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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 05:33:37 -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/t1259930062kzt2l48npo90mfn.htm/, Retrieved Fri, 04 Dec 2009 13:34:29 +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/t1259930062kzt2l48npo90mfn.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 «

89.1 82.6 102.7 91.8 94.1 103.1 93.2 91 94.3 99.4 115.7 116.8 99.8 96 115.9 109.1 117.3 109.8 112.8 110.7 100 113.3 122.4 112.5 104.2 92.5 117.2 109.3 106.1 118.8 105.3 106 102 112.9 116.5 114.8 100.5 85.4 114.6 109.9 100.7 115.5 100.7 99 102.3 108.8 105.9 113.2 95.7 80.9 113.9 98.1 102.8 104.7 95.9 94.6 101.6 103.9 110.3 114.1

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	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	89.1	89.1	0	0	0
2	82.6	87.6735675936756	0.070661335083685	-4.83289900147734	-1.26376710787920
3	102.7	92.5374206955054	0.441400645419908	9.8819388602758	1.83295820362419
4	91.8	93.7232253481621	0.506741004292658	-1.96641680831321	0.302144510099444
5	94.1	94.2127144407075	0.505352961175474	-0.111460861325777	-0.00839169356607527
6	103.1	97.0369780569355	0.665222298973029	5.86933568937909	1.24792503782846
7	93.2	96.9559592970436	0.620482294699894	-3.68996230465643	-0.416890858348134
8	91	95.254247741539	0.492271363529052	-4.04539168199824	-1.30837928549922
9	94.3	94.3799548114923	0.418622208156228	0.0430338458187371	-0.768405531047828
10	99.4	95.5301027953538	0.458578386588663	3.80440430179163	0.409135792443233
11	115.7	101.883034623722	0.790185927666442	13.2929205217028	3.27680620722125
12	116.8	108.687212662064	1.13961686611099	7.58180917928277	3.32436051732856
13	99.8	109.706911171590	1.13509570937778	-9.8961792436059	-0.0685715403112831
14	96	109.348257679236	1.06916975458905	-13.2145226927723	-0.854500864357059
15	115.9	108.907536709024	0.98186747869165	7.11765740644708	-0.806237121280075
16	109.1	109.866466339628	0.980334259507665	-0.764695170559177	-0.0116276766541316
17	117.3	112.950381503408	1.1284412143855	4.18933415614909	1.06458804620003
18	109.8	111.018918467751	0.912437316831462	-0.980416359416592	-1.58438149819009
19	112.8	111.726562209597	0.898253266301559	1.08980896582434	-0.108246170312348
20	110.7	113.231941288850	0.939299781689044	-2.58118068487424	0.324104624605673
21	100	111.216234790318	0.743772586705867	-10.9755267988505	-1.5798836516807
22	113.3	112.168052382820	0.757299078402837	1.11502307530452	0.110936266216029
23	122.4	113.011514904984	0.76281736576927	9.38149827131044	0.0457904039142626
24	112.5	110.950920554933	0.584392303800081	1.77759736505148	-1.49906264316161
25	104.2	110.987114149466	0.550036454056627	-6.74264463237395	-0.292175816684771
26	92.5	109.424087122979	0.415680887869005	-16.7526296803810	-1.12662006499606
27	117.2	109.360115617334	0.384313643632208	7.87838008183542	-0.253127173094381
28	109.3	109.786205766286	0.387116774161451	-0.489504658371663	0.0217605597666081
29	106.1	107.054852381076	0.174595490361852	-0.710786617790741	-1.61595075489152
30	118.8	109.944418691896	0.360637434850796	8.64266670831147	1.41228038032247
31	105.3	109.109408654162	0.278831216841328	-3.71495641353411	-0.626267073776282
32	106	108.171610411705	0.196038422195312	-2.07493289007177	-0.640119773120965
33	102	109.263521596501	0.256582016432027	-7.33483299174154	0.471591316201895
34	112.9	110.077054049504	0.293962998896268	2.77867847096424	0.292616067650864
35	116.5	108.793543513886	0.18868608367366	7.83157294837637	-0.827295293706676
36	114.8	109.310003369194	0.210486172286256	5.46401428385054	0.171907489087508
37	100.5	108.408106116676	0.136521188636719	-7.81982454891272	-0.584310444575924
38	85.4	106.130776274590	-0.0244901443439168	-20.5390709669054	-1.26870561735737
39	114.6	105.368748457967	-0.0739424434356452	9.28970419541597	-0.386825813918688
40	109.9	106.193972301926	-0.0133444342839474	3.63505965618523	0.469928404238995
41	100.7	105.432198674586	-0.0639627952181262	-4.67331363913502	-0.39031617435152
42	115.5	105.261801856565	-0.0711728571448316	10.2465704631829	-0.0555379637589362
43	100.7	104.792277590348	-0.0981582484897988	-4.06087983108222	-0.208301318247045
44	99	103.681141866864	-0.166706011980017	-4.60113639881148	-0.530579051070181
45	102.3	104.935775751787	-0.0706867075696512	-2.74810184645231	0.74460993716873
46	108.8	105.203826002547	-0.0478457458889582	3.56942454475373	0.177298497179398
47	105.9	102.940971897003	-0.196962352404455	3.13376480298004	-1.15838376518282
48	113.2	103.033898315068	-0.177465960388415	10.1432394481808	0.151602761441785
49	95.7	102.594631830461	-0.195070989924486	-6.87397399877705	-0.137002836868411
50	80.9	101.949997802972	-0.225322449647116	-21.0145067820685	-0.235361753324581
51	113.9	102.529918937718	-0.171076516455159	11.3065335220921	0.421389309133307
52	98.1	100.066550888803	-0.325670633845515	-1.78585664369489	-1.19832924639339
53	102.8	101.272461595013	-0.222297414340018	1.40693775932632	0.80002735298177
54	104.7	99.4336801714063	-0.331443103351116	5.39357434145746	-0.844394939938273
55	95.9	98.8169678705694	-0.350705345622336	-2.89449844264426	-0.149108533738204
56	94.6	98.8274489240714	-0.326321984914312	-4.2559174931242	0.188901504238435
57	101.6	100.150748940310	-0.214998427842097	1.31919845770031	0.86283759676451
58	103.9	100.068284042595	-0.206058489409072	3.8212703474185	0.0692984642297913
59	110.3	102.038582435518	-0.059316170606279	8.08996161315306	1.13755747034755
60	114.1	103.054531207217	0.0131635714385628	10.9607711642705	0.562005063556034

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259930062kzt2l48npo90mfn/1kzss1259930014.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259930062kzt2l48npo90mfn/1kzss1259930014.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259930062kzt2l48npo90mfn/2bmpy1259930014.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259930062kzt2l48npo90mfn/2bmpy1259930014.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259930062kzt2l48npo90mfn/35rwp1259930014.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259930062kzt2l48npo90mfn/35rwp1259930014.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259930062kzt2l48npo90mfn/4t2bi1259930014.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259930062kzt2l48npo90mfn/4t2bi1259930014.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259930062kzt2l48npo90mfn/5mz971259930014.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259930062kzt2l48npo90mfn/5mz971259930014.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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