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*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: Fri, 04 Dec 2009 02:37:55 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/04/t1259919630zljwdzhpi6pe0mt.htm/, Retrieved Fri, 04 Dec 2009 10:40:36 +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/2009/Dec/04/t1259919630zljwdzhpi6pe0mt.htm/},
    year = {2009},
}
@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 = {2009},
    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:

ws9.2st

Dataseries X:

» Textbox « » Textfile « » CSV «

2756.76 2849.27 2921.44 2981.85 3080.58 3106.22 3119.31 3061.26 3097.31 3161.69 3257.16 3277.01 3295.32 3363.99 3494.17 3667.03 3813.06 3917.96 3895.51 3801.06 3570.12 3701.61 3862.27 3970.1 4138.52 4199.75 4290.89 4443.91 4502.64 4356.98 4591.27 4696.96 4621.4 4562.84 4202.52 4296.49 4435.23 4105.18 4116.68 3844.49 3720.98 3674.4 3857.62 3801.06 3504.37 3032.6 3047.03 2962.34 2197.82 2014.45 1862.83 1905.41 1810.99 1670.07 1864.44 2052.02 2029.6 2070.83 2293.41 2443.27

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	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	2756.76	2756.76	0	0	0
2	2849.27	2844.55614325511	6.57276951199432	4.71385674489253	0.334856114850539
3	2921.44	2916.67107892756	13.7589455977700	4.7689210724361	0.397644653822629
4	2981.85	2977.04768952485	20.6338837113208	4.80231047514886	0.276723980078269
5	3080.58	3075.7315201141	34.22295532248	4.84847988589733	0.455956242881725
6	3106.22	3101.37562110096	32.576868839572	4.84437889903677	-0.0495684161884733
7	3119.31	3114.47303972618	28.6164405805693	4.83696027381733	-0.111740821245485
8	3061.26	3056.449090343	10.3784403234388	4.810909657	-0.494707706596145
9	3097.31	3092.49303216586	15.8953659189640	4.81696783414468	0.14612296011944
10	3161.69	3156.86408064757	26.4478909736399	4.82591935243379	0.275492913068759
11	3257.16	3252.32413225734	41.5859498976909	4.83586774266347	0.3917681298115
12	3277.01	3272.17657483093	36.7966192208381	4.83342516906696	-0.123292234285078
13	3295.32	3336.96217585882	42.7274960267156	-41.6421758588183	0.185097043221914
14	3363.99	3360.6329580874	38.6611670736743	3.35704191260091	-0.0909000087708877
15	3494.17	3490.89178905271	58.9736765641214	3.27821094728894	0.518584323520462
16	3667.03	3663.82811622644	84.2490489692648	3.20188377355824	0.645333722884836
17	3813.06	3809.89033304911	97.9598919806788	3.1696669508937	0.350081949503154
18	3917.96	3914.79314895211	99.5000520413303	3.16685104788675	0.0393262718754584
19	3895.51	3892.30464914865	72.4370731984709	3.20535085134800	-0.69103396764026
20	3801.06	3797.8136546744	35.4020464827425	3.24634532560158	-0.945672202688552
21	3570.12	3566.82274866132	-23.7033983585631	3.2972513386771	-1.50923883675795
22	3701.61	3698.33582833723	10.7363258884045	3.27417166277004	0.879410554312389
23	3862.27	3859.01317652126	44.0065579691642	3.25682347873649	0.849549644226362
24	3970.1	3966.84892286375	58.1698870600242	3.25107713624912	0.361658634020461
25	4138.52	4149.96738469958	85.4874292632685	-11.4473846995812	0.76665883299017
26	4199.75	4199.23244087076	77.6571108642264	0.51755912923884	-0.185278196338789
27	4290.89	4290.38056328525	80.6530533170265	0.509436714752725	0.0763872412502124
28	4443.91	4443.43448331256	96.7249603019899	0.475516687442993	0.410024742494637
29	4502.64	4502.15062818826	88.2893229295774	0.489371811736392	-0.215285665396504
30	4356.98	4356.42425417511	36.3577099325929	0.555745824886518	-1.32563082550640
31	4591.27	4590.75794587391	80.28931710263	0.512054126087165	1.12156519386773
32	4696.96	4696.45230844216	85.9266777509778	0.507691557843799	0.143932062087999
33	4621.4	4620.87072835058	50.0882494995261	0.529271649422923	-0.91506395027393
34	4562.84	4562.2994313748	25.9767629581173	0.54056862519734	-0.615657321927685
35	4202.52	4201.94817883528	-59.7498492655233	0.571821164718137	-2.18896256318707
36	4296.49	4295.92785537591	-25.6368024703155	0.562144624090286	0.871059436870004
37	4435.23	4422.08597986576	7.7275394260201	13.1440201342418	0.907704831720602
38	4105.18	4109.78394232916	-61.929438299715	-4.60394232915507	-1.68562661103423
39	4116.68	4121.31681963735	-45.6185323795723	-4.63681963735389	0.416033667024512
40	3844.49	3849.04789353429	-95.9275693601094	-4.55789353428539	-1.28377041015625
41	3720.98	3725.53041818677	-102.050680568908	-4.55041818677158	-0.156289252734622
42	3674.4	3678.96211488358	-89.7383050460216	-4.56211488357617	0.314317681527007
43	3857.62	3862.22689729918	-29.1571448128794	-4.60689729918087	1.54670297320979
44	3801.06	3805.66339925824	-35.2386997959309	-4.60339925823721	-0.155277891589227
45	3504.37	3508.94743107151	-93.2611460507691	-4.57743107151422	-1.48151671004765
46	3032.6	3037.14817938195	-177.259938429254	-4.54817938194637	-2.14483044050196
47	3047.03	3051.58970594275	-134.720540862608	-4.55970594275114	1.08621788741837
48	2962.34	2966.90204673031	-123.617953506867	-4.56204673031038	0.283500128762141
49	2197.82	2207.76348024009	-263.650756326525	-9.94348024009174	-3.75065326528572
50	2014.45	2012.96501405620	-248.603685559212	1.48498594380290	0.368587950599816
51	1862.83	1861.37949323273	-227.064987347400	1.45050676727145	0.549502112016056
52	1905.41	1904.03409089213	-167.198963998172	1.37590910786566	1.52785457454302
53	1810.99	1809.62975592235	-151.043718611370	1.36024407764641	0.412388934231326
54	1670.07	1668.71145132100	-148.796739178656	1.35854867899711	0.0573651508928167
55	1864.44	1863.12616616894	-72.6353668387049	1.31383383105621	1.94454261168317
56	2052.02	2050.73254766379	-14.8863389686501	1.28745233621247	1.47451012825262
57	2029.6	2028.31195337778	-16.5582263345466	1.28804662222115	-0.0426896344201635
58	2070.83	2069.54550031604	-3.73392340534191	1.28449968395841	0.327458793443655
59	2293.41	2292.13630846946	46.4889688057277	1.27369153053539	1.28241659775575
60	2443.27	2442.00014965887	69.4286246455843	1.26985034113002	0.585756406119439

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259919630zljwdzhpi6pe0mt/19ln31259919471.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259919630zljwdzhpi6pe0mt/19ln31259919471.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259919630zljwdzhpi6pe0mt/20cuq1259919471.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259919630zljwdzhpi6pe0mt/20cuq1259919471.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259919630zljwdzhpi6pe0mt/399s81259919471.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259919630zljwdzhpi6pe0mt/399s81259919471.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259919630zljwdzhpi6pe0mt/4e8bf1259919471.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259919630zljwdzhpi6pe0mt/4e8bf1259919471.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259919630zljwdzhpi6pe0mt/5emrq1259919471.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259919630zljwdzhpi6pe0mt/5emrq1259919471.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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