58337128262167 \tabularnewline
27 & 9214 & 9214.61938780211 & -4.81080269738311 & -0.216560409926335 & -0.181339244605956 \tabularnewline
28 & 9567 & 9224.51118253601 & -4.57455968023359 & 342.25676058547 & 0.105428869742625 \tabularnewline
29 & 8547 & 9155.4886485682 & -5.80592525102668 & -607.47431171241 & -0.463530804487792 \tabularnewline
30 & 9185 & 8982.93759019902 & -8.99015439781354 & 204.723302297932 & -1.21609902294576 \tabularnewline
31 & 9470 & 9195.9541349013 & -5.17658585074512 & 270.445224017985 & 1.64062702511872 \tabularnewline
32 & 9123 & 9183.67746128691 & -5.27971708127399 & -60.5609704574843 & -0.0528942848586842 \tabularnewline
33 & 9278 & 9382.2031240767 & -2.87382163726794 & -107.568470816054 & 1.52369097697964 \tabularnewline
34 & 10170 & 9524.10444499342 & -1.54094165229579 & 643.497644316276 & 1.08335330561814 \tabularnewline
35 & 9434 & 9459.83617457115 & -1.96760262952293 & -24.7956415240818 & -0.469416342075148 \tabularnewline
36 & 9655 & 9554.21997360096 & -1.49236275282901 & 99.1802314548596 & 0.721127399788619 \tabularnewline
37 & 9429 & 9426.43987264545 & -2.04200722937082 & 4.65470651173262 & -0.943949209605843 \tabularnewline
38 & 8739 & 9354.03907144591 & -2.44798555611793 & -613.880376278443 & -0.522600930760403 \tabularnewline
39 & 9552 & 9400.48683975417 & -2.02101862661404 & 150.718561101300 & 0.35935310438646 \tabularnewline
40 & 9687 & 9364.4635244278 & -2.42525722468452 & 323.0822973172 & -0.247867870689966 \tabularnewline
41 & 9019 & 9439.23652410943 & -1.34166618786891 & -421.470948589159 & 0.562508893296961 \tabularnewline
42 & 9672 & 9526.30772242682 & -0.0434007403760955 & 144.271582359633 & 0.648134938879188 \tabularnewline
43 & 9206 & 9354.36176555553 & -2.44614244313665 & -145.574980077923 & -1.27009877550764 \tabularnewline
44 & 9069 & 9291.78361543161 & -3.19031980157339 & -221.800829933417 & -0.446996838873957 \tabularnewline
45 & 9788 & 9527.2780010181 & -0.716325423929073 & 256.799394051602 & 1.78030332470969 \tabularnewline
46 & 10312 & 9624.43180272987 & 0.0997096557668707 & 685.954791821256 & 0.731002105273374 \tabularnewline
47 & 10105 & 9836.13464042212 & 1.50139418927993 & 265.371823556222 & 1.58104225512828 \tabularnewline
48 & 9863 & 9824.4503644363 & 1.42816634468154 & 38.7673703806751 & -0.0984793462368908 \tabularnewline
49 & 9656 & 9747.286363208 & 1.00202236663603 & -89.9909935668874 & -0.585846269053593 \tabularnewline
50 & 9295 & 9801.81202975727 & 1.34029273272877 & -507.689899547002 & 0.397289413220854 \tabularnewline
51 & 9946 & 9816.19904503698 & 1.44415573243535 & 129.588506984519 & 0.0962975321299138 \tabularnewline
52 & 9701 & 9676.9935877035 & 0.0708043166825023 & 26.2818444387936 & -1.03367139621804 \tabularnewline
53 & 9049 & 9569.02885731826 & -1.13267721713387 & -518.285700753553 & -0.793427719629616 \tabularnewline
54 & 10190 & 9686.2518677463 & 0.255068536707771 & 501.8347698235 & 0.87169897914784 \tabularnewline
55 & 9706 & 9795.08127075988 & 1.49910586267001 & -90.8449107253607 & 0.80323867926703 \tabularnewline
56 & 9765 & 9964.849448068 & 3.26747801761584 & -202.597015998292 & 1.24993666724777 \tabularnewline
57 & 9893 & 9928.37926227584 & 2.90299520624118 & -34.727741819565 & -0.295978019126401 \tabularnewline
58 & 9994 & 9736.87230358708 & 1.39266123286321 & 260.323497899433 & -1.45002304740247 \tabularnewline
59 & 10433 & 9841.17960383238 & 2.07165022719497 & 590.126436900106 & 0.767925760346507 \tabularnewline
60 & 10073 & 9924.93315908742 & 2.55379055226267 & 146.722325099137 & 0.609228534708351 \tabularnewline
61 & 10112 & 10052.8074290842 & 3.28444383430520 & 57.1328618713552 & 0.933264996691682 \tabularnewline
62 & 9266 & 9964.62261716207 & 2.70151742228969 & -697.124074751948 & -0.679309531053419 \tabularnewline
63 & 9820 & 9805.67637977983 & 1.51435467012268 & 16.9607325809287 & -1.19659604466942 \tabularnewline
64 & 10097 & 9863.90723044062 & 1.99248522598743 & 232.170938655058 & 0.418815616005065 \tabularnewline
65 & 9115 & 9841.33251937244 & 1.76394392356767 & -725.933900660862 & -0.181313146896724 \tabularnewline
66 & 10411 & 9901.65576116466 & 2.33360759523426 & 508.393293995989 & 0.432805119386746 \tabularnewline
67 & 9678 & 9895.09212324138 & 2.24798389845139 & -216.947256592625 & -0.0659276055973027 \tabularnewline
68 & 10408 & 10131.5254535969 & 4.36862516981357 & 272.649064651575 & 1.73983212739908 \tabularnewline
69 & 10153 & 10180.0090138092 & 4.7301202823308 & -27.7317050180063 & 0.328389718555463 \tabularnewline
70 & 10368 & 10200.9401338470 & 4.84774719815622 & 166.793929590140 & 0.120738774353953 \tabularnewline
71 & 10581 & 10156.2694936505 & 4.52735315252525 & 425.544193645666 & -0.369189195693014 \tabularnewline
72 & 10597 & 10266.9873704625 & 5.16385994100877 & 328.267620411163 & 0.791469925792096 \tabularnewline
73 & 10680 & 10388.5868128448 & 5.85328339486479 & 289.501799547680 & 0.866897317561849 \tabularnewline
74 & 9738 & 10404.4026099619 & 5.9154121077354 & -666.565820141497 & 0.0740447124641135 \tabularnewline
75 & 9556 & 10104.9821642460 & 3.83257015297632 & -543.992788832738 & -2.26492225140974 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=103061&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]9420.73826143724[/C][C]-4.57503397341958[/C][C]-334.787519603489[/C][C]-1.94833334163912[/C][/ROW]
[ROW][C]3[/C][C]9084[/C][C]9148.2321179393[/C][C]-22.2237094197417[/C][C]-61.4690304983253[/C][C]-1.35932643409782[/C][/ROW]
[ROW][C]4[/C][C]9743[/C][C]9343.34784279535[/C][C]-8.81409411905787[/C][C]396.793152678963[/C][C]1.35800127903027[/C][/ROW]
[ROW][C]5[/C][C]8587[/C][C]9095.71560122164[/C][C]-19.3900508950312[/C][C]-504.925703792404[/C][C]-1.70072005826550[/C][/ROW]
[ROW][C]6[/C][C]9731[/C][C]9271.81617651786[/C][C]-13.6794107595607[/C][C]455.865880905416[/C][C]1.44999185241013[/C][/ROW]
[ROW][C]7[/C][C]9563[/C][C]9434.35034089968[/C][C]-10.0342463289384[/C][C]125.601634726453[/C][C]1.31902540905375[/C][/ROW]
[ROW][C]8[/C][C]9998[/C][C]9698.06426815202[/C][C]-5.32959008439349[/C][C]295.180012471998[/C][C]2.05147092821893[/C][/ROW]
[ROW][C]9[/C][C]9437[/C][C]9674.89458065279[/C][C]-5.62085046102419[/C][C]-237.584715886029[/C][C]-0.133579165574056[/C][/ROW]
[ROW][C]10[/C][C]10038[/C][C]9807.96279120464[/C][C]-3.34319558001558[/C][C]227.631652073530[/C][C]1.03724338622322[/C][/ROW]
[ROW][C]11[/C][C]9918[/C][C]9889.11386429406[/C][C]-1.93755181317969[/C][C]27.4222804527869[/C][C]0.631414668717427[/C][/ROW]
[ROW][C]12[/C][C]9252[/C][C]9667.91369803597[/C][C]-5.59677101946833[/C][C]-412.117084956487[/C][C]-1.63793928486377[/C][/ROW]
[ROW][C]13[/C][C]9737[/C][C]9552.08919683104[/C][C]-3.60384830364244[/C][C]186.876824343213[/C][C]-0.86796446389266[/C][/ROW]
[ROW][C]14[/C][C]9035[/C][C]9409.59461289113[/C][C]-2.67899179874603[/C][C]-372.133903984141[/C][C]-1.07956785129385[/C][/ROW]
[ROW][C]15[/C][C]9133[/C][C]9311.85888699227[/C][C]-4.16496377652654[/C][C]-177.353888196247[/C][C]-0.67263041852816[/C][/ROW]
[ROW][C]16[/C][C]9487[/C][C]9154.6991129672[/C][C]-8.33751560952523[/C][C]334.592068482095[/C][C]-1.05060412474450[/C][/ROW]
[ROW][C]17[/C][C]8700[/C][C]9193.57962658768[/C][C]-6.97757667942651[/C][C]-494.303900122535[/C][C]0.333396634245948[/C][/ROW]
[ROW][C]18[/C][C]9627[/C][C]9253.45705313334[/C][C]-5.30704495076988[/C][C]372.475976880336[/C][C]0.487335939269192[/C][/ROW]
[ROW][C]19[/C][C]8947[/C][C]9171.22145721854[/C][C]-6.84965694819369[/C][C]-222.962111985044[/C][C]-0.570806365140045[/C][/ROW]
[ROW][C]20[/C][C]9283[/C][C]9097.54473044052[/C][C]-7.9282844438071[/C][C]186.562558772713[/C][C]-0.499507926303598[/C][/ROW]
[ROW][C]21[/C][C]8829[/C][C]9105.00140503028[/C][C]-7.72068337088595[/C][C]-276.257614638981[/C][C]0.115271254865714[/C][/ROW]
[ROW][C]22[/C][C]9947[/C][C]9330.41241252412[/C][C]-5.08131169335917[/C][C]612.697515391466[/C][C]1.74693468698770[/C][/ROW]
[ROW][C]23[/C][C]9628[/C][C]9424.01713036317[/C][C]-4.23441714346645[/C][C]202.334230294573[/C][C]0.739005531424524[/C][/ROW]
[ROW][C]24[/C][C]9318[/C][C]9518.23854501278[/C][C]-3.76445656788943[/C][C]-201.887755172809[/C][C]0.738190425668709[/C][/ROW]
[ROW][C]25[/C][C]9605[/C][C]9459.6764990432[/C][C]-3.82879668964206[/C][C]146.246535934106[/C][C]-0.413027727127945[/C][/ROW]
[ROW][C]26[/C][C]8640[/C][C]9244.04419693524[/C][C]-4.56210826835633[/C][C]-600.507662320528[/C][C]-1.58337128262167[/C][/ROW]
[ROW][C]27[/C][C]9214[/C][C]9214.61938780211[/C][C]-4.81080269738311[/C][C]-0.216560409926335[/C][C]-0.181339244605956[/C][/ROW]
[ROW][C]28[/C][C]9567[/C][C]9224.51118253601[/C][C]-4.57455968023359[/C][C]342.25676058547[/C][C]0.105428869742625[/C][/ROW]
[ROW][C]29[/C][C]8547[/C][C]9155.4886485682[/C][C]-5.80592525102668[/C][C]-607.47431171241[/C][C]-0.463530804487792[/C][/ROW]
[ROW][C]30[/C][C]9185[/C][C]8982.93759019902[/C][C]-8.99015439781354[/C][C]204.723302297932[/C][C]-1.21609902294576[/C][/ROW]
[ROW][C]31[/C][C]9470[/C][C]9195.9541349013[/C][C]-5.17658585074512[/C][C]270.445224017985[/C][C]1.64062702511872[/C][/ROW]
[ROW][C]32[/C][C]9123[/C][C]9183.67746128691[/C][C]-5.27971708127399[/C][C]-60.5609704574843[/C][C]-0.0528942848586842[/C][/ROW]
[ROW][C]33[/C][C]9278[/C][C]9382.2031240767[/C][C]-2.87382163726794[/C][C]-107.568470816054[/C][C]1.52369097697964[/C][/ROW]
[ROW][C]34[/C][C]10170[/C][C]9524.10444499342[/C][C]-1.54094165229579[/C][C]643.497644316276[/C][C]1.08335330561814[/C][/ROW]
[ROW][C]35[/C][C]9434[/C][C]9459.83617457115[/C][C]-1.96760262952293[/C][C]-24.7956415240818[/C][C]-0.469416342075148[/C][/ROW]
[ROW][C]36[/C][C]9655[/C][C]9554.21997360096[/C][C]-1.49236275282901[/C][C]99.1802314548596[/C][C]0.721127399788619[/C][/ROW]
[ROW][C]37[/C][C]9429[/C][C]9426.43987264545[/C][C]-2.04200722937082[/C][C]4.65470651173262[/C][C]-0.943949209605843[/C][/ROW]
[ROW][C]38[/C][C]8739[/C][C]9354.03907144591[/C][C]-2.44798555611793[/C][C]-613.880376278443[/C][C]-0.522600930760403[/C][/ROW]
[ROW][C]39[/C][C]9552[/C][C]9400.48683975417[/C][C]-2.02101862661404[/C][C]150.718561101300[/C][C]0.35935310438646[/C][/ROW]
[ROW][C]40[/C][C]9687[/C][C]9364.4635244278[/C][C]-2.42525722468452[/C][C]323.0822973172[/C][C]-0.247867870689966[/C][/ROW]
[ROW][C]41[/C][C]9019[/C][C]9439.23652410943[/C][C]-1.34166618786891[/C][C]-421.470948589159[/C][C]0.562508893296961[/C][/ROW]
[ROW][C]42[/C][C]9672[/C][C]9526.30772242682[/C][C]-0.0434007403760955[/C][C]144.271582359633[/C][C]0.648134938879188[/C][/ROW]
[ROW][C]43[/C][C]9206[/C][C]9354.36176555553[/C][C]-2.44614244313665[/C][C]-145.574980077923[/C][C]-1.27009877550764[/C][/ROW]
[ROW][C]44[/C][C]9069[/C][C]9291.78361543161[/C][C]-3.19031980157339[/C][C]-221.800829933417[/C][C]-0.446996838873957[/C][/ROW]
[ROW][C]45[/C][C]9788[/C][C]9527.2780010181[/C][C]-0.716325423929073[/C][C]256.799394051602[/C][C]1.78030332470969[/C][/ROW]
[ROW][C]46[/C][C]10312[/C][C]9624.43180272987[/C][C]0.0997096557668707[/C][C]685.954791821256[/C][C]0.731002105273374[/C][/ROW]
[ROW][C]47[/C][C]10105[/C][C]9836.13464042212[/C][C]1.50139418927993[/C][C]265.371823556222[/C][C]1.58104225512828[/C][/ROW]
[ROW][C]48[/C][C]9863[/C][C]9824.4503644363[/C][C]1.42816634468154[/C][C]38.7673703806751[/C][C]-0.0984793462368908[/C][/ROW]
[ROW][C]49[/C][C]9656[/C][C]9747.286363208[/C][C]1.00202236663603[/C][C]-89.9909935668874[/C][C]-0.585846269053593[/C][/ROW]
[ROW][C]50[/C][C]9295[/C][C]9801.81202975727[/C][C]1.34029273272877[/C][C]-507.689899547002[/C][C]0.397289413220854[/C][/ROW]
[ROW][C]51[/C][C]9946[/C][C]9816.19904503698[/C][C]1.44415573243535[/C][C]129.588506984519[/C][C]0.0962975321299138[/C][/ROW]
[ROW][C]52[/C][C]9701[/C][C]9676.9935877035[/C][C]0.0708043166825023[/C][C]26.2818444387936[/C][C]-1.03367139621804[/C][/ROW]
[ROW][C]53[/C][C]9049[/C][C]9569.02885731826[/C][C]-1.13267721713387[/C][C]-518.285700753553[/C][C]-0.793427719629616[/C][/ROW]
[ROW][C]54[/C][C]10190[/C][C]9686.2518677463[/C][C]0.255068536707771[/C][C]501.8347698235[/C][C]0.87169897914784[/C][/ROW]
[ROW][C]55[/C][C]9706[/C][C]9795.08127075988[/C][C]1.49910586267001[/C][C]-90.8449107253607[/C][C]0.80323867926703[/C][/ROW]
[ROW][C]56[/C][C]9765[/C][C]9964.849448068[/C][C]3.26747801761584[/C][C]-202.597015998292[/C][C]1.24993666724777[/C][/ROW]
[ROW][C]57[/C][C]9893[/C][C]9928.37926227584[/C][C]2.90299520624118[/C][C]-34.727741819565[/C][C]-0.295978019126401[/C][/ROW]
[ROW][C]58[/C][C]9994[/C][C]9736.87230358708[/C][C]1.39266123286321[/C][C]260.323497899433[/C][C]-1.45002304740247[/C][/ROW]
[ROW][C]59[/C][C]10433[/C][C]9841.17960383238[/C][C]2.07165022719497[/C][C]590.126436900106[/C][C]0.767925760346507[/C][/ROW]
[ROW][C]60[/C][C]10073[/C][C]9924.93315908742[/C][C]2.55379055226267[/C][C]146.722325099137[/C][C]0.609228534708351[/C][/ROW]
[ROW][C]61[/C][C]10112[/C][C]10052.8074290842[/C][C]3.28444383430520[/C][C]57.1328618713552[/C][C]0.933264996691682[/C][/ROW]
[ROW][C]62[/C][C]9266[/C][C]9964.62261716207[/C][C]2.70151742228969[/C][C]-697.124074751948[/C][C]-0.679309531053419[/C][/ROW]
[ROW][C]63[/C][C]9820[/C][C]9805.67637977983[/C][C]1.51435467012268[/C][C]16.9607325809287[/C][C]-1.19659604466942[/C][/ROW]
[ROW][C]64[/C][C]10097[/C][C]9863.90723044062[/C][C]1.99248522598743[/C][C]232.170938655058[/C][C]0.418815616005065[/C][/ROW]
[ROW][C]65[/C][C]9115[/C][C]9841.33251937244[/C][C]1.76394392356767[/C][C]-725.933900660862[/C][C]-0.181313146896724[/C][/ROW]
[ROW][C]66[/C][C]10411[/C][C]9901.65576116466[/C][C]2.33360759523426[/C][C]508.393293995989[/C][C]0.432805119386746[/C][/ROW]
[ROW][C]67[/C][C]9678[/C][C]9895.09212324138[/C][C]2.24798389845139[/C][C]-216.947256592625[/C][C]-0.0659276055973027[/C][/ROW]
[ROW][C]68[/C][C]10408[/C][C]10131.5254535969[/C][C]4.36862516981357[/C][C]272.649064651575[/C][C]1.73983212739908[/C][/ROW]
[ROW][C]69[/C][C]10153[/C][C]10180.0090138092[/C][C]4.7301202823308[/C][C]-27.7317050180063[/C][C]0.328389718555463[/C][/ROW]
[ROW][C]70[/C][C]10368[/C][C]10200.9401338470[/C][C]4.84774719815622[/C][C]166.793929590140[/C][C]0.120738774353953[/C][/ROW]
[ROW][C]71[/C][C]10581[/C][C]10156.2694936505[/C][C]4.52735315252525[/C][C]425.544193645666[/C][C]-0.369189195693014[/C][/ROW]
[ROW][C]72[/C][C]10597[/C][C]10266.9873704625[/C][C]5.16385994100877[/C][C]328.267620411163[/C][C]0.791469925792096[/C][/ROW]
[ROW][C]73[/C][C]10680[/C][C]10388.5868128448[/C][C]5.85328339486479[/C][C]289.501799547680[/C][C]0.866897317561849[/C][/ROW]
[ROW][C]74[/C][C]9738[/C][C]10404.4026099619[/C][C]5.9154121077354[/C][C]-666.565820141497[/C][C]0.0740447124641135[/C][/ROW]
[ROW][C]75[/C][C]9556[/C][C]10104.9821642460[/C][C]3.83257015297632[/C][C]-543.992788832738[/C][C]-2.26492225140974[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=103061&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=103061&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
290819420.73826143724-4.57503397341958-334.787519603489-1.94833334163912
390849148.2321179393-22.2237094197417-61.4690304983253-1.35932643409782
497439343.34784279535-8.81409411905787396.7931526789631.35800127903027
585879095.71560122164-19.3900508950312-504.925703792404-1.70072005826550
697319271.81617651786-13.6794107595607455.8658809054161.44999185241013
795639434.35034089968-10.0342463289384125.6016347264531.31902540905375
899989698.06426815202-5.32959008439349295.1800124719982.05147092821893
994379674.89458065279-5.62085046102419-237.584715886029-0.133579165574056
10100389807.96279120464-3.34319558001558227.6316520735301.03724338622322
1199189889.11386429406-1.9375518131796927.42228045278690.631414668717427
1292529667.91369803597-5.59677101946833-412.117084956487-1.63793928486377
1397379552.08919683104-3.60384830364244186.876824343213-0.86796446389266
1490359409.59461289113-2.67899179874603-372.133903984141-1.07956785129385
1591339311.85888699227-4.16496377652654-177.353888196247-0.67263041852816
1694879154.6991129672-8.33751560952523334.592068482095-1.05060412474450
1787009193.57962658768-6.97757667942651-494.3039001225350.333396634245948
1896279253.45705313334-5.30704495076988372.4759768803360.487335939269192
1989479171.22145721854-6.84965694819369-222.962111985044-0.570806365140045
2092839097.54473044052-7.9282844438071186.562558772713-0.499507926303598
2188299105.00140503028-7.72068337088595-276.2576146389810.115271254865714
2299479330.41241252412-5.08131169335917612.6975153914661.74693468698770
2396289424.01713036317-4.23441714346645202.3342302945730.739005531424524
2493189518.23854501278-3.76445656788943-201.8877551728090.738190425668709
2596059459.6764990432-3.82879668964206146.246535934106-0.413027727127945
2686409244.04419693524-4.56210826835633-600.507662320528-1.58337128262167
2792149214.61938780211-4.81080269738311-0.216560409926335-0.181339244605956
2895679224.51118253601-4.57455968023359342.256760585470.105428869742625
2985479155.4886485682-5.80592525102668-607.47431171241-0.463530804487792
3091858982.93759019902-8.99015439781354204.723302297932-1.21609902294576
3194709195.9541349013-5.17658585074512270.4452240179851.64062702511872
3291239183.67746128691-5.27971708127399-60.5609704574843-0.0528942848586842
3392789382.2031240767-2.87382163726794-107.5684708160541.52369097697964
34101709524.10444499342-1.54094165229579643.4976443162761.08335330561814
3594349459.83617457115-1.96760262952293-24.7956415240818-0.469416342075148
3696559554.21997360096-1.4923627528290199.18023145485960.721127399788619
3794299426.43987264545-2.042007229370824.65470651173262-0.943949209605843
3887399354.03907144591-2.44798555611793-613.880376278443-0.522600930760403
3995529400.48683975417-2.02101862661404150.7185611013000.35935310438646
4096879364.4635244278-2.42525722468452323.0822973172-0.247867870689966
4190199439.23652410943-1.34166618786891-421.4709485891590.562508893296961
4296729526.30772242682-0.0434007403760955144.2715823596330.648134938879188
4392069354.36176555553-2.44614244313665-145.574980077923-1.27009877550764
4490699291.78361543161-3.19031980157339-221.800829933417-0.446996838873957
4597889527.2780010181-0.716325423929073256.7993940516021.78030332470969
46103129624.431802729870.0997096557668707685.9547918212560.731002105273374
47101059836.134640422121.50139418927993265.3718235562221.58104225512828
4898639824.45036443631.4281663446815438.7673703806751-0.0984793462368908
4996569747.2863632081.00202236663603-89.9909935668874-0.585846269053593
5092959801.812029757271.34029273272877-507.6898995470020.397289413220854
5199469816.199045036981.44415573243535129.5885069845190.0962975321299138
5297019676.99358770350.070804316682502326.2818444387936-1.03367139621804
5390499569.02885731826-1.13267721713387-518.285700753553-0.793427719629616
54101909686.25186774630.255068536707771501.83476982350.87169897914784
5597069795.081270759881.49910586267001-90.84491072536070.80323867926703
5697659964.8494480683.26747801761584-202.5970159982921.24993666724777
5798939928.379262275842.90299520624118-34.727741819565-0.295978019126401
5899949736.872303587081.39266123286321260.323497899433-1.45002304740247
59104339841.179603832382.07165022719497590.1264369001060.767925760346507
60100739924.933159087422.55379055226267146.7223250991370.609228534708351
611011210052.80742908423.2844438343052057.13286187135520.933264996691682
6292669964.622617162072.70151742228969-697.124074751948-0.679309531053419
6398209805.676379779831.5143546701226816.9607325809287-1.19659604466942
64100979863.907230440621.99248522598743232.1709386550580.418815616005065
6591159841.332519372441.76394392356767-725.933900660862-0.181313146896724
66104119901.655761164662.33360759523426508.3932939959890.432805119386746
6796789895.092123241382.24798389845139-216.947256592625-0.0659276055973027
681040810131.52545359694.36862516981357272.6490646515751.73983212739908
691015310180.00901380924.7301202823308-27.73170501800630.328389718555463
701036810200.94013384704.84774719815622166.7939295901400.120738774353953
711058110156.26949365054.52735315252525425.544193645666-0.369189195693014
721059710266.98737046255.16385994100877328.2676204111630.791469925792096
731068010388.58681284485.85328339486479289.5017995476800.866897317561849
74973810404.40260996195.9154121077354-666.5658201414970.0740447124641135
75955610104.98216424603.83257015297632-543.992788832738-2.26492225140974


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$resid)
myfit <- mylevel+myseas
bitmap(file='test1.png')
plot(as.numeric(m$resid),main='Standardized Residuals',ylab='Residuals',xlab='time')
grid()
dev.off()
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='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')