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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: Thu, 03 Dec 2009 11:24:15 -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/03/t1259864807l40oh1x97ipc41m.htm/, Retrieved Thu, 03 Dec 2009 19:26:54 +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/03/t1259864807l40oh1x97ipc41m.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 «

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 8 8.1 8

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	8.1	8.1	0	0	0
2	7.7	7.70255673257361	-0.397654567698998	-0.00255673257360823	-1.23520546066601
3	7.5	7.49489669492155	-0.211174078741286	0.00510330507845288	0.582804441865597
4	7.6	7.59569645560671	0.0934160143173236	0.00430354439329310	0.942920929924098
5	7.8	7.7993825242758	0.201121008367081	0.000617475724206775	0.333533634956366
6	7.8	7.80346592948066	0.00865740305028759	-0.00346592948065967	-0.596001298891416
7	7.8	7.79928988768668	-0.00387800293414725	0.0007101123133146	-0.0388183381561296
8	7.5	7.50446420003691	-0.288068718009973	-0.00446420003691253	-0.880052173394744
9	7.5	7.49427947229257	-0.0166381905979773	0.00572052770743157	0.840537754486445
10	7.1	7.10690986218564	-0.378759894815383	-0.00690986218564131	-1.12138073420551
11	7.5	7.48630685196682	0.36178985460667	0.0136931480331752	2.29325724487263
12	7.5	7.50835699008641	0.0299401183446609	-0.00835699008640986	-1.02763766038116
13	7.6	7.59789715389164	0.0881474617866507	0.00210284610835877	0.180289630740346
14	7.7	7.70155588306465	0.103302538349973	-0.00155588306464919	0.0470458683674718
15	7.7	7.70329411603176	0.00558305067796482	-0.00329411603175623	-0.304688822394776
16	7.9	7.89526414781655	0.184490440702731	0.00473585218345467	0.553686999538775
17	8.1	8.09523937723554	0.19935541259305	0.00476062276445696	0.046034554943113
18	8.2	8.2104487505738	0.118569235237501	-0.0104487505738044	-0.2501699501135
19	8.2	8.19142007994629	-0.013533186733441	0.00857992005370687	-0.409081071479970
20	8.2	8.21620359729254	0.0232530085837302	-0.0162035972925366	0.113915653261319
21	7.9	7.88396454635163	-0.318039695756277	0.0160354536483722	-1.05687965998974
22	7.3	7.33390409274867	-0.540792910621740	-0.0339040927486718	-0.689798930240939
23	6.9	6.87381767498871	-0.463309814882401	0.0261823250112894	0.239941586523382
24	6.6	6.60463692943745	-0.276935581305291	-0.00463692943744613	0.57714468085457
25	6.7	6.69091033448657	0.0717118683733375	0.00908966551343184	1.07992154152149
26	6.9	6.89113157358593	0.195129219064833	0.0088684264140757	0.382752681603925
27	7	7.01386355878197	0.126330843643383	-0.0138635587819723	-0.213991760031918
28	7.1	7.09884536639562	0.0870508092175772	0.00115463360437555	-0.121568169407592
29	7.2	7.19394345057423	0.0946932345682354	0.00605654942577448	0.0236676906645659
30	7.1	7.1089902381741	-0.0759408952527884	-0.00899023817409676	-0.52840113790303
31	6.9	6.90412059679866	-0.198401705913208	-0.00412059679866323	-0.379224050060212
32	7	6.99705372903545	0.0783149585242846	0.00294627096455227	0.856907296032036
33	6.8	6.78538678111635	-0.197116472744618	0.0146132188836501	-0.852927344943819
34	6.4	6.4376234193637	-0.340204553727664	-0.0376234193636979	-0.443100252369668
35	6.7	6.65332840894995	0.187815237276742	0.0466715910500487	1.63511749661135
36	6.6	6.62644266576581	-0.0161097996663322	-0.0264426657658141	-0.631494753731989
37	6.4	6.4041331520194	-0.211931831054026	-0.0041331520194012	-0.606586612876887
38	6.3	6.28361242048162	-0.125085726249095	0.0163875795183786	0.269124863321676
39	6.2	6.2095157389639	-0.0769735396405751	-0.00951573896390027	0.149396470400398
40	6.5	6.49204198979235	0.262436074793489	0.00795801020764919	1.05063559813044
41	6.8	6.78811394552979	0.294175282806328	0.0118860544702104	0.0982895948557093
42	6.8	6.80549277832682	0.0329419259274602	-0.00549277832681824	-0.808962585659557
43	6.4	6.44149526477237	-0.341684370456125	-0.0414952647723735	-1.16010380687189
44	6.1	6.08413228524105	-0.356481460895329	0.0158677147589512	-0.0458220897755935
45	5.8	5.7599093543658	-0.326036753909576	0.0400906456342063	0.0942779972191758
46	6.1	6.14536710186944	0.345454695558719	-0.0453671018694404	2.07940472039105
47	7.2	7.12837326388787	0.947164761929533	0.07162673611213	1.86331593617394
48	7.3	7.34615581697957	0.258814331735642	-0.0461558169795662	-2.1316170463579
49	6.9	6.93055891689458	-0.377588104499472	-0.030558916894576	-1.97142932402068
50	6.1	6.0882733484193	-0.816192245348685	0.0117266515806964	-1.35856658116138
51	5.8	5.80312939773405	-0.31718610017511	-0.00312939773405062	1.54791396820684
52	6.2	6.17568000616938	0.331486770938726	0.0243199938306198	2.00833139546841
53	7.1	7.06652078620405	0.857215544801277	0.0334792137959525	1.62799411243550
54	7.7	7.69899860853004	0.645953410599213	0.0010013914699612	-0.654221551016279
55	7.9	7.95599722881851	0.280310792972354	-0.0559972288185112	-1.13228288505511
56	7.7	7.68102995309995	-0.241680984377733	0.0189700469000546	-1.61645008446091
57	7.4	7.37941566361595	-0.298021236211346	0.0205843363840541	-0.174468623858556
58	7.5	7.58068076428983	0.171335087180122	-0.0806807642898314	1.45345384493380
59	8	7.90455145702767	0.314727585850782	0.0954485429723267	0.444044005965626
60	8.1	8.12852543807911	0.229418842255042	-0.0285254380791152	-0.264176949136665
61	8	8.00403422492856	-0.103240101283659	-0.0040342249285615	-1.03050743528850

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259864807l40oh1x97ipc41m/13xt01259864651.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259864807l40oh1x97ipc41m/13xt01259864651.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259864807l40oh1x97ipc41m/2ehnq1259864651.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259864807l40oh1x97ipc41m/2ehnq1259864651.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259864807l40oh1x97ipc41m/3g7ns1259864651.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259864807l40oh1x97ipc41m/3g7ns1259864651.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259864807l40oh1x97ipc41m/44mw61259864651.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259864807l40oh1x97ipc41m/44mw61259864651.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259864807l40oh1x97ipc41m/54o6j1259864651.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259864807l40oh1x97ipc41m/54o6j1259864651.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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