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Structural Time Series Models

*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 12:26:25 -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/t125995488925cjzhv214d9lm0.htm/, Retrieved Fri, 04 Dec 2009 20:28:16 +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/t125995488925cjzhv214d9lm0.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 «

7.3 7.6 7.5 7.6 7.9 7.9 8.1 8.2 8 7.5 6.8 6.5 6.6 7.6 8 8.1 7.7 7.5 7.6 7.8 7.8 7.8 7.5 7.5 7.1 7.5 7.5 7.6 7.7 7.7 7.9 8.1 8.2 8.2 8.2 7.9 7.3 6.9 6.6 6.7 6.9 7 7.1 7.2 7.1 6.9 7 6.8 6.4 6.7 6.6 6.4 6.3 6.2 6.5 6.8 6.8 6.4 6.1 5.8 6.1 7.2 7.3 6.9 6.1 5.8 6.2 7.1 7.7 7.9 7.7 7.4 7.5

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	7.3	7.3	0	0	0
2	7.6	7.59639540237201	0.23428542226864	0.0036045976279917	0.872311949205638
3	7.5	7.49357827748373	-0.0750679612131155	0.00642172251626942	-0.970173911050916
4	7.6	7.59369924340227	0.0856459617000033	0.00630075659772915	0.532724146801564
5	7.9	7.89371139460658	0.282414165992223	0.00628860539342368	0.652468147237377
6	7.9	7.89371008117575	0.0231696542248448	0.00628991882425245	-0.859636822184238
7	8.1	8.09371014864573	0.185492590053274	0.00628985135426768	0.538251606697165
8	8.2	8.19371014596955	0.107013932173819	0.00628985403044805	-0.260229791212702
9	8	7.9937101451811	-0.174812145762042	0.00628985481890516	-0.93451574480604
10	7.5	7.49371014511258	-0.473321131668179	0.00628985488742043	-0.989835111564299
11	6.8	6.79371014510866	-0.681402947241058	0.00628985489133873	-0.689984881047587
12	6.5	6.4937101451092	-0.331290833523464	0.00628985489079784	1.16094750745841
13	6.6	6.62249402481947	0.0871420213598957	-0.0224940248194680	1.46296838828869
14	7.6	7.58753610682519	0.797227751356276	0.0124638931748074	2.31033551408993
15	8	7.98559055868502	0.430975128467969	0.0144094413149839	-1.17879502927377
16	8.1	8.08545760895555	0.127144615791027	0.0145423910444483	-1.00728304615704
17	7.7	7.6854402367889	-0.356752412277474	0.0145597632110952	-1.60456689144521
18	7.5	7.48544066059922	-0.212860187888970	0.0145593394007775	0.477136640564384
19	7.6	7.58544072999622	0.0743325107339263	0.0145592700037798	0.95231108705789
20	7.8	7.78544073228312	0.189690062663704	0.0145592677168839	0.382517648296371
21	7.8	7.78544073199991	0.0155624391861711	0.0145592680000890	-0.57739513297434
22	7.8	7.78544073199800	0.00127676437037538	0.0145592680019952	-0.0473703077384437
23	7.5	7.48544073199498	-0.275282831067262	0.0145592680050227	-0.917052453792022
24	7.5	7.4854407319952	-0.0225845901325705	0.0145592680047958	0.837929855774401
25	7.1	7.27226335877404	-0.196530167346724	-0.172263358774043	-0.596561262010691
26	7.5	7.48090615231051	0.143834523550880	0.0190938476894929	1.11702491797441
27	7.5	7.48039425359165	0.0113757242717072	0.0196057464083517	-0.429865863048256
28	7.6	7.58042012422508	0.092730900711259	0.0195798757749171	0.269729622804666
29	7.7	7.68042029831248	0.0994036338559933	0.0195797016875153	0.0221262994531427
30	7.7	7.68042010300356	0.008155213657866	0.0195798969964388	-0.302573436202211
31	7.9	7.88042013392808	0.184260784257813	0.0195798660719226	0.58395386854156
32	8.1	8.08042013413622	0.198708732632663	0.0195798658637762	0.0479083956152225
33	8.2	8.18042013402913	0.108098203074893	0.0195798659708724	-0.300458236998992
34	8.2	8.1804201340195	0.00886852841874838	0.0195798659804946	-0.329038724866522
35	8.2	8.18042013401944	0.000727586528516767	0.0195798659805593	-0.0269947991672508
36	7.9	7.88042013401926	-0.275327886388801	0.0195798659807396	-0.91538081844869
37	7.3	7.5193445893845	-0.353709715765585	-0.219344589384493	-0.266412201014775
38	6.9	6.88192914455305	-0.596951364659631	0.0180708554469515	-0.801098916764735
39	6.6	6.5827591201618	-0.323673772835834	0.0172408798382020	0.891022041950161
40	6.7	6.68285625148906	0.0652478194236635	0.0171437485109373	1.28949248454303
41	6.9	6.88285878601113	0.188944755980244	0.0171412139888740	0.410170160360221
42	7	6.9828586487607	0.107297152652633	0.0171413512393016	-0.270737793346502
43	7.1	7.0828586478369	0.100598668653421	0.0171413521631056	-0.0222117087575052
44	7.2	7.18285864783068	0.100049115617238	0.0171413521693236	-0.00182227978574612
45	7.1	7.08285864766021	-0.0835876895588362	0.0171413523397862	-0.608926920531383
46	6.9	6.88285864765208	-0.190449370534637	0.0171413523479243	-0.354345928949323
47	7	6.98285864765374	0.0761711256660793	0.0171413523462585	0.884095089469596
48	6.8	6.78285864765361	-0.177342532930814	0.0171413523463885	-0.840633724236474
49	6.4	6.58914992692075	-0.192316358738675	-0.189149926920748	-0.0506304848348785
50	6.7	6.6812711421843	0.0546877202695599	0.0187288578157056	0.814982755297965
51	6.6	6.58091521163117	-0.0876044754305867	0.0190847883688329	-0.465341983043639
52	6.4	6.38089399715998	-0.190780357170881	0.0191060028400165	-0.342092499914615
53	6.3	6.28089540290874	-0.107447740166072	0.019104597091258	0.276325011665894
54	6.2	6.18089541237053	-0.100611023060244	0.0191045876294654	0.0226700800659161
55	6.5	6.48089545412519	0.267133308957569	0.0191045458748114	1.21941472145232
56	6.8	6.78089545440623	0.297303570501186	0.0191045455937696	0.100042496577755
57	6.8	6.78089545419766	0.0243912025268236	0.0191045458023379	-0.904958500264783
58	6.4	6.38089545417324	-0.365182349630097	0.0191045458267636	-1.29179890277406
59	6.1	6.08089545417354	-0.305347651521043	0.0191045458264558	0.198407712579930
60	5.8	5.78089545417355	-0.300438728842283	0.0191045458264538	0.0162776474304136
61	6.1	6.28602251203299	0.437023850462163	-0.186022512032987	2.48511089966492
62	7.2	7.1810000224947	0.838202003351515	0.0189999775052993	1.32513066817445
63	7.3	7.27955653815045	0.159365640619195	0.0204434618495487	-2.22467789645746
64	6.9	6.87946681357677	-0.354114963910708	0.0205331864232308	-1.70253256245747
65	6.1	6.07946094583202	-0.763418998098226	0.0205390541679799	-1.35722309747112
66	5.8	5.77946144616051	-0.338019545309172	0.0205385538394887	1.41059510164002
67	6.2	6.17946151153109	0.339451839857443	0.0205384884689067	2.24644816659836
68	7.1	7.07946151560453	0.85401184157653	0.0205384843954744	1.70624530836807
69	7.7	7.67946151545309	0.620839488276781	0.0205384845469122	-0.773183365457345
70	7.9	7.8794615154325	0.234526262743969	0.0205384845674963	-1.28098788561853
71	7.7	7.67946151543076	-0.164350855053826	0.0205384845692399	-1.3226488817324
72	7.4	7.37946151543072	-0.288871153611122	0.0205384845692847	-0.412900681164878
73	7.5	7.71014714151173	0.278539781442523	-0.210147141511725	1.90750876607253

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t125995488925cjzhv214d9lm0/1ktuf1259954782.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t125995488925cjzhv214d9lm0/1ktuf1259954782.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t125995488925cjzhv214d9lm0/2eepu1259954782.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t125995488925cjzhv214d9lm0/2eepu1259954782.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t125995488925cjzhv214d9lm0/3ls7k1259954782.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t125995488925cjzhv214d9lm0/3ls7k1259954782.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t125995488925cjzhv214d9lm0/4cx3q1259954782.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t125995488925cjzhv214d9lm0/4cx3q1259954782.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t125995488925cjzhv214d9lm0/5xc6t1259954782.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t125995488925cjzhv214d9lm0/5xc6t1259954782.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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