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ws 9

*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, 15 Dec 2009 13:39:33 -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/15/t1260909609rg06vp1fjkqv8th.htm/, Retrieved Tue, 15 Dec 2009 21:40:17 +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/15/t1260909609rg06vp1fjkqv8th.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 «

25.6 23.7 22 21.3 20.7 20.4 20.3 20.4 19.8 19.5 23.1 23.5 23.5 22.9 21.9 21.5 20.5 20.2 19.4 19.2 18.8 18.8 22.6 23.3 23 21.4 19.9 18.8 18.6 18.4 18.6 19.9 19.2 18.4 21.1 20.5 19.1 18.1 17 17.1 17.4 16.8 15.3 14.3 13.4 15.3 22.1 23.7 22.2 19.5 16.6 17.3 19.8 21.2 21.5 20.6 19.1 19.6 23.5 24

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	25.6	25.6	0	0	0
2	23.7	23.7748301328505	-1.83135417540214	-0.0748301328505352	-1.44810168374356
3	22	21.9465372012102	-1.82858782162249	0.0534627987897712	0.00223915999513986
4	21.3	21.2147836974749	-0.84154377676446	0.0852163025250775	0.762499701415953
5	20.7	20.6960169894596	-0.551665609120559	0.00398301054043314	0.224942038467864
6	20.4	20.3864496111449	-0.334039498355909	0.0135503888550789	0.168803164391284
7	20.3	20.2854751743608	-0.124526240806792	0.0145248256391764	0.162510907529433
8	20.4	20.3859127839187	0.0776922219204941	0.0140872160812504	0.156852187410448
9	19.8	19.8500810490141	-0.473795942760007	-0.0500810490140693	-0.427765696544395
10	19.5	19.4780164212245	-0.382350527753403	0.0219835787754529	0.070930282436396
11	23.1	22.8150786476378	2.96100191245392	0.284921352362178	2.59329494336066
12	23.5	23.7314950576765	1.12314013941252	-0.231495057676515	-1.42555047010573
13	23.5	23.5622425604115	-0.0377602015796381	-0.0622425604114833	-0.90134728997822
14	22.9	22.9521955245003	-0.552642969998991	-0.0521955245002888	-0.40294974639098
15	21.9	21.9706969947931	-0.922509942553642	-0.0706969947931021	-0.290274379802242
16	21.5	21.3900118177106	-0.62534426428897	0.109988182289448	0.230478927215265
17	20.5	20.5307927472549	-0.827683523507809	-0.0307927472549413	-0.156886744404214
18	20.2	20.1588994712089	-0.433022016310337	0.0411005287911376	0.306170675989697
19	19.4	19.4887954702558	-0.638360236265276	-0.0887954702558011	-0.159269963078949
20	19.2	19.0657634775065	-0.451869580381373	0.134236522493470	0.144653294991571
21	18.8	18.6805102261044	-0.394177532663560	0.119489773895616	0.0447492369805966
22	18.8	19.1657406944248	0.367427207661509	-0.365740694424839	0.590744251909306
23	22.6	21.9449950068195	2.45623756440693	0.655004993180487	1.62020863417254
24	23.3	23.5628371945116	1.73025116135588	-0.262837194511553	-0.56312255012981
25	23	23.2244276416474	-0.0602066067708931	-0.224427641647447	-1.39058359824642
26	21.4	21.5227040000091	-1.48276851213894	-0.122704000009090	-1.10542355132324
27	19.9	19.9850042003555	-1.52962624574123	-0.0850042003554598	-0.0364664986028825
28	18.8	18.6068530924527	-1.39975380788440	0.193146907547254	0.100894234343623
29	18.6	18.5638121856395	-0.239921772462379	0.0361878143605198	0.898864720290756
30	18.4	18.3456330967770	-0.221335176901465	0.0543669032230243	0.0144194645201181
31	18.6	18.6634999770377	0.239799162959192	-0.0634999770376788	0.357682098145959
32	19.9	19.6131870294856	0.846923711073342	0.286812970514353	0.470919293061608
33	19.2	19.2094264779113	-0.222672912896664	-0.00942647791128964	-0.829640810164218
34	18.4	19.1290634011095	-0.100967612841749	-0.729063401109502	0.0944018439297358
35	21.1	20.3260088251693	1.00901148179725	0.773991174830726	0.860967642123709
36	20.5	20.6556556449211	0.428193039487809	-0.155655644921101	-0.450547456268020
37	19.1	19.2964161808192	-1.09994836037982	-0.196416180819169	-1.18680540313525
38	18.1	18.1709759820258	-1.12174323724086	-0.0709759820258269	-0.0169063811079794
39	17	17.0352854081878	-1.13358183698342	-0.0352854081877549	-0.00919402025465744
40	17.1	16.9665961484334	-0.227126735454729	0.133403851566621	0.704217799230097
41	17.4	17.2757647168222	0.228809320403739	0.124235283177842	0.353379938932194
42	16.8	16.8944635864297	-0.289560415791683	-0.09446358642972	-0.402100881756414
43	15.3	15.6214506212061	-1.12550080591388	-0.3214506212061	-0.648429295827709
44	14.3	13.8443364896018	-1.67943220210800	0.455663510398215	-0.429656037037202
45	13.4	13.2543344898595	-0.753323752279421	0.145665510140453	0.718344339003485
46	15.3	15.9358915294317	2.16659309092805	-0.635891529431705	2.26487757993197
47	22.1	21.0400303279409	4.66352659954477	1.05996967205909	1.93675298877730
48	23.7	23.8302671800425	3.07172722790736	-0.130267180042515	-1.23489682234395
49	22.2	22.8068540711887	-0.408988081556008	-0.606854071188698	-2.70245694173248
50	19.5	19.7612055099355	-2.64881609368622	-0.261205509935523	-1.73680562086236
51	16.6	16.7838923072824	-2.92676321861172	-0.18389230728238	-0.215719083988144
52	17.3	16.9630543452069	-0.294357843734779	0.336945654793067	2.04447234367712
53	19.8	19.3860795401536	2.00791194556179	0.413920459846449	1.78481278060656
54	21.2	21.1905811853676	1.83571274414042	0.00941881463237196	-0.133558544746134
55	21.5	21.7183643893044	0.728111053498361	-0.218364389304364	-0.859176709977856
56	20.6	20.2821364371752	-1.10503088638280	0.317863562824792	-1.42187340015066
57	19.1	19.3444888265633	-0.96325943109401	-0.244488826563278	0.109966450751919
58	19.6	20.6282648016024	0.939906914563213	-1.02826480160236	1.47622697555587
59	23.5	22.3459626444705	1.59857481094797	1.15403735552951	0.510895478470541
60	24	23.6823907604055	1.37663438016731	0.317609239594518	-0.172190609779713

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/15/t1260909609rg06vp1fjkqv8th/1gxti1260909569.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/15/t1260909609rg06vp1fjkqv8th/1gxti1260909569.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/15/t1260909609rg06vp1fjkqv8th/2isd41260909569.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/15/t1260909609rg06vp1fjkqv8th/2isd41260909569.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/15/t1260909609rg06vp1fjkqv8th/3og6o1260909569.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/15/t1260909609rg06vp1fjkqv8th/3og6o1260909569.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/15/t1260909609rg06vp1fjkqv8th/4wgsh1260909569.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/15/t1260909609rg06vp1fjkqv8th/4wgsh1260909569.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/15/t1260909609rg06vp1fjkqv8th/5hnxi1260909569.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/15/t1260909609rg06vp1fjkqv8th/5hnxi1260909569.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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