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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: Tue, 01 Dec 2009 14:20:48 -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/01/t12597025191munz8zvuete3fx.htm/, Retrieved Tue, 01 Dec 2009 22:22:06 +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/01/t12597025191munz8zvuete3fx.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

111.4 87.4 96.8 114.1 110.3 103.9 101.6 94.6 95.9 104.7 102.8 98.1 113.9 80.9 95.7 113.2 105.9 108.8 102.3 99 100.7 115.5 100.7 109.9 114.6 85.4 100.5 114.8 116.5 112.9 102 106 105.3 118.8 106.1 109.3 117.2 92.5 104.2 112.5 122.4 113.3 100 110.7 112.8 109.8 117.3 109.1 115.9 96 99.8 116.8 115.7 99.4 94.3 91 93.2 103.1 94.1 91.8 102.7

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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	111.4	111.4	0	0	0
2	87.4	99.8959539316997	-0.224183712393462	-12.4959539316997	-3.77471157315384
3	96.8	94.339309268493	-0.569131348621291	2.46069073150694	-1.33271605733773
4	114.1	101.723564933706	-0.0988441724438671	12.3764350662943	2.46831244139248
5	110.3	106.859804053141	0.116819811641048	3.44019594685947	1.83558024291616
6	103.9	107.063970905857	0.119137784906014	-3.16397090585739	0.0316988220915472
7	101.6	104.948128028468	0.0773151079021414	-3.348128028468	-0.816544568468068
8	94.6	100.232015862647	0.0016220913592343	-5.63201586264684	-1.75189481224714
9	95.9	97.1668014595735	-0.0452188529674338	-1.26680145957346	-1.11964241708753
10	104.7	99.2958365156745	-0.0114825539596751	5.4041634843255	0.792862361470975
11	102.8	101.296936222331	0.0202459237017574	1.50306377766911	0.733381500474781
12	98.1	100.591111703502	0.0087643243230906	-2.49111170350176	-0.264507486948939
13	113.9	102.814221941408	-0.0318593510066001	11.0857780585917	0.849107270893794
14	80.9	99.7935477949431	-0.0117124586909016	-18.8935477949431	-1.13177845328493
15	95.7	98.987425219725	-0.024086084943073	-3.28742521972501	-0.273720806017243
16	113.2	100.821593902115	0.0257799528720589	12.3784060978848	0.623623446985644
17	105.9	101.609855341732	0.0470167145532073	4.29014465826797	0.263729185843117
18	108.8	104.728303064001	0.119765190151101	4.0716969359988	1.09584152464600
19	102.3	104.485408696034	0.112983400460035	-2.18540869603425	-0.131478232683559
20	99	104.042183923285	0.104658715053347	-5.04218392328478	-0.20288370454963
21	100.7	103.846293945630	0.100876708529739	-3.14629394563046	-0.109821794033034
22	115.5	106.651232474146	0.129654255774177	8.84876752585427	0.987908168694762
23	100.7	104.489210383621	0.111252194241004	-3.78921038362127	-0.83656361546845
24	109.9	107.228668010539	0.122407658233233	2.67133198946094	0.960554293568703
25	114.6	105.884017559837	0.121336014739735	8.71598244016299	-0.539045021946316
26	85.4	105.122614461517	0.118582981810548	-19.7226144615167	-0.321690397564941
27	100.5	105.143153537253	0.117625156977526	-4.64315353725302	-0.0348528561178327
28	114.8	104.620365045659	0.107496289118277	10.1796349543411	-0.223986585483039
29	116.5	108.143511635826	0.171337116420478	8.35648836417352	1.19974494886135
30	112.9	109.104914131069	0.185930298729379	3.79508586893128	0.281552001571018
31	102	107.402868396962	0.154943985213279	-5.40286839696195	-0.68149192715483
32	106	108.604171570326	0.169321676514080	-2.60417157032571	0.380494672759458
33	105.3	109.364808944887	0.175880164664117	-4.06480894488655	0.215661624190514
34	118.8	109.507922805753	0.175598725468891	9.29207719424673	-0.0119566864945872
35	106.1	110.158244289759	0.178568838772146	-4.05824428975929	0.173204522851695
36	109.3	108.588350629317	0.170817746450212	0.711649370683478	-0.637986259099148
37	117.2	108.049112317866	0.168039804163992	9.15088768213435	-0.258756733401266
38	92.5	109.660093389787	0.175858398132718	-17.1600933897867	0.522480712336001
39	104.2	110.049179881987	0.177665422541725	-5.84917988198659	0.0763843959498218
40	112.5	108.043011623097	0.152169523350219	4.45698837690309	-0.776126929599112
41	122.4	109.985855610696	0.176858386032477	12.4141443893039	0.636497263966404
42	113.3	110.023077976287	0.174855751904514	3.27692202371337	-0.0499614453383717
43	100	108.645603649194	0.153848165145766	-8.64560364919415	-0.559863637242873
44	110.7	110.305101237087	0.171707941163754	0.394898762912872	0.546220229590452
45	112.8	113.217060017035	0.198633909638723	-0.41706001703455	0.997129139653574
46	109.8	109.030296798522	0.164403277977921	0.769703201477491	-1.59748156769750
47	117.3	112.370138977343	0.183820112320123	4.92986102265674	1.15692001427661
48	109.1	111.706875313938	0.179516311244377	-2.60687531393763	-0.308471097693046
49	115.9	110.011860855866	0.170129700851168	5.88813914413376	-0.681263823932619
50	96	110.767733414340	0.173635599652390	-14.7677334143401	0.211947954752422
51	99.8	108.719273771245	0.156503024925510	-8.91927377124538	-0.799428676081407
52	116.8	110.067692960709	0.167911013648672	6.73230703929065	0.426988954180712
53	115.7	107.728951054722	0.140447058280278	7.97104894527806	-0.897619062052119
54	99.4	102.695974272664	0.0809280947449408	-3.29597427266353	-1.85854962906632
55	94.3	102.256967692620	0.0751193400567024	-7.95696769261977	-0.187663958651076
56	91	98.1206288792811	0.0323539467074631	-7.12062887928114	-1.52625463107751
57	93.2	94.8211628678034	0.00315485374652326	-1.62116286780336	-1.21053837022496
58	103.1	97.5671834813805	0.0232589938868739	5.5328165186195	0.997738158170022
59	94.1	94.6454119296282	0.00513789010988046	-0.545411929628159	-1.07157936364149
60	91.8	93.409164439378	-0.00166425573088006	-1.60916443937796	-0.451452290412623
61	102.7	94.317388015458	0.00329904417405525	8.38261198454195	0.330353121774033

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/01/t12597025191munz8zvuete3fx/1xjww1259702445.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t12597025191munz8zvuete3fx/1xjww1259702445.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t12597025191munz8zvuete3fx/2eolv1259702445.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t12597025191munz8zvuete3fx/2eolv1259702445.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t12597025191munz8zvuete3fx/3icom1259702445.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t12597025191munz8zvuete3fx/3icom1259702445.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t12597025191munz8zvuete3fx/44xfg1259702445.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t12597025191munz8zvuete3fx/44xfg1259702445.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t12597025191munz8zvuete3fx/5jtsx1259702445.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t12597025191munz8zvuete3fx/5jtsx1259702445.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = periodic ; par3 = 0 ; par5 = 1 ; par7 = 1 ; par8 = FALSE ;

Parameters (R input):

par1 = 12 ; par2 = periodic ; par3 = 0 ; par5 = 1 ; par7 = 1 ; par8 = FALSE ;

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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