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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 computationFri, 25 Nov 2011 09:44:26 -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/25/t1322232385ejoedxt5ea0mmil.htm/, Retrieved Fri, 02 Jun 2023 09:40:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=147323, Retrieved Fri, 02 Jun 2023 09:40:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact90

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]
- RM D        [Structural Time Series Models] [WS8] [2011-11-25 14:44:26] [7a9891c1925ad1e8ddfe52b8c5887b5b] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
68897
38683
44720
39525
45315
50380
40600
36279
42438
38064
31879
11379
70249
39253
47060
41697
38708
49267
39018
32228
40870
39383
34571
12066
70938
34077
45409
40809
37013
44953
37848
32745
39401
34931
33008
8620
68906
39556
50669
36432
40891
48428
36222
33425
39401
37967
34801
12657
69116
41519
51321
38529
41547
52073
38401
40898
40439
41888
37898
8771
68184
50530
47221
41756
45633
48138
39486
39341
41117
41629
29722
7054
56676
34870
35117
30169
30936
35699
33228
27733
33666
35429
27438
8170

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' @ yule.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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147323&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' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147323&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147323&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' @ yule.wessa.net






Structural Time Series Model
tObservedLevelSlopeSeasonalStand. Residuals
16889768897000
23868346220.024705057-1041.16528899006-7537.024705057-3.90585273555604
34472042974.6491048626-1154.486494106171745.35089513737-0.460469734365187
43952540880.6823010863-1184.14883489966-1355.68230108627-0.230350559527975
54531543436.6426156671-1112.990652518821878.357384332870.936217528267848
65038048260.3170777132-1018.017997133792119.68292228681.48395393566453
74060045041.4958071015-1055.69635192669-4441.49580710146-0.548793408631984
83627939770.4180547933-1136.00064815917-3491.41805479327-1.04897288853221
94243840758.5526376441-1091.991851589991679.447362355930.527713818330193
103806439738.6321387395-1090.40166758102-1674.63213873950.0178806274781367
113187935371.1508924434-1166.53680517257-3492.15089244337-0.811996060198095
121137921050.2743452747-1486.44290600067-9671.27434527474-3.25536398285996
137024935363.0531598219-1624.073975222234885.94684017814.23373201286705
143925342236.1815394034-1447.55171181498-2983.181539403352.08248194116293
154706045047.4372612872-1287.798449284922012.562738712780.97174802995881
164169745707.2237435084-1213.41443358458-4010.223743508360.462538951120114
173870842346.3542835281-1285.51003284955-3638.35428352814-0.524667808746566
184926743824.0159709013-1202.200941437485442.984029098680.6784099782396
193901843008.3094713851-1190.9439885153-3990.309471385140.0947877107682116
203222839432.0337776318-1261.55176022795-7204.03377763176-0.584204446969156
214087038432.8827936403-1253.527572294562437.117206359730.064201137373208
223938337892.7057789803-1231.226250626941490.294221019750.174365287526989
233457135216.1245323056-1275.6588277677-645.124532305584-0.352627536527848
241206631249.6913392591-1351.58897511951-19183.6913392591-0.656708011790571
257093835296.7960797119-1215.7950861387135641.20392028811.33923181300638
263407737673.983032593-1105.04791665343-3596.983032592970.87494033083517
274540941317.0885167782-928.3364912769154091.911483221831.12109338955825
284080943248.7078558542-815.519566909012-2439.70785585420.678920177130717
293701342624.9506686401-808.113443299924-5611.950668640070.0462589549281739
304495340613.5628352074-852.7234289030964339.4371647926-0.292206284320128
313784840230.3155590609-835.77684558935-2382.315559060850.114050568494819
323274539809.4324916529-820.913177695299-7064.432491652930.100697843598049
333940137823.4523995741-862.7024822028291577.54760042588-0.282498440405328
343493134176.9693422626-962.221113483782754.030657737389-0.67409357181314
353300832666.0671112807-981.517935161443341.932888719294-0.132699186747811
36862031032.0921793746-1003.93296196442-22412.0921793746-0.158125121447522
376890632984.1041546611-902.39924123700535921.89584533890.719730993139648
383955639983.8622840992-616.068457979114-427.8622840992391.90998487606706
395066945157.9252992211-392.7250494152035511.074700778921.38083715367614
403643242311.7251092892-490.477291728709-5879.72510928925-0.58464739455055
414089144006.6559123779-403.283905162012-3115.655912377920.524937476662095
424842844399.9999456239-371.9335800923254028.000054376120.192418616530821
433622241161.6356071285-483.10780029676-4939.63560712848-0.693103990926147
443342539642.9285711514-522.882848154507-6217.92857115141-0.250173276491603
453940137375.9762513072-589.4355102819632025.02374869281-0.42073470118426
463796736463.2849632308-601.68612827721503.71503676919-0.0778782575926734
473480135068.5384965148-631.49031242686-267.538496514813-0.191025121616656
481265736021.8224693757-572.248445989284-23364.82246937570.382548616556821
496911636770.322323167-522.56495364244832345.6776768330.319438424150413
504151940859.2242336029-345.474246787035659.7757663970571.11108776071277
515132143622.2992049083-223.199619823817698.70079509170.743915782875368
523852944983.3904071258-159.91861424094-6454.390407125770.378591786000154
534154744967.2466647145-154.155198682632-3420.24666471450.0344979890369746
545207345831.5067491934-113.5108754962756241.49325080660.245352072378347
553840144139.1461993073-176.065649599875-5738.14619930725-0.380818851517686
564089844978.8527052718-136.098519626914-4080.852705271770.244777851170619
574043941233.4445496084-277.273460878826-794.444549608444-0.868394564012734
584188840055.3546321345-312.323989636821832.64536786545-0.21649620157021
593789839270.7630902289-330.624603485718-1372.76309022885-0.113541018391587
60877135841.2878441499-450.586876256947-27070.2878441499-0.746398566269161
616818436672.1058114119-400.76892678869431511.89418858810.308984964598216
625053044815.7238326438-65.5291624465755714.27616735622.0557424394921
634722143337.8645288225-121.5111718443063883.13547117747-0.338493028941166
644175645917.021262385-13.6939538109498-4161.021262384990.64648431777277
654563348172.093392062277.102738976144-2539.093392062160.544308465559436
664813844700.7802110025-64.7025715076413437.21978899751-0.853697479158119
673948644509.820197455-69.7304479640724-5023.82019745495-0.0304067937665069
683934142869.9921036289-131.998833985873-3528.99210362888-0.377827014177128
694111741722.6097331917-172.110976628629-605.609733191652-0.243985648634321
704162940069.8850523399-230.4109154897111559.11494766012-0.355468686169117
712972234269.6274269138-449.272120784821-4547.62742691381-1.33788774628906
72705434282.7658818765-431.103640584311-27228.76588187650.111236593639713
735667631240.3302365759-533.9517273044325435.6697634241-0.628644883609773
743487029449.5748206831-583.6653338440145420.42517931691-0.302148694753612
753511730850.6999319558-504.7907642119674266.300068044160.476036930077661
763016933086.3045064283-395.521583019731-2917.304506428310.656670548336699
773093632536.3263287067-401.688690045216-1600.3263287067-0.0370595160412192
783569932036.171382424-405.6183396612923662.82861757599-0.0236704764917075
793322834772.3506189983-280.445915775804-1544.350618998350.755864327693937
802773332637.8584195127-354.147441326347-4904.85841951266-0.445772940390027
813366632335.3404874431-352.0997364630041330.659512556910.0123985586181123
823542931615.3919659671-366.6617474677483813.6080340329-0.0882791224562238
832743831487.8742381075-357.205045897558-4049.874238107470.0574182711240023
84817032772.50420025-292.276509332724-24602.504200250.394648646693754

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 68897 & 68897 & 0 & 0 & 0 \tabularnewline
2 & 38683 & 46220.024705057 & -1041.16528899006 & -7537.024705057 & -3.90585273555604 \tabularnewline
3 & 44720 & 42974.6491048626 & -1154.48649410617 & 1745.35089513737 & -0.460469734365187 \tabularnewline
4 & 39525 & 40880.6823010863 & -1184.14883489966 & -1355.68230108627 & -0.230350559527975 \tabularnewline
5 & 45315 & 43436.6426156671 & -1112.99065251882 & 1878.35738433287 & 0.936217528267848 \tabularnewline
6 & 50380 & 48260.3170777132 & -1018.01799713379 & 2119.6829222868 & 1.48395393566453 \tabularnewline
7 & 40600 & 45041.4958071015 & -1055.69635192669 & -4441.49580710146 & -0.548793408631984 \tabularnewline
8 & 36279 & 39770.4180547933 & -1136.00064815917 & -3491.41805479327 & -1.04897288853221 \tabularnewline
9 & 42438 & 40758.5526376441 & -1091.99185158999 & 1679.44736235593 & 0.527713818330193 \tabularnewline
10 & 38064 & 39738.6321387395 & -1090.40166758102 & -1674.6321387395 & 0.0178806274781367 \tabularnewline
11 & 31879 & 35371.1508924434 & -1166.53680517257 & -3492.15089244337 & -0.811996060198095 \tabularnewline
12 & 11379 & 21050.2743452747 & -1486.44290600067 & -9671.27434527474 & -3.25536398285996 \tabularnewline
13 & 70249 & 35363.0531598219 & -1624.0739752222 & 34885.9468401781 & 4.23373201286705 \tabularnewline
14 & 39253 & 42236.1815394034 & -1447.55171181498 & -2983.18153940335 & 2.08248194116293 \tabularnewline
15 & 47060 & 45047.4372612872 & -1287.79844928492 & 2012.56273871278 & 0.97174802995881 \tabularnewline
16 & 41697 & 45707.2237435084 & -1213.41443358458 & -4010.22374350836 & 0.462538951120114 \tabularnewline
17 & 38708 & 42346.3542835281 & -1285.51003284955 & -3638.35428352814 & -0.524667808746566 \tabularnewline
18 & 49267 & 43824.0159709013 & -1202.20094143748 & 5442.98402909868 & 0.6784099782396 \tabularnewline
19 & 39018 & 43008.3094713851 & -1190.9439885153 & -3990.30947138514 & 0.0947877107682116 \tabularnewline
20 & 32228 & 39432.0337776318 & -1261.55176022795 & -7204.03377763176 & -0.584204446969156 \tabularnewline
21 & 40870 & 38432.8827936403 & -1253.52757229456 & 2437.11720635973 & 0.064201137373208 \tabularnewline
22 & 39383 & 37892.7057789803 & -1231.22625062694 & 1490.29422101975 & 0.174365287526989 \tabularnewline
23 & 34571 & 35216.1245323056 & -1275.6588277677 & -645.124532305584 & -0.352627536527848 \tabularnewline
24 & 12066 & 31249.6913392591 & -1351.58897511951 & -19183.6913392591 & -0.656708011790571 \tabularnewline
25 & 70938 & 35296.7960797119 & -1215.79508613871 & 35641.2039202881 & 1.33923181300638 \tabularnewline
26 & 34077 & 37673.983032593 & -1105.04791665343 & -3596.98303259297 & 0.87494033083517 \tabularnewline
27 & 45409 & 41317.0885167782 & -928.336491276915 & 4091.91148322183 & 1.12109338955825 \tabularnewline
28 & 40809 & 43248.7078558542 & -815.519566909012 & -2439.7078558542 & 0.678920177130717 \tabularnewline
29 & 37013 & 42624.9506686401 & -808.113443299924 & -5611.95066864007 & 0.0462589549281739 \tabularnewline
30 & 44953 & 40613.5628352074 & -852.723428903096 & 4339.4371647926 & -0.292206284320128 \tabularnewline
31 & 37848 & 40230.3155590609 & -835.77684558935 & -2382.31555906085 & 0.114050568494819 \tabularnewline
32 & 32745 & 39809.4324916529 & -820.913177695299 & -7064.43249165293 & 0.100697843598049 \tabularnewline
33 & 39401 & 37823.4523995741 & -862.702482202829 & 1577.54760042588 & -0.282498440405328 \tabularnewline
34 & 34931 & 34176.9693422626 & -962.221113483782 & 754.030657737389 & -0.67409357181314 \tabularnewline
35 & 33008 & 32666.0671112807 & -981.517935161443 & 341.932888719294 & -0.132699186747811 \tabularnewline
36 & 8620 & 31032.0921793746 & -1003.93296196442 & -22412.0921793746 & -0.158125121447522 \tabularnewline
37 & 68906 & 32984.1041546611 & -902.399241237005 & 35921.8958453389 & 0.719730993139648 \tabularnewline
38 & 39556 & 39983.8622840992 & -616.068457979114 & -427.862284099239 & 1.90998487606706 \tabularnewline
39 & 50669 & 45157.9252992211 & -392.725049415203 & 5511.07470077892 & 1.38083715367614 \tabularnewline
40 & 36432 & 42311.7251092892 & -490.477291728709 & -5879.72510928925 & -0.58464739455055 \tabularnewline
41 & 40891 & 44006.6559123779 & -403.283905162012 & -3115.65591237792 & 0.524937476662095 \tabularnewline
42 & 48428 & 44399.9999456239 & -371.933580092325 & 4028.00005437612 & 0.192418616530821 \tabularnewline
43 & 36222 & 41161.6356071285 & -483.10780029676 & -4939.63560712848 & -0.693103990926147 \tabularnewline
44 & 33425 & 39642.9285711514 & -522.882848154507 & -6217.92857115141 & -0.250173276491603 \tabularnewline
45 & 39401 & 37375.9762513072 & -589.435510281963 & 2025.02374869281 & -0.42073470118426 \tabularnewline
46 & 37967 & 36463.2849632308 & -601.6861282772 & 1503.71503676919 & -0.0778782575926734 \tabularnewline
47 & 34801 & 35068.5384965148 & -631.49031242686 & -267.538496514813 & -0.191025121616656 \tabularnewline
48 & 12657 & 36021.8224693757 & -572.248445989284 & -23364.8224693757 & 0.382548616556821 \tabularnewline
49 & 69116 & 36770.322323167 & -522.564953642448 & 32345.677676833 & 0.319438424150413 \tabularnewline
50 & 41519 & 40859.2242336029 & -345.474246787035 & 659.775766397057 & 1.11108776071277 \tabularnewline
51 & 51321 & 43622.2992049083 & -223.19961982381 & 7698.7007950917 & 0.743915782875368 \tabularnewline
52 & 38529 & 44983.3904071258 & -159.91861424094 & -6454.39040712577 & 0.378591786000154 \tabularnewline
53 & 41547 & 44967.2466647145 & -154.155198682632 & -3420.2466647145 & 0.0344979890369746 \tabularnewline
54 & 52073 & 45831.5067491934 & -113.510875496275 & 6241.4932508066 & 0.245352072378347 \tabularnewline
55 & 38401 & 44139.1461993073 & -176.065649599875 & -5738.14619930725 & -0.380818851517686 \tabularnewline
56 & 40898 & 44978.8527052718 & -136.098519626914 & -4080.85270527177 & 0.244777851170619 \tabularnewline
57 & 40439 & 41233.4445496084 & -277.273460878826 & -794.444549608444 & -0.868394564012734 \tabularnewline
58 & 41888 & 40055.3546321345 & -312.32398963682 & 1832.64536786545 & -0.21649620157021 \tabularnewline
59 & 37898 & 39270.7630902289 & -330.624603485718 & -1372.76309022885 & -0.113541018391587 \tabularnewline
60 & 8771 & 35841.2878441499 & -450.586876256947 & -27070.2878441499 & -0.746398566269161 \tabularnewline
61 & 68184 & 36672.1058114119 & -400.768926788694 & 31511.8941885881 & 0.308984964598216 \tabularnewline
62 & 50530 & 44815.7238326438 & -65.529162446575 & 5714.2761673562 & 2.0557424394921 \tabularnewline
63 & 47221 & 43337.8645288225 & -121.511171844306 & 3883.13547117747 & -0.338493028941166 \tabularnewline
64 & 41756 & 45917.021262385 & -13.6939538109498 & -4161.02126238499 & 0.64648431777277 \tabularnewline
65 & 45633 & 48172.0933920622 & 77.102738976144 & -2539.09339206216 & 0.544308465559436 \tabularnewline
66 & 48138 & 44700.7802110025 & -64.702571507641 & 3437.21978899751 & -0.853697479158119 \tabularnewline
67 & 39486 & 44509.820197455 & -69.7304479640724 & -5023.82019745495 & -0.0304067937665069 \tabularnewline
68 & 39341 & 42869.9921036289 & -131.998833985873 & -3528.99210362888 & -0.377827014177128 \tabularnewline
69 & 41117 & 41722.6097331917 & -172.110976628629 & -605.609733191652 & -0.243985648634321 \tabularnewline
70 & 41629 & 40069.8850523399 & -230.410915489711 & 1559.11494766012 & -0.355468686169117 \tabularnewline
71 & 29722 & 34269.6274269138 & -449.272120784821 & -4547.62742691381 & -1.33788774628906 \tabularnewline
72 & 7054 & 34282.7658818765 & -431.103640584311 & -27228.7658818765 & 0.111236593639713 \tabularnewline
73 & 56676 & 31240.3302365759 & -533.95172730443 & 25435.6697634241 & -0.628644883609773 \tabularnewline
74 & 34870 & 29449.5748206831 & -583.665333844014 & 5420.42517931691 & -0.302148694753612 \tabularnewline
75 & 35117 & 30850.6999319558 & -504.790764211967 & 4266.30006804416 & 0.476036930077661 \tabularnewline
76 & 30169 & 33086.3045064283 & -395.521583019731 & -2917.30450642831 & 0.656670548336699 \tabularnewline
77 & 30936 & 32536.3263287067 & -401.688690045216 & -1600.3263287067 & -0.0370595160412192 \tabularnewline
78 & 35699 & 32036.171382424 & -405.618339661292 & 3662.82861757599 & -0.0236704764917075 \tabularnewline
79 & 33228 & 34772.3506189983 & -280.445915775804 & -1544.35061899835 & 0.755864327693937 \tabularnewline
80 & 27733 & 32637.8584195127 & -354.147441326347 & -4904.85841951266 & -0.445772940390027 \tabularnewline
81 & 33666 & 32335.3404874431 & -352.099736463004 & 1330.65951255691 & 0.0123985586181123 \tabularnewline
82 & 35429 & 31615.3919659671 & -366.661747467748 & 3813.6080340329 & -0.0882791224562238 \tabularnewline
83 & 27438 & 31487.8742381075 & -357.205045897558 & -4049.87423810747 & 0.0574182711240023 \tabularnewline
84 & 8170 & 32772.50420025 & -292.276509332724 & -24602.50420025 & 0.394648646693754 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147323&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]68897[/C][C]68897[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]38683[/C][C]46220.024705057[/C][C]-1041.16528899006[/C][C]-7537.024705057[/C][C]-3.90585273555604[/C][/ROW]
[ROW][C]3[/C][C]44720[/C][C]42974.6491048626[/C][C]-1154.48649410617[/C][C]1745.35089513737[/C][C]-0.460469734365187[/C][/ROW]
[ROW][C]4[/C][C]39525[/C][C]40880.6823010863[/C][C]-1184.14883489966[/C][C]-1355.68230108627[/C][C]-0.230350559527975[/C][/ROW]
[ROW][C]5[/C][C]45315[/C][C]43436.6426156671[/C][C]-1112.99065251882[/C][C]1878.35738433287[/C][C]0.936217528267848[/C][/ROW]
[ROW][C]6[/C][C]50380[/C][C]48260.3170777132[/C][C]-1018.01799713379[/C][C]2119.6829222868[/C][C]1.48395393566453[/C][/ROW]
[ROW][C]7[/C][C]40600[/C][C]45041.4958071015[/C][C]-1055.69635192669[/C][C]-4441.49580710146[/C][C]-0.548793408631984[/C][/ROW]
[ROW][C]8[/C][C]36279[/C][C]39770.4180547933[/C][C]-1136.00064815917[/C][C]-3491.41805479327[/C][C]-1.04897288853221[/C][/ROW]
[ROW][C]9[/C][C]42438[/C][C]40758.5526376441[/C][C]-1091.99185158999[/C][C]1679.44736235593[/C][C]0.527713818330193[/C][/ROW]
[ROW][C]10[/C][C]38064[/C][C]39738.6321387395[/C][C]-1090.40166758102[/C][C]-1674.6321387395[/C][C]0.0178806274781367[/C][/ROW]
[ROW][C]11[/C][C]31879[/C][C]35371.1508924434[/C][C]-1166.53680517257[/C][C]-3492.15089244337[/C][C]-0.811996060198095[/C][/ROW]
[ROW][C]12[/C][C]11379[/C][C]21050.2743452747[/C][C]-1486.44290600067[/C][C]-9671.27434527474[/C][C]-3.25536398285996[/C][/ROW]
[ROW][C]13[/C][C]70249[/C][C]35363.0531598219[/C][C]-1624.0739752222[/C][C]34885.9468401781[/C][C]4.23373201286705[/C][/ROW]
[ROW][C]14[/C][C]39253[/C][C]42236.1815394034[/C][C]-1447.55171181498[/C][C]-2983.18153940335[/C][C]2.08248194116293[/C][/ROW]
[ROW][C]15[/C][C]47060[/C][C]45047.4372612872[/C][C]-1287.79844928492[/C][C]2012.56273871278[/C][C]0.97174802995881[/C][/ROW]
[ROW][C]16[/C][C]41697[/C][C]45707.2237435084[/C][C]-1213.41443358458[/C][C]-4010.22374350836[/C][C]0.462538951120114[/C][/ROW]
[ROW][C]17[/C][C]38708[/C][C]42346.3542835281[/C][C]-1285.51003284955[/C][C]-3638.35428352814[/C][C]-0.524667808746566[/C][/ROW]
[ROW][C]18[/C][C]49267[/C][C]43824.0159709013[/C][C]-1202.20094143748[/C][C]5442.98402909868[/C][C]0.6784099782396[/C][/ROW]
[ROW][C]19[/C][C]39018[/C][C]43008.3094713851[/C][C]-1190.9439885153[/C][C]-3990.30947138514[/C][C]0.0947877107682116[/C][/ROW]
[ROW][C]20[/C][C]32228[/C][C]39432.0337776318[/C][C]-1261.55176022795[/C][C]-7204.03377763176[/C][C]-0.584204446969156[/C][/ROW]
[ROW][C]21[/C][C]40870[/C][C]38432.8827936403[/C][C]-1253.52757229456[/C][C]2437.11720635973[/C][C]0.064201137373208[/C][/ROW]
[ROW][C]22[/C][C]39383[/C][C]37892.7057789803[/C][C]-1231.22625062694[/C][C]1490.29422101975[/C][C]0.174365287526989[/C][/ROW]
[ROW][C]23[/C][C]34571[/C][C]35216.1245323056[/C][C]-1275.6588277677[/C][C]-645.124532305584[/C][C]-0.352627536527848[/C][/ROW]
[ROW][C]24[/C][C]12066[/C][C]31249.6913392591[/C][C]-1351.58897511951[/C][C]-19183.6913392591[/C][C]-0.656708011790571[/C][/ROW]
[ROW][C]25[/C][C]70938[/C][C]35296.7960797119[/C][C]-1215.79508613871[/C][C]35641.2039202881[/C][C]1.33923181300638[/C][/ROW]
[ROW][C]26[/C][C]34077[/C][C]37673.983032593[/C][C]-1105.04791665343[/C][C]-3596.98303259297[/C][C]0.87494033083517[/C][/ROW]
[ROW][C]27[/C][C]45409[/C][C]41317.0885167782[/C][C]-928.336491276915[/C][C]4091.91148322183[/C][C]1.12109338955825[/C][/ROW]
[ROW][C]28[/C][C]40809[/C][C]43248.7078558542[/C][C]-815.519566909012[/C][C]-2439.7078558542[/C][C]0.678920177130717[/C][/ROW]
[ROW][C]29[/C][C]37013[/C][C]42624.9506686401[/C][C]-808.113443299924[/C][C]-5611.95066864007[/C][C]0.0462589549281739[/C][/ROW]
[ROW][C]30[/C][C]44953[/C][C]40613.5628352074[/C][C]-852.723428903096[/C][C]4339.4371647926[/C][C]-0.292206284320128[/C][/ROW]
[ROW][C]31[/C][C]37848[/C][C]40230.3155590609[/C][C]-835.77684558935[/C][C]-2382.31555906085[/C][C]0.114050568494819[/C][/ROW]
[ROW][C]32[/C][C]32745[/C][C]39809.4324916529[/C][C]-820.913177695299[/C][C]-7064.43249165293[/C][C]0.100697843598049[/C][/ROW]
[ROW][C]33[/C][C]39401[/C][C]37823.4523995741[/C][C]-862.702482202829[/C][C]1577.54760042588[/C][C]-0.282498440405328[/C][/ROW]
[ROW][C]34[/C][C]34931[/C][C]34176.9693422626[/C][C]-962.221113483782[/C][C]754.030657737389[/C][C]-0.67409357181314[/C][/ROW]
[ROW][C]35[/C][C]33008[/C][C]32666.0671112807[/C][C]-981.517935161443[/C][C]341.932888719294[/C][C]-0.132699186747811[/C][/ROW]
[ROW][C]36[/C][C]8620[/C][C]31032.0921793746[/C][C]-1003.93296196442[/C][C]-22412.0921793746[/C][C]-0.158125121447522[/C][/ROW]
[ROW][C]37[/C][C]68906[/C][C]32984.1041546611[/C][C]-902.399241237005[/C][C]35921.8958453389[/C][C]0.719730993139648[/C][/ROW]
[ROW][C]38[/C][C]39556[/C][C]39983.8622840992[/C][C]-616.068457979114[/C][C]-427.862284099239[/C][C]1.90998487606706[/C][/ROW]
[ROW][C]39[/C][C]50669[/C][C]45157.9252992211[/C][C]-392.725049415203[/C][C]5511.07470077892[/C][C]1.38083715367614[/C][/ROW]
[ROW][C]40[/C][C]36432[/C][C]42311.7251092892[/C][C]-490.477291728709[/C][C]-5879.72510928925[/C][C]-0.58464739455055[/C][/ROW]
[ROW][C]41[/C][C]40891[/C][C]44006.6559123779[/C][C]-403.283905162012[/C][C]-3115.65591237792[/C][C]0.524937476662095[/C][/ROW]
[ROW][C]42[/C][C]48428[/C][C]44399.9999456239[/C][C]-371.933580092325[/C][C]4028.00005437612[/C][C]0.192418616530821[/C][/ROW]
[ROW][C]43[/C][C]36222[/C][C]41161.6356071285[/C][C]-483.10780029676[/C][C]-4939.63560712848[/C][C]-0.693103990926147[/C][/ROW]
[ROW][C]44[/C][C]33425[/C][C]39642.9285711514[/C][C]-522.882848154507[/C][C]-6217.92857115141[/C][C]-0.250173276491603[/C][/ROW]
[ROW][C]45[/C][C]39401[/C][C]37375.9762513072[/C][C]-589.435510281963[/C][C]2025.02374869281[/C][C]-0.42073470118426[/C][/ROW]
[ROW][C]46[/C][C]37967[/C][C]36463.2849632308[/C][C]-601.6861282772[/C][C]1503.71503676919[/C][C]-0.0778782575926734[/C][/ROW]
[ROW][C]47[/C][C]34801[/C][C]35068.5384965148[/C][C]-631.49031242686[/C][C]-267.538496514813[/C][C]-0.191025121616656[/C][/ROW]
[ROW][C]48[/C][C]12657[/C][C]36021.8224693757[/C][C]-572.248445989284[/C][C]-23364.8224693757[/C][C]0.382548616556821[/C][/ROW]
[ROW][C]49[/C][C]69116[/C][C]36770.322323167[/C][C]-522.564953642448[/C][C]32345.677676833[/C][C]0.319438424150413[/C][/ROW]
[ROW][C]50[/C][C]41519[/C][C]40859.2242336029[/C][C]-345.474246787035[/C][C]659.775766397057[/C][C]1.11108776071277[/C][/ROW]
[ROW][C]51[/C][C]51321[/C][C]43622.2992049083[/C][C]-223.19961982381[/C][C]7698.7007950917[/C][C]0.743915782875368[/C][/ROW]
[ROW][C]52[/C][C]38529[/C][C]44983.3904071258[/C][C]-159.91861424094[/C][C]-6454.39040712577[/C][C]0.378591786000154[/C][/ROW]
[ROW][C]53[/C][C]41547[/C][C]44967.2466647145[/C][C]-154.155198682632[/C][C]-3420.2466647145[/C][C]0.0344979890369746[/C][/ROW]
[ROW][C]54[/C][C]52073[/C][C]45831.5067491934[/C][C]-113.510875496275[/C][C]6241.4932508066[/C][C]0.245352072378347[/C][/ROW]
[ROW][C]55[/C][C]38401[/C][C]44139.1461993073[/C][C]-176.065649599875[/C][C]-5738.14619930725[/C][C]-0.380818851517686[/C][/ROW]
[ROW][C]56[/C][C]40898[/C][C]44978.8527052718[/C][C]-136.098519626914[/C][C]-4080.85270527177[/C][C]0.244777851170619[/C][/ROW]
[ROW][C]57[/C][C]40439[/C][C]41233.4445496084[/C][C]-277.273460878826[/C][C]-794.444549608444[/C][C]-0.868394564012734[/C][/ROW]
[ROW][C]58[/C][C]41888[/C][C]40055.3546321345[/C][C]-312.32398963682[/C][C]1832.64536786545[/C][C]-0.21649620157021[/C][/ROW]
[ROW][C]59[/C][C]37898[/C][C]39270.7630902289[/C][C]-330.624603485718[/C][C]-1372.76309022885[/C][C]-0.113541018391587[/C][/ROW]
[ROW][C]60[/C][C]8771[/C][C]35841.2878441499[/C][C]-450.586876256947[/C][C]-27070.2878441499[/C][C]-0.746398566269161[/C][/ROW]
[ROW][C]61[/C][C]68184[/C][C]36672.1058114119[/C][C]-400.768926788694[/C][C]31511.8941885881[/C][C]0.308984964598216[/C][/ROW]
[ROW][C]62[/C][C]50530[/C][C]44815.7238326438[/C][C]-65.529162446575[/C][C]5714.2761673562[/C][C]2.0557424394921[/C][/ROW]
[ROW][C]63[/C][C]47221[/C][C]43337.8645288225[/C][C]-121.511171844306[/C][C]3883.13547117747[/C][C]-0.338493028941166[/C][/ROW]
[ROW][C]64[/C][C]41756[/C][C]45917.021262385[/C][C]-13.6939538109498[/C][C]-4161.02126238499[/C][C]0.64648431777277[/C][/ROW]
[ROW][C]65[/C][C]45633[/C][C]48172.0933920622[/C][C]77.102738976144[/C][C]-2539.09339206216[/C][C]0.544308465559436[/C][/ROW]
[ROW][C]66[/C][C]48138[/C][C]44700.7802110025[/C][C]-64.702571507641[/C][C]3437.21978899751[/C][C]-0.853697479158119[/C][/ROW]
[ROW][C]67[/C][C]39486[/C][C]44509.820197455[/C][C]-69.7304479640724[/C][C]-5023.82019745495[/C][C]-0.0304067937665069[/C][/ROW]
[ROW][C]68[/C][C]39341[/C][C]42869.9921036289[/C][C]-131.998833985873[/C][C]-3528.99210362888[/C][C]-0.377827014177128[/C][/ROW]
[ROW][C]69[/C][C]41117[/C][C]41722.6097331917[/C][C]-172.110976628629[/C][C]-605.609733191652[/C][C]-0.243985648634321[/C][/ROW]
[ROW][C]70[/C][C]41629[/C][C]40069.8850523399[/C][C]-230.410915489711[/C][C]1559.11494766012[/C][C]-0.355468686169117[/C][/ROW]
[ROW][C]71[/C][C]29722[/C][C]34269.6274269138[/C][C]-449.272120784821[/C][C]-4547.62742691381[/C][C]-1.33788774628906[/C][/ROW]
[ROW][C]72[/C][C]7054[/C][C]34282.7658818765[/C][C]-431.103640584311[/C][C]-27228.7658818765[/C][C]0.111236593639713[/C][/ROW]
[ROW][C]73[/C][C]56676[/C][C]31240.3302365759[/C][C]-533.95172730443[/C][C]25435.6697634241[/C][C]-0.628644883609773[/C][/ROW]
[ROW][C]74[/C][C]34870[/C][C]29449.5748206831[/C][C]-583.665333844014[/C][C]5420.42517931691[/C][C]-0.302148694753612[/C][/ROW]
[ROW][C]75[/C][C]35117[/C][C]30850.6999319558[/C][C]-504.790764211967[/C][C]4266.30006804416[/C][C]0.476036930077661[/C][/ROW]
[ROW][C]76[/C][C]30169[/C][C]33086.3045064283[/C][C]-395.521583019731[/C][C]-2917.30450642831[/C][C]0.656670548336699[/C][/ROW]
[ROW][C]77[/C][C]30936[/C][C]32536.3263287067[/C][C]-401.688690045216[/C][C]-1600.3263287067[/C][C]-0.0370595160412192[/C][/ROW]
[ROW][C]78[/C][C]35699[/C][C]32036.171382424[/C][C]-405.618339661292[/C][C]3662.82861757599[/C][C]-0.0236704764917075[/C][/ROW]
[ROW][C]79[/C][C]33228[/C][C]34772.3506189983[/C][C]-280.445915775804[/C][C]-1544.35061899835[/C][C]0.755864327693937[/C][/ROW]
[ROW][C]80[/C][C]27733[/C][C]32637.8584195127[/C][C]-354.147441326347[/C][C]-4904.85841951266[/C][C]-0.445772940390027[/C][/ROW]
[ROW][C]81[/C][C]33666[/C][C]32335.3404874431[/C][C]-352.099736463004[/C][C]1330.65951255691[/C][C]0.0123985586181123[/C][/ROW]
[ROW][C]82[/C][C]35429[/C][C]31615.3919659671[/C][C]-366.661747467748[/C][C]3813.6080340329[/C][C]-0.0882791224562238[/C][/ROW]
[ROW][C]83[/C][C]27438[/C][C]31487.8742381075[/C][C]-357.205045897558[/C][C]-4049.87423810747[/C][C]0.0574182711240023[/C][/ROW]
[ROW][C]84[/C][C]8170[/C][C]32772.50420025[/C][C]-292.276509332724[/C][C]-24602.50420025[/C][C]0.394648646693754[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147323&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147323&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
16889768897000
23868346220.024705057-1041.16528899006-7537.024705057-3.90585273555604
34472042974.6491048626-1154.486494106171745.35089513737-0.460469734365187
43952540880.6823010863-1184.14883489966-1355.68230108627-0.230350559527975
54531543436.6426156671-1112.990652518821878.357384332870.936217528267848
65038048260.3170777132-1018.017997133792119.68292228681.48395393566453
74060045041.4958071015-1055.69635192669-4441.49580710146-0.548793408631984
83627939770.4180547933-1136.00064815917-3491.41805479327-1.04897288853221
94243840758.5526376441-1091.991851589991679.447362355930.527713818330193
103806439738.6321387395-1090.40166758102-1674.63213873950.0178806274781367
113187935371.1508924434-1166.53680517257-3492.15089244337-0.811996060198095
121137921050.2743452747-1486.44290600067-9671.27434527474-3.25536398285996
137024935363.0531598219-1624.073975222234885.94684017814.23373201286705
143925342236.1815394034-1447.55171181498-2983.181539403352.08248194116293
154706045047.4372612872-1287.798449284922012.562738712780.97174802995881
164169745707.2237435084-1213.41443358458-4010.223743508360.462538951120114
173870842346.3542835281-1285.51003284955-3638.35428352814-0.524667808746566
184926743824.0159709013-1202.200941437485442.984029098680.6784099782396
193901843008.3094713851-1190.9439885153-3990.309471385140.0947877107682116
203222839432.0337776318-1261.55176022795-7204.03377763176-0.584204446969156
214087038432.8827936403-1253.527572294562437.117206359730.064201137373208
223938337892.7057789803-1231.226250626941490.294221019750.174365287526989
233457135216.1245323056-1275.6588277677-645.124532305584-0.352627536527848
241206631249.6913392591-1351.58897511951-19183.6913392591-0.656708011790571
257093835296.7960797119-1215.7950861387135641.20392028811.33923181300638
263407737673.983032593-1105.04791665343-3596.983032592970.87494033083517
274540941317.0885167782-928.3364912769154091.911483221831.12109338955825
284080943248.7078558542-815.519566909012-2439.70785585420.678920177130717
293701342624.9506686401-808.113443299924-5611.950668640070.0462589549281739
304495340613.5628352074-852.7234289030964339.4371647926-0.292206284320128
313784840230.3155590609-835.77684558935-2382.315559060850.114050568494819
323274539809.4324916529-820.913177695299-7064.432491652930.100697843598049
333940137823.4523995741-862.7024822028291577.54760042588-0.282498440405328
343493134176.9693422626-962.221113483782754.030657737389-0.67409357181314
353300832666.0671112807-981.517935161443341.932888719294-0.132699186747811
36862031032.0921793746-1003.93296196442-22412.0921793746-0.158125121447522
376890632984.1041546611-902.39924123700535921.89584533890.719730993139648
383955639983.8622840992-616.068457979114-427.8622840992391.90998487606706
395066945157.9252992211-392.7250494152035511.074700778921.38083715367614
403643242311.7251092892-490.477291728709-5879.72510928925-0.58464739455055
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832743831487.8742381075-357.205045897558-4049.874238107470.0574182711240023
84817032772.50420025-292.276509332724-24602.504200250.394648646693754


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')