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Structural time series model

*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 12:54:39 -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/t1259956546q4nqzesrcfcbbai.htm/, Retrieved Fri, 04 Dec 2009 20:55:53 +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/t1259956546q4nqzesrcfcbbai.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 «

19 18 19 19 22 23 20 14 14 14 15 11 17 16 20 24 23 20 21 19 23 23 23 23 27 26 17 24 26 24 27 27 26 24 23 23 24 17 21 19 22 22 18 16 14 12 14 16 8 3 0 5 1 1 3 6 7 8 14 14 13

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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	19	19	0	0	0
2	18	18.1108869988334	-0.051231097300266	-0.0512310975556439	-0.200626530440003
3	19	18.9004944082692	-0.0398278045332988	-0.0398278045332993	0.305317779906727
4	19	19.0130083739769	-0.0387673174784865	-0.0387673174784865	0.0558017298893943
5	22	21.5816274608516	-0.0231613156477001	-0.0231613156477002	0.955488215616181
6	23	22.8048158117019	-0.0159126167790224	-0.0159126167790226	0.456747429571069
7	20	20.4291933373491	-0.0295117081831036	-0.0295117081831038	-0.864754732546442
8	14	14.9787506804773	-0.0605586504685541	-0.0605586504685542	-1.98657023864225
9	14	14.1883374202623	-0.0647146027942089	-0.0647146027942088	-0.267461831052249
10	14	14.0734899979576	-0.0649984508668466	-0.0649984508668466	-0.0183714315332262
11	15	14.9076372112654	-0.0599362284161829	-0.059936228416183	0.329493139930105
12	11	11.6240202077550	-0.0779840534106643	-0.0779840534106638	-1.18130993359118
13	17	14.1818883581347	-0.215206807423069	2.36727488408787	1.18240948626271
14	16	15.9234675080638	-0.163118067413767	-0.163118068548667	0.6029756395653
15	20	19.5104961529234	-0.139743618970718	-0.139743618970719	1.36721031481802
16	24	23.4378945844903	-0.126594440155188	-0.126594440155188	1.48864076745306
17	23	23.1537340304521	-0.127034667374350	-0.127034667374350	-0.0576835873659201
18	20	20.5529785008708	-0.133773463631006	-0.133773463631006	-0.905625815193748
19	21	21.0288148620954	-0.132122767105274	-0.132122767105273	0.223177467762196
20	19	19.3912991965062	-0.136186099490365	-0.136186099490366	-0.551121555475307
21	23	22.5661621676204	-0.127273647106577	-0.127273647106577	1.21216611578203
22	23	23.0261721454294	-0.125697097346314	-0.125697097346314	0.215002437889736
23	23	23.0926204103863	-0.125182669142621	-0.125182669142621	0.0703435644992861
24	23	23.1020166422713	-0.124823324997941	-0.124823324997940	0.0492686224335875
25	27	24.813743856618	-0.170324774837437	1.87357252721930	0.747681575636689
26	26	25.9640351458097	-0.147401698739636	-0.147401702017821	0.434638135554451
27	17	18.4225733035037	-0.177377590719308	-0.177377590719307	-2.69880043671563
28	24	23.3088895353951	-0.166710614046131	-0.166710614046129	1.85296511339913
29	26	25.7243704807678	-0.162004721025879	-0.162004721025879	0.945031693393256
30	24	24.3667736706542	-0.164131260759238	-0.164131260759239	-0.437569293181091
31	27	26.7311014851556	-0.159656812215594	-0.159656812215593	0.925380102187874
32	27	27.0736498418047	-0.158770088205344	-0.158770088205345	0.183799821206169
33	26	26.2693249146466	-0.159907830926560	-0.159907830926559	-0.23626349252131
34	24	24.4449516761456	-0.162836137744504	-0.162836137744503	-0.609169023074157
35	23	23.326487029547	-0.164514427257566	-0.164514427257565	-0.349745143263629
36	23	23.1641427901844	-0.164510622622709	-0.164510622622707	0.000794254146383672
37	24	22.3996663722857	-0.154757675496872	1.70233443029569	-0.235995945432381
38	17	17.8555214912224	-0.211281772688481	-0.211281774705440	-1.48747864115771
39	21	20.6885603225443	-0.202136810370800	-0.202136810370798	1.11177867158714
40	19	19.3896836800057	-0.203850179065471	-0.203850179065470	-0.401286596692104
41	22	21.7634623739253	-0.200364583841613	-0.200364583841614	0.943223462991855
42	22	22.1073863965383	-0.199645920035348	-0.199645920035348	0.199171826098259
43	18	18.7406488578405	-0.203808368649554	-0.203808368649553	-1.15893662772088
44	16	16.5441890055514	-0.206422580280858	-0.206422580280858	-0.729172455501753
45	14	14.5173749489054	-0.208807504442529	-0.208807504442529	-0.666136864396173
46	12	12.5151493740287	-0.211153992432317	-0.211153992432317	-0.656266102712891
47	14	13.9329137669097	-0.209025521960652	-0.209025521960652	0.596070339424432
48	16	15.8464655201049	-0.206255618643653	-0.206255618643651	0.776714571134126
49	8	8.03514433471271	-0.114262851701417	1.25689137184811	-2.93909960858519
50	3	3.78323541200469	-0.156613578762039	-0.156613583824149	-1.42555589150619
51	0	0.663991842963106	-0.163682187017350	-0.163682187017348	-1.08229674760542
52	5	4.48370083080553	-0.158736990329350	-0.158736990329348	1.45738813912598
53	1	1.62013270355226	-0.161644462252316	-0.161644462252317	-0.98968450708988
54	1	1.20489755816989	-0.161910699284411	-0.161910699284411	-0.0927883578614771
55	3	2.85316816971688	-0.160018502727007	-0.160018502727007	0.662342510925763
56	6	5.65487429964198	-0.156927305944377	-0.156927305944378	1.08369020628696
57	7	6.91520497503423	-0.155449737473623	-0.155449737473623	0.518572207386821
58	8	7.95209064425682	-0.154207970164030	-0.15420797016403	0.436273277376316
59	14	13.2280670938837	-0.148558552781648	-0.148558552781648	1.98689353198937
60	14	13.9927947018899	-0.147609382190291	-0.147609382190292	0.334169445813131
61	13	11.9099693457891	-0.128970020093468	1.41867022554141	-0.739898804466961

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259956546q4nqzesrcfcbbai/17zo21259956476.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259956546q4nqzesrcfcbbai/17zo21259956476.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259956546q4nqzesrcfcbbai/27ayp1259956476.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259956546q4nqzesrcfcbbai/27ayp1259956476.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259956546q4nqzesrcfcbbai/3y9o71259956476.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259956546q4nqzesrcfcbbai/3y9o71259956476.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259956546q4nqzesrcfcbbai/42ufj1259956476.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259956546q4nqzesrcfcbbai/42ufj1259956476.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259956546q4nqzesrcfcbbai/56xd01259956476.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259956546q4nqzesrcfcbbai/56xd01259956476.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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