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Structural Time Series Models

*The author of this computation has been verified*

R Software Module: /rwasp_structuraltimeseries.wasp (opens new window with default values)

Title produced by software: Structural Time Series Models

Date of computation: Tue, 28 Dec 2010 11:49:59 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/28/t1293536908i1g8zjvaur187cd.htm/, Retrieved Tue, 28 Dec 2010 12:48:34 +0100

BibTeX entries for LaTeX users:

@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Dec/28/t1293536908i1g8zjvaur187cd.htm/},
    year = {2010},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2010},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

621 587 655 517 646 657 382 345 625 654 606 510 614 647 580 614 636 388 356 639 753 611 639 630 586 695 552 619 681 421 307 754 690 644 643 608 651 691 627 634 731 475 337 803 722 590 724 627 696 825 677 656 785 412 352 839 729 696 641 695 638 762 635 721 854 418 367 824 687 601 676 740 691 683 594 729 731 386 331 706 715 657 653 642 643 718 654 632 731 392 344 792 852 649 629 685 617 715 715 629 916 531 357 917 828 708 858 775 785 1006 789 734 906 532 387 991 841 892 782 813 793 978 775 797 946 594 438 1022 868 795

Output produced by software:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	6 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	621	621	0	0	0
2	587	608.77098293182	-0.457029630606978	-15.1574639493343	-0.46781160979471
3	655	624.585272219781	0.841245852901682	25.4003335052864	0.428890000761588
4	517	586.465726157435	-1.92478391657941	-55.4286075192865	-1.18105343404841
5	646	599.850778532084	-1.08612382719182	39.6789350415096	0.522285943566346
6	657	622.25515888051	-0.105258441708400	24.0215548655193	0.845927991724805
7	382	546.008355326935	-2.67664199316742	-128.113390545872	-2.80183895345711
8	345	459.943035686867	-5.13740127537003	-75.120546104286	-3.09400965205076
9	625	494.706815567802	-4.04485749192906	111.142356167958	1.48496242341417
10	654	556.308470751571	-2.31851830651843	66.1251819453168	2.44557844414699
11	606	587.525480990667	-1.45798142715996	2.33742604031028	1.24971155673083
12	510	568.697202855142	-1.89552278121732	-50.3357120615608	-0.64738744682891
13	614	572.250500305224	-2.08610185058685	38.9212523787227	0.230969132616398
14	647	600.983265593104	-1.99009976459817	31.5495590506249	1.17235415241348
15	580	586.226037070328	-2.35599813800913	-1.03972473354552	-0.433850432379405
16	614	614.342559589628	-1.25319274740779	-12.4170203497891	1.02770463716922
17	636	612.031960869023	-1.29001996226939	24.4031411983240	-0.0369297761523492
18	388	511.692876005303	-4.303396568697	-81.2797777888639	-3.57073956757405
19	356	466.307425345646	-5.37321938506412	-92.2585362686458	-1.50955357530999
20	639	542.802123574905	-3.51026151063354	59.7256510800657	3.03785386079080
21	753	602.841823609167	-2.2078727964014	121.644663892949	2.36909371732910
22	611	603.258776300688	-2.15907954363693	6.55897315730887	0.0980474355147776
23	639	611.819851252373	-1.98815407907637	22.3364519826641	0.400822062084261
24	630	638.442512506838	-1.67518347796536	-21.4472961760856	1.07341239749444
25	586	622.133358808472	-1.69302677303452	-29.3440153369266	-0.56116244342708
26	695	630.205336756158	-1.61325889620705	60.380865466204	0.365476329508416
27	552	608.750192802577	-1.97329989298572	-48.2275917249707	-0.71296342829598
28	619	600.689339908611	-2.11948679300902	20.8596004778360	-0.215358333088907
29	681	594.383044764793	-2.22667704776392	88.3789033877845	-0.149342826050015
30	421	562.111760846053	-2.96508938111127	-128.245552105742	-1.08870869752609
31	307	524.024981542537	-3.75439885877948	-201.732348792529	-1.28987195686643
32	754	580.767433379845	-2.53303674714980	146.580320560859	2.24120703380798
33	690	589.542584793103	-2.32938966587949	95.4393417668576	0.420932197722659
34	644	609.851502485735	-1.97130942827454	24.0595076533150	0.844552864550726
35	643	621.776542187702	-1.78560130870115	15.0120655486108	0.519041157009959
36	608	623.540824294328	-1.74782442418364	-17.1327274760061	0.132858990255110
37	651	640.94101018189	-1.58220576801607	1.44603956092786	0.718483062662077
38	691	635.631699085548	-1.62332443698287	57.0258623707766	-0.138443997933265
39	627	643.483111289272	-1.47791578234435	-20.6080472153400	0.345998611251437
40	634	630.627411607222	-1.69217833793495	8.25242546629732	-0.411386558057923
41	731	623.946802266965	-1.79447254940086	109.188924797363	-0.180569852188678
42	475	613.686350554475	-1.96866576009505	-135.035385432936	-0.308747886460838
43	337	600.806323844922	-2.18271197697785	-259.054757747277	-0.401258546006242
44	803	619.097284026921	-1.81128030894418	174.912555802609	0.75771959755711
45	722	630.18207267864	-1.59903381756483	86.1223128180933	0.479133557912105
46	590	615.453374009324	-1.79214434148784	-19.6337033381906	-0.488783055232906
47	724	643.120877435123	-1.40900205080723	67.7919717289004	1.09784679736256
48	627	652.16828426199	-1.28745567322089	-29.8198702618583	0.389928755431202
49	696	666.339324084548	-1.11508247109218	22.7883552361092	0.575971901724822
50	825	701.292844903496	-0.671393384782864	107.772065807677	1.3365663954281
51	677	704.123634514612	-0.620918729099026	-28.6550749599137	0.128719650590822
52	656	684.98296158411	-0.924748997579368	-20.9516605022626	-0.676826656574083
53	785	676.060030419167	-1.06572357526415	112.400273080222	-0.292168275896699
54	412	633.10719804537	-1.81711738242252	-202.930856972486	-1.53555949633318
55	352	621.818262874004	-1.98298519254837	-265.685510422510	-0.348938324879473
56	839	634.405431249039	-1.74108437046113	198.202753824826	0.539045358103248
57	729	639.357579730207	-1.63771628939421	86.6939754541648	0.248332286286509
58	696	671.15813964896	-1.16209682443139	10.0720142960903	1.24259482556811
59	641	651.280535083776	-1.40775901034266	-2.00071385198322	-0.696024750007052
60	695	675.560517673485	-1.08978042044173	8.06872849183365	0.955428323014933
61	638	667.57848435152	-1.17418726961684	-26.5309242129937	-0.256055514260866
62	762	659.300742226267	-1.26566166259239	105.828715770000	-0.263065293459633
63	635	652.278610715343	-1.34626880522629	-14.7563856761802	-0.212260059134228
64	721	672.985772032546	-1.01210855673648	38.3963855563151	0.810567366105447
65	854	689.751806449676	-0.728500241438924	156.508797888657	0.65301587060007
66	418	671.208813117774	-1.01793830502444	-245.44387303271	-0.655482137368702
67	367	659.528943872454	-1.18917309756548	-287.867428218858	-0.393414750224318
68	824	649.957025133187	-1.31922044538525	177.720438402894	-0.310153172232603
69	687	637.734297143313	-1.48017395483181	54.0623919102231	-0.404212492074054
70	601	618.137899936111	-1.73309585227055	-9.15290568198557	-0.672387330779044
71	676	636.274103360507	-1.46947646193621	30.9586854480501	0.737858622326889
72	740	667.135621242642	-1.05452254423450	58.5949741381707	1.20058086039231
73	691	687.600410432093	-0.77940423008278	-6.08984707852706	0.798392170950982
74	683	658.013798118804	-1.15802728968394	37.6614294848401	-1.06675151639112
75	594	641.188822704551	-1.37382979987935	-40.3163121777086	-0.578763224685468
76	729	653.955892675977	-1.16953657891463	68.8575746492839	0.52141944534227
77	731	625.995007377817	-1.57011764564309	116.711920097518	-0.98738172003967
78	386	618.012122023127	-1.66741466902773	-229.208483631222	-0.236542346122302
79	331	613.118539412001	-1.71610409726735	-280.705660102587	-0.119194125160116
80	706	582.451149916966	-2.14363322441074	136.254200402822	-1.07143670154653
81	715	599.305588164758	-1.87207518228141	107.341835613924	0.704006055071197
82	657	629.63961206741	-1.42815202796696	13.1823711947994	1.19443422218725
83	653	639.615028048671	-1.27593432620173	8.36110865959837	0.423087885211165
84	642	624.650954562691	-1.45504256245903	23.3801769942602	-0.507818262702407
85	643	621.480329145757	-1.47744151179037	22.2751339716811	-0.0636087685384157
86	718	635.388778069596	-1.27340004650516	75.8449614938698	0.569813235567022
87	654	655.976837804265	-0.97553666369995	-11.5739756014158	0.80851384281048
88	632	624.298641517965	-1.40609186814535	21.1587647339096	-1.13425862673243
89	731	612.050837209052	-1.56152856199170	123.697585528878	-0.400387398236031
90	392	609.826912515841	-1.57112542773569	-217.536734987818	-0.0244731298740309
91	344	610.519622101672	-1.53840237875069	-267.512300197305	0.0837185905122837
92	792	630.867041236609	-1.22625500767058	151.524073071899	0.810194216984395
93	852	676.749855698353	-0.568159785211801	154.542934184500	1.74542190475153
94	649	674.149377770956	-0.595899610253425	-24.2552797243459	-0.0753408918796882
95	629	654.52758315293	-0.850391654729315	-17.1531932033344	-0.705501806771062
96	685	653.712202098903	-0.849929119021646	31.2723864138528	0.00129817759552111
97	617	638.409682026268	-1.04055275350547	-15.0500601187458	-0.535692805971087
98	715	636.419770257486	-1.05318577032379	78.997646976741	-0.035164371491228
99	715	656.862829514019	-0.762576034453439	48.6953802579499	0.795577263933655
100	629	643.810657405746	-0.931642481550809	-9.4176764466217	-0.454545437421962
101	916	688.768023886694	-0.291480656918096	207.104469948607	1.69686083789203
102	531	720.227913164101	0.154615745349867	-203.155668303637	1.17434988968461
103	357	704.737612000818	-0.0649873767470255	-340.871211899862	-0.578952297308622
104	917	728.907308983821	0.272434359994997	177.448232640891	0.897390366024121
105	828	714.262374273252	0.0674211954527441	120.294529985932	-0.552679284685347
106	708	712.791417276777	0.0465858003787882	-4.11484250426232	-0.0570172389326116
107	858	762.242404471211	0.707236459529172	74.0225070895943	1.83141410520292
108	775	764.748760558954	0.731106339609664	9.45968188700372	0.0666915443393308
109	785	778.856376938914	0.908344229504944	0.259680039294548	0.49573786647434
110	1006	833.805170384898	1.62796873335074	148.435328423141	2.00193181356576
111	789	819.125853007679	1.40878172503416	-22.9605532293672	-0.60381381317988
112	734	804.980557654964	1.19750128286981	-64.1499726398601	-0.5757023262697
113	906	775.431001796747	0.776192668393245	144.067515816919	-1.13786546360258
114	532	756.191026241127	0.500642625919868	-215.403299092785	-0.740830848502529
115	387	748.183248888348	0.383549058208852	-357.446617512852	-0.315009315688191
116	991	766.258740922955	0.625836602479941	216.967942413959	0.655265634842063
117	841	760.637560279432	0.540972144364167	83.108465096877	-0.231454166914231
118	892	813.239112415817	1.24175749110983	55.8680307397057	1.92933611495761
119	782	794.638641597445	0.976797113598297	-3.91141493290453	-0.735431409482744
120	813	800.433646083426	1.04081268941329	10.4470588395289	0.178580028311706
121	793	807.71536379231	1.12364257364201	-17.4600720307446	0.231277606022705
122	978	810.346092759279	1.14370088782955	166.991289910576	0.0558363090836428
123	775	800.980044593906	1.00305255874989	-21.3609316892798	-0.389265791214877
124	797	810.542988329192	1.11833942004229	-17.3038811069407	0.316972230061722
125	946	806.484630276868	1.04824142081894	141.789387714637	-0.191673987913987
126	594	807.495723491526	1.04773688685236	-213.479404920941	-0.00137554507840970
127	438	809.169279508838	1.05623603275497	-371.444240613927	0.0231774436329254
128	1022	811.432206712518	1.07257568478584	210.037471982115	0.0447007517877364
129	868	813.022800352097	1.07955528551371	54.7494732998991	0.0191936889291054
130	795	787.531345305311	0.723585967650354	19.1523093908025	-0.98467096989025

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293536908i1g8zjvaur187cd/1690z1293536993.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293536908i1g8zjvaur187cd/1690z1293536993.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293536908i1g8zjvaur187cd/2690z1293536993.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293536908i1g8zjvaur187cd/2690z1293536993.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293536908i1g8zjvaur187cd/3ziik1293536993.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293536908i1g8zjvaur187cd/3ziik1293536993.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293536908i1g8zjvaur187cd/4a9zn1293536993.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293536908i1g8zjvaur187cd/4a9zn1293536993.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293536908i1g8zjvaur187cd/5a9zn1293536993.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293536908i1g8zjvaur187cd/5a9zn1293536993.ps (open in new window)

Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = 12 ;

R code (references can be found in the software module):

par1 <- as.numeric(par1)

nx <- length(x)

x <- ts(x,frequency=par1)

m <- StructTS(x,type='BSM')

m$coef

m$fitted

m$resid

mylevel <- as.numeric(m$fitted[,'level'])

myslope <- as.numeric(m$fitted[,'slope'])

myseas <- as.numeric(m$fitted[,'sea'])

myresid <- as.numeric(m$resid)

myfit <- mylevel+myseas

mylagmax <- nx/2

bitmap(file='test2.png')

op <- par(mfrow = c(2,2))

acf(as.numeric(x),lag.max = mylagmax,main='Observed')

acf(mylevel,na.action=na.pass,lag.max = mylagmax,main='Level')

acf(myseas,na.action=na.pass,lag.max = mylagmax,main='Seasonal')

acf(myresid,na.action=na.pass,lag.max = mylagmax,main='Standardized Residals')

par(op)

dev.off()

bitmap(file='test3.png')

op <- par(mfrow = c(2,2))

spectrum(as.numeric(x),main='Observed')

spectrum(mylevel,main='Level')

spectrum(myseas,main='Seasonal')

spectrum(myresid,main='Standardized Residals')

par(op)

dev.off()

bitmap(file='test4.png')

op <- par(mfrow = c(2,2))

cpgram(as.numeric(x),main='Observed')

cpgram(mylevel,main='Level')

cpgram(myseas,main='Seasonal')

cpgram(myresid,main='Standardized Residals')

par(op)

dev.off()

bitmap(file='test1.png')

plot(as.numeric(m$resid),main='Standardized Residuals',ylab='Residuals',xlab='time',type='b')

grid()

dev.off()

bitmap(file='test5.png')

op <- par(mfrow = c(2,2))

hist(m$resid,main='Residual Histogram')

plot(density(m$resid),main='Residual Kernel Density')

qqnorm(m$resid,main='Residual Normal QQ Plot')

qqline(m$resid)

plot(m$resid^2, myfit^2,main='Sq.Resid vs. Sq.Fit',xlab='Squared residuals',ylab='Squared Fit')

par(op)

dev.off()

load(file='createtable')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a,'Structural Time Series Model',6,TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'t',header=TRUE)

a<-table.element(a,'Observed',header=TRUE)

a<-table.element(a,'Level',header=TRUE)

a<-table.element(a,'Slope',header=TRUE)

a<-table.element(a,'Seasonal',header=TRUE)

a<-table.element(a,'Stand. Residuals',header=TRUE)

a<-table.row.end(a)

for (i in 1:nx) {

a<-table.row.start(a)

a<-table.element(a,i,header=TRUE)

a<-table.element(a,x[i])

a<-table.element(a,mylevel[i])

a<-table.element(a,myslope[i])

a<-table.element(a,myseas[i])

a<-table.element(a,myresid[i])

a<-table.row.end(a)

}

a<-table.end(a)

table.save(a,file='mytable.tab')

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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