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Author*The author of this computation has been verified*
R Software Modulerwasp_structuraltimeseries.wasp
Title produced by softwareStructural Time Series Models
Date of computationSat, 17 Dec 2016 10:54:29 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/17/t14819685085xm5qjf96dqmjae.htm/, Retrieved Wed, 01 May 2024 23:36:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300657, Retrieved Wed, 01 May 2024 23:36:57 +0000
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IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact78
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Structural Time Series Models] [N2983] [2016-12-17 09:54:29] [563c2945bc7c763925d38f2fb19cdb55] [Current]
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Dataseries X:
15283
14698
14664
14660
14605
14480
14412
14454
13915
13858
13768
13738
13647
13591
13589
13294
13418
13251
13156
13045
12980
12910
12851
12907
12586
12384
12297
12312
12301
12218
11897
11877
11802
11582
11493
11390
11162
10962
10805
10602
10552
10373
10279
10131
10164
10090
10107
10042
10029
9950
9781
9559
9275
9275
9219
9192
9105
9100
9083
9092
9098
9195
9087




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time3 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300657&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]3 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=300657&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300657&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R ServerBig Analytics Cloud Computing Center







Structural Time Series Model -- Interpolation
tObservedLevelSlopeSeasonalStand. Residuals
11528315283000
21469814746.6518074082-33.7515156539011-29.983443921592-2.73695234336692
31466414695.6726016391-34.5090909526598-30.1238883555463-0.141757502703502
41466014687.6699251304-32.9712336545741-30.02221725979130.216164272944241
51460514636.6538890677-34.2833988351958-30.0804554520408-0.145724988869715
61448014517.6062165807-41.5163502756105-30.3278769093746-0.678781102482594
71441214445.0413874208-44.4887159226063-30.4095970205891-0.246874277516106
81445414477.7530849845-36.4502848951034-30.22793219515430.610267733676781
91391513984.1947957874-87.0879576967468-31.1825482948092-3.5964296133015
101385813889.7995709831-87.9354872139931-31.1960123976709-0.0572764468988623
111376813799.40225852-88.2309425382439-31.1999962993236-0.0192394337201159
121373813764.7410167284-81.6360267057043-31.12412626399370.417684815471054
131364713442.2267795571-107.742627890366223.798790373646-2.22239351682569
141359113590.2778774214-74.3926447179129-14.1926145487421.68296477180207
151358913596.4867601733-64.0286212977832-14.0261171827080.625790798773415
161329413324.8854951095-90.8931151898425-14.0618099834971-1.60930794271861
171341813417.2265604227-67.0331604284741-14.06003455786591.41960115331285
181325113271.4307954288-77.337433448193-14.0597491335622-0.60994610122619
191315613171.8572572455-80.2567668786078-14.0596562082436-0.17214418768644
201304513061.4924484082-84.2200246522599-14.0595444682315-0.233030624928595
211298012992.804897707-82.1713727292545-14.05959453341840.120197015609723
221291012923.0563747462-80.5304375149647-14.05962922714580.096120534839149
231285112863.3761558946-77.7732750923042-14.05967965940450.161310256131575
241290712910.9410910449-61.1851979799834-14.05994219312790.969621386361536
251258612532.7653793041-102.24951954444778.2621834097589-2.68008900196814
261238412394.0918294378-107.039575076223-7.67698078392633-0.255467312159065
271229712303.3444599084-104.881189762729-7.659636074236870.126092481156421
281231212310.6241827347-90.0113234559728-7.675209870245470.867420956965301
291230112302.1162222918-79.2039934614486-7.692449451510920.63025996097905
301221812225.4853260056-78.8627609138613-7.692940885354280.0198977993192114
311189711922.7218391067-108.558182731194-7.65576959806933-1.73146031522625
321187711879.4011988411-99.9052629194415-7.66514919634950.504501353404571
331180211807.4157720309-96.2018479412805-7.668624324867790.215915852880214
341158211598.7327246478-111.12253198367-7.65650466430781-0.86987684267482
351149311499.6834194188-109.520956376811-7.657630778551380.0933698482724327
361139011397.0985031651-108.600829162601-7.658190816212650.0536413524172739
371116211118.4696393862-130.9402697541257.0405830501674-1.39745757987086
381096210968.7185415202-133.414089830744-5.40067996535823-0.135608724276451
391080510812.2765820313-136.46772401048-5.41801167167354-0.178179762051363
401060210612.5162219699-144.865422746434-5.40937733835854-0.489453558083086
411055210550.7225432532-133.843507626397-5.424832318004750.642370720870023
421037310381.2902920863-138.565270200736-5.41889224398308-0.275204114960736
431027910281.3111590547-133.445925684394-5.424486819885130.298390303677605
441013110137.2774550015-134.850622798785-5.42315749287824-0.0818781328526161
451016410156.9700450904-114.347270694471-5.439954526827441.19514688880575
461009010091.5005905181-107.862637814782-5.444553244896050.377998594117404
471010710102.8359991314-92.0486107493155-5.454261364919740.921835744932029
481004210044.718656121-87.5469385320659-5.456653616662270.262415593523324
49100299967.01443849254-86.249653915212661.20048289312110.0797309960520816
5099509949.93725066885-77.140167828037-4.934264853520510.50633634181417
5197819792.46535432216-87.7938086712316-4.98199803697573-0.621517145972445
5295599574.47273031028-105.068960063253-4.96724842699307-1.00687390131815
5392759294.08586753017-128.330379514978-4.94056873579257-1.35573277904453
5492759271.42868885016-114.30990437774-4.954982562374990.817186163054117
5592199218.97156788999-106.103580943871-4.962310650694540.478326717640411
5691929190.69083804888-95.7785569765117-4.970294731312760.601839314009388
5791059108.84712275333-93.9297878085699-4.971532313971520.107766129819552
5891009098.25340983286-82.8734339252777-4.977939195344790.644494336363351
5990839082.56136296884-73.9603675960651-4.982410176686230.519565124079577
6090929090.38748081185-63.1096189712702-4.987121854107660.63252371101273
6190989040.773965421-61.328270893012356.14702191194280.108355975746022
6291959183.52646883398-34.42016982896-3.562004071687931.50853727207844
6390879094.95871176587-41.6017427435389-3.58868513431122-0.41890982863017

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Interpolation \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 15283 & 15283 & 0 & 0 & 0 \tabularnewline
2 & 14698 & 14746.6518074082 & -33.7515156539011 & -29.983443921592 & -2.73695234336692 \tabularnewline
3 & 14664 & 14695.6726016391 & -34.5090909526598 & -30.1238883555463 & -0.141757502703502 \tabularnewline
4 & 14660 & 14687.6699251304 & -32.9712336545741 & -30.0222172597913 & 0.216164272944241 \tabularnewline
5 & 14605 & 14636.6538890677 & -34.2833988351958 & -30.0804554520408 & -0.145724988869715 \tabularnewline
6 & 14480 & 14517.6062165807 & -41.5163502756105 & -30.3278769093746 & -0.678781102482594 \tabularnewline
7 & 14412 & 14445.0413874208 & -44.4887159226063 & -30.4095970205891 & -0.246874277516106 \tabularnewline
8 & 14454 & 14477.7530849845 & -36.4502848951034 & -30.2279321951543 & 0.610267733676781 \tabularnewline
9 & 13915 & 13984.1947957874 & -87.0879576967468 & -31.1825482948092 & -3.5964296133015 \tabularnewline
10 & 13858 & 13889.7995709831 & -87.9354872139931 & -31.1960123976709 & -0.0572764468988623 \tabularnewline
11 & 13768 & 13799.40225852 & -88.2309425382439 & -31.1999962993236 & -0.0192394337201159 \tabularnewline
12 & 13738 & 13764.7410167284 & -81.6360267057043 & -31.1241262639937 & 0.417684815471054 \tabularnewline
13 & 13647 & 13442.2267795571 & -107.742627890366 & 223.798790373646 & -2.22239351682569 \tabularnewline
14 & 13591 & 13590.2778774214 & -74.3926447179129 & -14.192614548742 & 1.68296477180207 \tabularnewline
15 & 13589 & 13596.4867601733 & -64.0286212977832 & -14.026117182708 & 0.625790798773415 \tabularnewline
16 & 13294 & 13324.8854951095 & -90.8931151898425 & -14.0618099834971 & -1.60930794271861 \tabularnewline
17 & 13418 & 13417.2265604227 & -67.0331604284741 & -14.0600345578659 & 1.41960115331285 \tabularnewline
18 & 13251 & 13271.4307954288 & -77.337433448193 & -14.0597491335622 & -0.60994610122619 \tabularnewline
19 & 13156 & 13171.8572572455 & -80.2567668786078 & -14.0596562082436 & -0.17214418768644 \tabularnewline
20 & 13045 & 13061.4924484082 & -84.2200246522599 & -14.0595444682315 & -0.233030624928595 \tabularnewline
21 & 12980 & 12992.804897707 & -82.1713727292545 & -14.0595945334184 & 0.120197015609723 \tabularnewline
22 & 12910 & 12923.0563747462 & -80.5304375149647 & -14.0596292271458 & 0.096120534839149 \tabularnewline
23 & 12851 & 12863.3761558946 & -77.7732750923042 & -14.0596796594045 & 0.161310256131575 \tabularnewline
24 & 12907 & 12910.9410910449 & -61.1851979799834 & -14.0599421931279 & 0.969621386361536 \tabularnewline
25 & 12586 & 12532.7653793041 & -102.249519544447 & 78.2621834097589 & -2.68008900196814 \tabularnewline
26 & 12384 & 12394.0918294378 & -107.039575076223 & -7.67698078392633 & -0.255467312159065 \tabularnewline
27 & 12297 & 12303.3444599084 & -104.881189762729 & -7.65963607423687 & 0.126092481156421 \tabularnewline
28 & 12312 & 12310.6241827347 & -90.0113234559728 & -7.67520987024547 & 0.867420956965301 \tabularnewline
29 & 12301 & 12302.1162222918 & -79.2039934614486 & -7.69244945151092 & 0.63025996097905 \tabularnewline
30 & 12218 & 12225.4853260056 & -78.8627609138613 & -7.69294088535428 & 0.0198977993192114 \tabularnewline
31 & 11897 & 11922.7218391067 & -108.558182731194 & -7.65576959806933 & -1.73146031522625 \tabularnewline
32 & 11877 & 11879.4011988411 & -99.9052629194415 & -7.6651491963495 & 0.504501353404571 \tabularnewline
33 & 11802 & 11807.4157720309 & -96.2018479412805 & -7.66862432486779 & 0.215915852880214 \tabularnewline
34 & 11582 & 11598.7327246478 & -111.12253198367 & -7.65650466430781 & -0.86987684267482 \tabularnewline
35 & 11493 & 11499.6834194188 & -109.520956376811 & -7.65763077855138 & 0.0933698482724327 \tabularnewline
36 & 11390 & 11397.0985031651 & -108.600829162601 & -7.65819081621265 & 0.0536413524172739 \tabularnewline
37 & 11162 & 11118.4696393862 & -130.94026975412 & 57.0405830501674 & -1.39745757987086 \tabularnewline
38 & 10962 & 10968.7185415202 & -133.414089830744 & -5.40067996535823 & -0.135608724276451 \tabularnewline
39 & 10805 & 10812.2765820313 & -136.46772401048 & -5.41801167167354 & -0.178179762051363 \tabularnewline
40 & 10602 & 10612.5162219699 & -144.865422746434 & -5.40937733835854 & -0.489453558083086 \tabularnewline
41 & 10552 & 10550.7225432532 & -133.843507626397 & -5.42483231800475 & 0.642370720870023 \tabularnewline
42 & 10373 & 10381.2902920863 & -138.565270200736 & -5.41889224398308 & -0.275204114960736 \tabularnewline
43 & 10279 & 10281.3111590547 & -133.445925684394 & -5.42448681988513 & 0.298390303677605 \tabularnewline
44 & 10131 & 10137.2774550015 & -134.850622798785 & -5.42315749287824 & -0.0818781328526161 \tabularnewline
45 & 10164 & 10156.9700450904 & -114.347270694471 & -5.43995452682744 & 1.19514688880575 \tabularnewline
46 & 10090 & 10091.5005905181 & -107.862637814782 & -5.44455324489605 & 0.377998594117404 \tabularnewline
47 & 10107 & 10102.8359991314 & -92.0486107493155 & -5.45426136491974 & 0.921835744932029 \tabularnewline
48 & 10042 & 10044.718656121 & -87.5469385320659 & -5.45665361666227 & 0.262415593523324 \tabularnewline
49 & 10029 & 9967.01443849254 & -86.2496539152126 & 61.2004828931211 & 0.0797309960520816 \tabularnewline
50 & 9950 & 9949.93725066885 & -77.140167828037 & -4.93426485352051 & 0.50633634181417 \tabularnewline
51 & 9781 & 9792.46535432216 & -87.7938086712316 & -4.98199803697573 & -0.621517145972445 \tabularnewline
52 & 9559 & 9574.47273031028 & -105.068960063253 & -4.96724842699307 & -1.00687390131815 \tabularnewline
53 & 9275 & 9294.08586753017 & -128.330379514978 & -4.94056873579257 & -1.35573277904453 \tabularnewline
54 & 9275 & 9271.42868885016 & -114.30990437774 & -4.95498256237499 & 0.817186163054117 \tabularnewline
55 & 9219 & 9218.97156788999 & -106.103580943871 & -4.96231065069454 & 0.478326717640411 \tabularnewline
56 & 9192 & 9190.69083804888 & -95.7785569765117 & -4.97029473131276 & 0.601839314009388 \tabularnewline
57 & 9105 & 9108.84712275333 & -93.9297878085699 & -4.97153231397152 & 0.107766129819552 \tabularnewline
58 & 9100 & 9098.25340983286 & -82.8734339252777 & -4.97793919534479 & 0.644494336363351 \tabularnewline
59 & 9083 & 9082.56136296884 & -73.9603675960651 & -4.98241017668623 & 0.519565124079577 \tabularnewline
60 & 9092 & 9090.38748081185 & -63.1096189712702 & -4.98712185410766 & 0.63252371101273 \tabularnewline
61 & 9098 & 9040.773965421 & -61.3282708930123 & 56.1470219119428 & 0.108355975746022 \tabularnewline
62 & 9195 & 9183.52646883398 & -34.42016982896 & -3.56200407168793 & 1.50853727207844 \tabularnewline
63 & 9087 & 9094.95871176587 & -41.6017427435389 & -3.58868513431122 & -0.41890982863017 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300657&T=1

[TABLE]
[ROW][C]Structural Time Series Model -- Interpolation[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Level[/C][C]Slope[/C][C]Seasonal[/C][C]Stand. Residuals[/C][/ROW]
[ROW][C]1[/C][C]15283[/C][C]15283[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]14698[/C][C]14746.6518074082[/C][C]-33.7515156539011[/C][C]-29.983443921592[/C][C]-2.73695234336692[/C][/ROW]
[ROW][C]3[/C][C]14664[/C][C]14695.6726016391[/C][C]-34.5090909526598[/C][C]-30.1238883555463[/C][C]-0.141757502703502[/C][/ROW]
[ROW][C]4[/C][C]14660[/C][C]14687.6699251304[/C][C]-32.9712336545741[/C][C]-30.0222172597913[/C][C]0.216164272944241[/C][/ROW]
[ROW][C]5[/C][C]14605[/C][C]14636.6538890677[/C][C]-34.2833988351958[/C][C]-30.0804554520408[/C][C]-0.145724988869715[/C][/ROW]
[ROW][C]6[/C][C]14480[/C][C]14517.6062165807[/C][C]-41.5163502756105[/C][C]-30.3278769093746[/C][C]-0.678781102482594[/C][/ROW]
[ROW][C]7[/C][C]14412[/C][C]14445.0413874208[/C][C]-44.4887159226063[/C][C]-30.4095970205891[/C][C]-0.246874277516106[/C][/ROW]
[ROW][C]8[/C][C]14454[/C][C]14477.7530849845[/C][C]-36.4502848951034[/C][C]-30.2279321951543[/C][C]0.610267733676781[/C][/ROW]
[ROW][C]9[/C][C]13915[/C][C]13984.1947957874[/C][C]-87.0879576967468[/C][C]-31.1825482948092[/C][C]-3.5964296133015[/C][/ROW]
[ROW][C]10[/C][C]13858[/C][C]13889.7995709831[/C][C]-87.9354872139931[/C][C]-31.1960123976709[/C][C]-0.0572764468988623[/C][/ROW]
[ROW][C]11[/C][C]13768[/C][C]13799.40225852[/C][C]-88.2309425382439[/C][C]-31.1999962993236[/C][C]-0.0192394337201159[/C][/ROW]
[ROW][C]12[/C][C]13738[/C][C]13764.7410167284[/C][C]-81.6360267057043[/C][C]-31.1241262639937[/C][C]0.417684815471054[/C][/ROW]
[ROW][C]13[/C][C]13647[/C][C]13442.2267795571[/C][C]-107.742627890366[/C][C]223.798790373646[/C][C]-2.22239351682569[/C][/ROW]
[ROW][C]14[/C][C]13591[/C][C]13590.2778774214[/C][C]-74.3926447179129[/C][C]-14.192614548742[/C][C]1.68296477180207[/C][/ROW]
[ROW][C]15[/C][C]13589[/C][C]13596.4867601733[/C][C]-64.0286212977832[/C][C]-14.026117182708[/C][C]0.625790798773415[/C][/ROW]
[ROW][C]16[/C][C]13294[/C][C]13324.8854951095[/C][C]-90.8931151898425[/C][C]-14.0618099834971[/C][C]-1.60930794271861[/C][/ROW]
[ROW][C]17[/C][C]13418[/C][C]13417.2265604227[/C][C]-67.0331604284741[/C][C]-14.0600345578659[/C][C]1.41960115331285[/C][/ROW]
[ROW][C]18[/C][C]13251[/C][C]13271.4307954288[/C][C]-77.337433448193[/C][C]-14.0597491335622[/C][C]-0.60994610122619[/C][/ROW]
[ROW][C]19[/C][C]13156[/C][C]13171.8572572455[/C][C]-80.2567668786078[/C][C]-14.0596562082436[/C][C]-0.17214418768644[/C][/ROW]
[ROW][C]20[/C][C]13045[/C][C]13061.4924484082[/C][C]-84.2200246522599[/C][C]-14.0595444682315[/C][C]-0.233030624928595[/C][/ROW]
[ROW][C]21[/C][C]12980[/C][C]12992.804897707[/C][C]-82.1713727292545[/C][C]-14.0595945334184[/C][C]0.120197015609723[/C][/ROW]
[ROW][C]22[/C][C]12910[/C][C]12923.0563747462[/C][C]-80.5304375149647[/C][C]-14.0596292271458[/C][C]0.096120534839149[/C][/ROW]
[ROW][C]23[/C][C]12851[/C][C]12863.3761558946[/C][C]-77.7732750923042[/C][C]-14.0596796594045[/C][C]0.161310256131575[/C][/ROW]
[ROW][C]24[/C][C]12907[/C][C]12910.9410910449[/C][C]-61.1851979799834[/C][C]-14.0599421931279[/C][C]0.969621386361536[/C][/ROW]
[ROW][C]25[/C][C]12586[/C][C]12532.7653793041[/C][C]-102.249519544447[/C][C]78.2621834097589[/C][C]-2.68008900196814[/C][/ROW]
[ROW][C]26[/C][C]12384[/C][C]12394.0918294378[/C][C]-107.039575076223[/C][C]-7.67698078392633[/C][C]-0.255467312159065[/C][/ROW]
[ROW][C]27[/C][C]12297[/C][C]12303.3444599084[/C][C]-104.881189762729[/C][C]-7.65963607423687[/C][C]0.126092481156421[/C][/ROW]
[ROW][C]28[/C][C]12312[/C][C]12310.6241827347[/C][C]-90.0113234559728[/C][C]-7.67520987024547[/C][C]0.867420956965301[/C][/ROW]
[ROW][C]29[/C][C]12301[/C][C]12302.1162222918[/C][C]-79.2039934614486[/C][C]-7.69244945151092[/C][C]0.63025996097905[/C][/ROW]
[ROW][C]30[/C][C]12218[/C][C]12225.4853260056[/C][C]-78.8627609138613[/C][C]-7.69294088535428[/C][C]0.0198977993192114[/C][/ROW]
[ROW][C]31[/C][C]11897[/C][C]11922.7218391067[/C][C]-108.558182731194[/C][C]-7.65576959806933[/C][C]-1.73146031522625[/C][/ROW]
[ROW][C]32[/C][C]11877[/C][C]11879.4011988411[/C][C]-99.9052629194415[/C][C]-7.6651491963495[/C][C]0.504501353404571[/C][/ROW]
[ROW][C]33[/C][C]11802[/C][C]11807.4157720309[/C][C]-96.2018479412805[/C][C]-7.66862432486779[/C][C]0.215915852880214[/C][/ROW]
[ROW][C]34[/C][C]11582[/C][C]11598.7327246478[/C][C]-111.12253198367[/C][C]-7.65650466430781[/C][C]-0.86987684267482[/C][/ROW]
[ROW][C]35[/C][C]11493[/C][C]11499.6834194188[/C][C]-109.520956376811[/C][C]-7.65763077855138[/C][C]0.0933698482724327[/C][/ROW]
[ROW][C]36[/C][C]11390[/C][C]11397.0985031651[/C][C]-108.600829162601[/C][C]-7.65819081621265[/C][C]0.0536413524172739[/C][/ROW]
[ROW][C]37[/C][C]11162[/C][C]11118.4696393862[/C][C]-130.94026975412[/C][C]57.0405830501674[/C][C]-1.39745757987086[/C][/ROW]
[ROW][C]38[/C][C]10962[/C][C]10968.7185415202[/C][C]-133.414089830744[/C][C]-5.40067996535823[/C][C]-0.135608724276451[/C][/ROW]
[ROW][C]39[/C][C]10805[/C][C]10812.2765820313[/C][C]-136.46772401048[/C][C]-5.41801167167354[/C][C]-0.178179762051363[/C][/ROW]
[ROW][C]40[/C][C]10602[/C][C]10612.5162219699[/C][C]-144.865422746434[/C][C]-5.40937733835854[/C][C]-0.489453558083086[/C][/ROW]
[ROW][C]41[/C][C]10552[/C][C]10550.7225432532[/C][C]-133.843507626397[/C][C]-5.42483231800475[/C][C]0.642370720870023[/C][/ROW]
[ROW][C]42[/C][C]10373[/C][C]10381.2902920863[/C][C]-138.565270200736[/C][C]-5.41889224398308[/C][C]-0.275204114960736[/C][/ROW]
[ROW][C]43[/C][C]10279[/C][C]10281.3111590547[/C][C]-133.445925684394[/C][C]-5.42448681988513[/C][C]0.298390303677605[/C][/ROW]
[ROW][C]44[/C][C]10131[/C][C]10137.2774550015[/C][C]-134.850622798785[/C][C]-5.42315749287824[/C][C]-0.0818781328526161[/C][/ROW]
[ROW][C]45[/C][C]10164[/C][C]10156.9700450904[/C][C]-114.347270694471[/C][C]-5.43995452682744[/C][C]1.19514688880575[/C][/ROW]
[ROW][C]46[/C][C]10090[/C][C]10091.5005905181[/C][C]-107.862637814782[/C][C]-5.44455324489605[/C][C]0.377998594117404[/C][/ROW]
[ROW][C]47[/C][C]10107[/C][C]10102.8359991314[/C][C]-92.0486107493155[/C][C]-5.45426136491974[/C][C]0.921835744932029[/C][/ROW]
[ROW][C]48[/C][C]10042[/C][C]10044.718656121[/C][C]-87.5469385320659[/C][C]-5.45665361666227[/C][C]0.262415593523324[/C][/ROW]
[ROW][C]49[/C][C]10029[/C][C]9967.01443849254[/C][C]-86.2496539152126[/C][C]61.2004828931211[/C][C]0.0797309960520816[/C][/ROW]
[ROW][C]50[/C][C]9950[/C][C]9949.93725066885[/C][C]-77.140167828037[/C][C]-4.93426485352051[/C][C]0.50633634181417[/C][/ROW]
[ROW][C]51[/C][C]9781[/C][C]9792.46535432216[/C][C]-87.7938086712316[/C][C]-4.98199803697573[/C][C]-0.621517145972445[/C][/ROW]
[ROW][C]52[/C][C]9559[/C][C]9574.47273031028[/C][C]-105.068960063253[/C][C]-4.96724842699307[/C][C]-1.00687390131815[/C][/ROW]
[ROW][C]53[/C][C]9275[/C][C]9294.08586753017[/C][C]-128.330379514978[/C][C]-4.94056873579257[/C][C]-1.35573277904453[/C][/ROW]
[ROW][C]54[/C][C]9275[/C][C]9271.42868885016[/C][C]-114.30990437774[/C][C]-4.95498256237499[/C][C]0.817186163054117[/C][/ROW]
[ROW][C]55[/C][C]9219[/C][C]9218.97156788999[/C][C]-106.103580943871[/C][C]-4.96231065069454[/C][C]0.478326717640411[/C][/ROW]
[ROW][C]56[/C][C]9192[/C][C]9190.69083804888[/C][C]-95.7785569765117[/C][C]-4.97029473131276[/C][C]0.601839314009388[/C][/ROW]
[ROW][C]57[/C][C]9105[/C][C]9108.84712275333[/C][C]-93.9297878085699[/C][C]-4.97153231397152[/C][C]0.107766129819552[/C][/ROW]
[ROW][C]58[/C][C]9100[/C][C]9098.25340983286[/C][C]-82.8734339252777[/C][C]-4.97793919534479[/C][C]0.644494336363351[/C][/ROW]
[ROW][C]59[/C][C]9083[/C][C]9082.56136296884[/C][C]-73.9603675960651[/C][C]-4.98241017668623[/C][C]0.519565124079577[/C][/ROW]
[ROW][C]60[/C][C]9092[/C][C]9090.38748081185[/C][C]-63.1096189712702[/C][C]-4.98712185410766[/C][C]0.63252371101273[/C][/ROW]
[ROW][C]61[/C][C]9098[/C][C]9040.773965421[/C][C]-61.3282708930123[/C][C]56.1470219119428[/C][C]0.108355975746022[/C][/ROW]
[ROW][C]62[/C][C]9195[/C][C]9183.52646883398[/C][C]-34.42016982896[/C][C]-3.56200407168793[/C][C]1.50853727207844[/C][/ROW]
[ROW][C]63[/C][C]9087[/C][C]9094.95871176587[/C][C]-41.6017427435389[/C][C]-3.58868513431122[/C][C]-0.41890982863017[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300657&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300657&T=1

As an alternative you can also use a QR Code:  

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

Structural Time Series Model -- Interpolation
tObservedLevelSlopeSeasonalStand. Residuals
11528315283000
21469814746.6518074082-33.7515156539011-29.983443921592-2.73695234336692
31466414695.6726016391-34.5090909526598-30.1238883555463-0.141757502703502
41466014687.6699251304-32.9712336545741-30.02221725979130.216164272944241
51460514636.6538890677-34.2833988351958-30.0804554520408-0.145724988869715
61448014517.6062165807-41.5163502756105-30.3278769093746-0.678781102482594
71441214445.0413874208-44.4887159226063-30.4095970205891-0.246874277516106
81445414477.7530849845-36.4502848951034-30.22793219515430.610267733676781
91391513984.1947957874-87.0879576967468-31.1825482948092-3.5964296133015
101385813889.7995709831-87.9354872139931-31.1960123976709-0.0572764468988623
111376813799.40225852-88.2309425382439-31.1999962993236-0.0192394337201159
121373813764.7410167284-81.6360267057043-31.12412626399370.417684815471054
131364713442.2267795571-107.742627890366223.798790373646-2.22239351682569
141359113590.2778774214-74.3926447179129-14.1926145487421.68296477180207
151358913596.4867601733-64.0286212977832-14.0261171827080.625790798773415
161329413324.8854951095-90.8931151898425-14.0618099834971-1.60930794271861
171341813417.2265604227-67.0331604284741-14.06003455786591.41960115331285
181325113271.4307954288-77.337433448193-14.0597491335622-0.60994610122619
191315613171.8572572455-80.2567668786078-14.0596562082436-0.17214418768644
201304513061.4924484082-84.2200246522599-14.0595444682315-0.233030624928595
211298012992.804897707-82.1713727292545-14.05959453341840.120197015609723
221291012923.0563747462-80.5304375149647-14.05962922714580.096120534839149
231285112863.3761558946-77.7732750923042-14.05967965940450.161310256131575
241290712910.9410910449-61.1851979799834-14.05994219312790.969621386361536
251258612532.7653793041-102.24951954444778.2621834097589-2.68008900196814
261238412394.0918294378-107.039575076223-7.67698078392633-0.255467312159065
271229712303.3444599084-104.881189762729-7.659636074236870.126092481156421
281231212310.6241827347-90.0113234559728-7.675209870245470.867420956965301
291230112302.1162222918-79.2039934614486-7.692449451510920.63025996097905
301221812225.4853260056-78.8627609138613-7.692940885354280.0198977993192114
311189711922.7218391067-108.558182731194-7.65576959806933-1.73146031522625
321187711879.4011988411-99.9052629194415-7.66514919634950.504501353404571
331180211807.4157720309-96.2018479412805-7.668624324867790.215915852880214
341158211598.7327246478-111.12253198367-7.65650466430781-0.86987684267482
351149311499.6834194188-109.520956376811-7.657630778551380.0933698482724327
361139011397.0985031651-108.600829162601-7.658190816212650.0536413524172739
371116211118.4696393862-130.9402697541257.0405830501674-1.39745757987086
381096210968.7185415202-133.414089830744-5.40067996535823-0.135608724276451
391080510812.2765820313-136.46772401048-5.41801167167354-0.178179762051363
401060210612.5162219699-144.865422746434-5.40937733835854-0.489453558083086
411055210550.7225432532-133.843507626397-5.424832318004750.642370720870023
421037310381.2902920863-138.565270200736-5.41889224398308-0.275204114960736
431027910281.3111590547-133.445925684394-5.424486819885130.298390303677605
441013110137.2774550015-134.850622798785-5.42315749287824-0.0818781328526161
451016410156.9700450904-114.347270694471-5.439954526827441.19514688880575
461009010091.5005905181-107.862637814782-5.444553244896050.377998594117404
471010710102.8359991314-92.0486107493155-5.454261364919740.921835744932029
481004210044.718656121-87.5469385320659-5.456653616662270.262415593523324
49100299967.01443849254-86.249653915212661.20048289312110.0797309960520816
5099509949.93725066885-77.140167828037-4.934264853520510.50633634181417
5197819792.46535432216-87.7938086712316-4.98199803697573-0.621517145972445
5295599574.47273031028-105.068960063253-4.96724842699307-1.00687390131815
5392759294.08586753017-128.330379514978-4.94056873579257-1.35573277904453
5492759271.42868885016-114.30990437774-4.954982562374990.817186163054117
5592199218.97156788999-106.103580943871-4.962310650694540.478326717640411
5691929190.69083804888-95.7785569765117-4.970294731312760.601839314009388
5791059108.84712275333-93.9297878085699-4.971532313971520.107766129819552
5891009098.25340983286-82.8734339252777-4.977939195344790.644494336363351
5990839082.56136296884-73.9603675960651-4.982410176686230.519565124079577
6090929090.38748081185-63.1096189712702-4.987121854107660.63252371101273
6190989040.773965421-61.328270893012356.14702191194280.108355975746022
6291959183.52646883398-34.42016982896-3.562004071687931.50853727207844
6390879094.95871176587-41.6017427435389-3.58868513431122-0.41890982863017







Structural Time Series Model -- Extrapolation
tObservedLevelSeasonal
19096.662798826599144.45563319525-47.7928343686578
29160.034330097499152.91620032297.11812977459878
39164.028738600559161.376767450552.65197115000776
49148.246019491019169.83733457819-21.591315087185
59202.686158031779178.2979017058424.388256325925
69159.549179869299186.75846883349-27.2092889642045
79174.035056505669195.21903596114-21.1839794554827
89222.343789599989203.6796030887918.6641865111896
99287.875386014299212.1401702164475.7352157978512
109263.09793845989220.6007373440942.4972011157048
119200.517061819599229.06130447174-28.5442426521481
129212.788571451799237.52187159939-24.733300147599

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model -- Extrapolation \tabularnewline
t & Observed & Level & Seasonal \tabularnewline
1 & 9096.66279882659 & 9144.45563319525 & -47.7928343686578 \tabularnewline
2 & 9160.03433009749 & 9152.9162003229 & 7.11812977459878 \tabularnewline
3 & 9164.02873860055 & 9161.37676745055 & 2.65197115000776 \tabularnewline
4 & 9148.24601949101 & 9169.83733457819 & -21.591315087185 \tabularnewline
5 & 9202.68615803177 & 9178.29790170584 & 24.388256325925 \tabularnewline
6 & 9159.54917986929 & 9186.75846883349 & -27.2092889642045 \tabularnewline
7 & 9174.03505650566 & 9195.21903596114 & -21.1839794554827 \tabularnewline
8 & 9222.34378959998 & 9203.67960308879 & 18.6641865111896 \tabularnewline
9 & 9287.87538601429 & 9212.14017021644 & 75.7352157978512 \tabularnewline
10 & 9263.0979384598 & 9220.60073734409 & 42.4972011157048 \tabularnewline
11 & 9200.51706181959 & 9229.06130447174 & -28.5442426521481 \tabularnewline
12 & 9212.78857145179 & 9237.52187159939 & -24.733300147599 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300657&T=2

[TABLE]
[ROW][C]Structural Time Series Model -- Extrapolation[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Level[/C][C]Seasonal[/C][/ROW]
[ROW][C]1[/C][C]9096.66279882659[/C][C]9144.45563319525[/C][C]-47.7928343686578[/C][/ROW]
[ROW][C]2[/C][C]9160.03433009749[/C][C]9152.9162003229[/C][C]7.11812977459878[/C][/ROW]
[ROW][C]3[/C][C]9164.02873860055[/C][C]9161.37676745055[/C][C]2.65197115000776[/C][/ROW]
[ROW][C]4[/C][C]9148.24601949101[/C][C]9169.83733457819[/C][C]-21.591315087185[/C][/ROW]
[ROW][C]5[/C][C]9202.68615803177[/C][C]9178.29790170584[/C][C]24.388256325925[/C][/ROW]
[ROW][C]6[/C][C]9159.54917986929[/C][C]9186.75846883349[/C][C]-27.2092889642045[/C][/ROW]
[ROW][C]7[/C][C]9174.03505650566[/C][C]9195.21903596114[/C][C]-21.1839794554827[/C][/ROW]
[ROW][C]8[/C][C]9222.34378959998[/C][C]9203.67960308879[/C][C]18.6641865111896[/C][/ROW]
[ROW][C]9[/C][C]9287.87538601429[/C][C]9212.14017021644[/C][C]75.7352157978512[/C][/ROW]
[ROW][C]10[/C][C]9263.0979384598[/C][C]9220.60073734409[/C][C]42.4972011157048[/C][/ROW]
[ROW][C]11[/C][C]9200.51706181959[/C][C]9229.06130447174[/C][C]-28.5442426521481[/C][/ROW]
[ROW][C]12[/C][C]9212.78857145179[/C][C]9237.52187159939[/C][C]-24.733300147599[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300657&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300657&T=2

As an alternative you can also use a QR Code:  

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

Structural Time Series Model -- Extrapolation
tObservedLevelSeasonal
19096.662798826599144.45563319525-47.7928343686578
29160.034330097499152.91620032297.11812977459878
39164.028738600559161.376767450552.65197115000776
49148.246019491019169.83733457819-21.591315087185
59202.686158031779178.2979017058424.388256325925
69159.549179869299186.75846883349-27.2092889642045
79174.035056505669195.21903596114-21.1839794554827
89222.343789599989203.6796030887918.6641865111896
99287.875386014299212.1401702164475.7352157978512
109263.09793845989220.6007373440942.4972011157048
119200.517061819599229.06130447174-28.5442426521481
129212.788571451799237.52187159939-24.733300147599



Parameters (Session):
par1 = 12 ; par2 = 12 ; par3 = BFGS ;
Parameters (R input):
par1 = 12 ; par2 = 12 ; par3 = BFGS ;
R code (references can be found in the software module):
require('stsm')
require('stsm.class')
require('KFKSDS')
par1 <- as.numeric(par1)
par2 <- as.numeric(par2)
nx <- length(x)
x <- ts(x,frequency=par1)
m <- StructTS(x,type='BSM')
print(m$coef)
print(m$fitted)
print(m$resid)
mylevel <- as.numeric(m$fitted[,'level'])
myslope <- as.numeric(m$fitted[,'slope'])
myseas <- as.numeric(m$fitted[,'sea'])
myresid <- as.numeric(m$resid)
myfit <- mylevel+myseas
mm <- stsm.model(model = 'BSM', y = x, transPars = 'StructTS')
fit2 <- stsmFit(mm, stsm.method = 'maxlik.td.optim', method = par3, KF.args = list(P0cov = TRUE))
(fit2.comps <- tsSmooth(fit2, P0cov = FALSE)$states)
m2 <- set.pars(mm, pmax(fit2$par, .Machine$double.eps))
(ss <- char2numeric(m2))
(pred <- predict(ss, x, n.ahead = par2))
mylagmax <- nx/2
bitmap(file='test2.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(x),lag.max = mylagmax,main='Observed')
acf(mylevel,na.action=na.pass,lag.max = mylagmax,main='Level')
acf(myseas,na.action=na.pass,lag.max = mylagmax,main='Seasonal')
acf(myresid,na.action=na.pass,lag.max = mylagmax,main='Standardized Residals')
par(op)
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
spectrum(as.numeric(x),main='Observed')
spectrum(mylevel,main='Level')
spectrum(myseas,main='Seasonal')
spectrum(myresid,main='Standardized Residals')
par(op)
dev.off()
bitmap(file='test4.png')
op <- par(mfrow = c(2,2))
cpgram(as.numeric(x),main='Observed')
cpgram(mylevel,main='Level')
cpgram(myseas,main='Seasonal')
cpgram(myresid,main='Standardized Residals')
par(op)
dev.off()
bitmap(file='test1.png')
plot(as.numeric(m$resid),main='Standardized Residuals',ylab='Residuals',xlab='time',type='b')
grid()
dev.off()
bitmap(file='test5.png')
op <- par(mfrow = c(2,2))
hist(m$resid,main='Residual Histogram')
plot(density(m$resid),main='Residual Kernel Density')
qqnorm(m$resid,main='Residual Normal QQ Plot')
qqline(m$resid)
plot(m$resid^2, myfit^2,main='Sq.Resid vs. Sq.Fit',xlab='Squared residuals',ylab='Squared Fit')
par(op)
dev.off()
bitmap(file='test6.png')
par(mfrow = c(3,1), mar = c(3,3,3,3))
plot(cbind(x, pred$pred), type = 'n', plot.type = 'single', ylab = '')
lines(x)
polygon(c(time(pred$pred), rev(time(pred$pred))), c(pred$pred + 2 * pred$se, rev(pred$pred)), col = 'gray85', border = NA)
polygon(c(time(pred$pred), rev(time(pred$pred))), c(pred$pred - 2 * pred$se, rev(pred$pred)), col = ' gray85', border = NA)
lines(pred$pred, col = 'blue', lwd = 1.5)
mtext(text = 'forecasts of the observed series', side = 3, adj = 0)
plot(cbind(x, pred$a[,1]), type = 'n', plot.type = 'single', ylab = '')
lines(x)
polygon(c(time(pred$a[,1]), rev(time(pred$a[,1]))), c(pred$a[,1] + 2 * sqrt(pred$P[,1]), rev(pred$a[,1])), col = 'gray85', border = NA)
polygon(c(time(pred$a[,1]), rev(time(pred$a[,1]))), c(pred$a[,1] - 2 * sqrt(pred$P[,1]), rev(pred$a[,1])), col = ' gray85', border = NA)
lines(pred$a[,1], col = 'blue', lwd = 1.5)
mtext(text = 'forecasts of the level component', side = 3, adj = 0)
plot(cbind(fit2.comps[,3], pred$a[,3]), type = 'n', plot.type = 'single', ylab = '')
lines(fit2.comps[,3])
polygon(c(time(pred$a[,3]), rev(time(pred$a[,3]))), c(pred$a[,3] + 2 * sqrt(pred$P[,3]), rev(pred$a[,3])), col = 'gray85', border = NA)
polygon(c(time(pred$a[,3]), rev(time(pred$a[,3]))), c(pred$a[,3] - 2 * sqrt(pred$P[,3]), rev(pred$a[,3])), col = ' gray85', border = NA)
lines(pred$a[,3], col = 'blue', lwd = 1.5)
mtext(text = 'forecasts of the seasonal component', side = 3, adj = 0)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Structural Time Series Model -- Interpolation',6,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Level',header=TRUE)
a<-table.element(a,'Slope',header=TRUE)
a<-table.element(a,'Seasonal',header=TRUE)
a<-table.element(a,'Stand. Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nx) {
a<-table.row.start(a)
a<-table.element(a,i,header=TRUE)
a<-table.element(a,x[i])
a<-table.element(a,mylevel[i])
a<-table.element(a,myslope[i])
a<-table.element(a,myseas[i])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Structural Time Series Model -- Extrapolation',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Level',header=TRUE)
a<-table.element(a,'Seasonal',header=TRUE)
a<-table.row.end(a)
for (i in 1:par2) {
a<-table.row.start(a)
a<-table.element(a,i,header=TRUE)
a<-table.element(a,pred$pred[i])
a<-table.element(a,pred$a[i,1])
a<-table.element(a,pred$a[i,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')