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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: Sun, 06 Dec 2009 13:06:51 -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/06/t1260130179lhurq7av1gecypf.htm/, Retrieved Sun, 06 Dec 2009 21:09:46 +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/06/t1260130179lhurq7av1gecypf.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 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

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	8	8	0	0	0
2	8.1	8.09930444919887	0.0993619327261385	0.000695550801130709	0.308511249714436
3	7.7	7.70967023168305	-0.379823096535826	-0.00967023168305377	-1.49769065662826
4	7.5	7.4954508121445	-0.218449601623505	0.00454918785550643	0.499193671101117
5	7.6	7.59575237338374	0.0922966337891054	0.0042476266162609	0.961635756904163
6	7.8	7.79998651726657	0.201429193707602	1.34827334256824e-05	0.337716734691692
7	7.8	7.80440578508284	0.0093581382982604	-0.00440578508283849	-0.594374418874952
8	7.8	7.79989706675575	-0.00416107944976505	0.000102933244253802	-0.0418359609874697
9	7.5	7.50546242137795	-0.287157700128211	-0.00546242137795457	-0.875748567568387
10	7.5	7.49448998041217	-0.0178962028258241	0.00551001958783016	0.833244474791906
11	7.1	7.10808047676384	-0.377171139797197	-0.0080804767638441	-1.11179600188506
12	7.5	7.48589570393107	0.358888261947246	0.0141042960689254	2.27777619810589
13	7.5	7.5081715272232	0.030766744971273	-0.00817152722320605	-1.01562861635822
14	7.6	7.5857758430221	0.076443186856889	0.0142241569778975	0.141721318024696
15	7.7	7.70808490254969	0.120444402834582	-0.00808490254968673	0.137155056554520
16	7.7	7.70503396076909	0.00224290686069793	-0.00503396076908836	-0.365535498036017
17	7.9	7.8949439847997	0.181877837955256	0.00505601520030615	0.555922000900198
18	8.1	8.09522232288309	0.199492864384523	0.00477767711691332	0.054510592384948
19	8.2	8.21156863672521	0.119896450216909	-0.0115686367252141	-0.246315523744929
20	8.2	8.19136317121849	-0.0142226437383779	0.00863682878151016	-0.415038890572853
21	8.2	8.21762093618107	0.0245291499262838	-0.0176209361810702	0.11991955150004
22	7.9	7.88334811969565	-0.318951136719168	0.0166518803043466	-1.06291859284222
23	7.3	7.3366405515546	-0.536982619866879	-0.0366405515545952	-0.674710439127613
24	6.9	6.87274831376788	-0.467013724302097	0.0272516862321208	0.216522756053243
25	6.6	6.60322880781594	-0.277984677233863	-0.00322880781593666	0.585118113270929
26	6.7	6.68077828080492	0.0624884851555574	0.0192217191950844	1.05523538936971
27	6.9	6.89553893442975	0.206713094994031	0.00446106557024695	0.448346259232338
28	7	7.01670798630837	0.125703228716512	-0.0167079863083701	-0.250537507528987
29	7.1	7.09877709700471	0.084397080645465	0.00122290299528812	-0.127832287785298
30	7.2	7.19359486422646	0.0942634662767699	0.00640513577354281	0.0305320301909731
31	7.1	7.1097016351423	-0.0744170650141647	-0.00970163514229267	-0.521991434909512
32	6.9	6.90500525228746	-0.197765369007872	-0.00500525228745867	-0.381708087264946
33	7	6.99683489403354	0.076422523579298	0.00316510596645533	0.848489486405636
34	6.8	6.78486847607902	-0.196624015855256	0.0151315239209758	-0.844957502523326
35	6.4	6.43998676398004	-0.336995346712752	-0.0399867639800414	-0.434387071684056
36	6.7	6.65150330654255	0.182325881130079	0.0484966934574537	1.60707073403234
37	6.6	6.62560915364917	-0.0147828240076449	-0.0256091536491688	-0.61016753382485
38	6.4	6.39911093706961	-0.215285324908693	0.00088906293038985	-0.620897814428474
39	6.3	6.28569187521146	-0.119487006451253	0.0143081247885372	0.297268925891285
40	6.2	6.21185284272088	-0.0765268697523408	-0.0118528427208787	0.13289122419191
41	6.5	6.49181616988196	0.258765320956135	0.0081838301180381	1.0376043736334
42	6.8	6.78713450151195	0.293151256863413	0.0128654984880542	0.106409678177342
43	6.8	6.80608827599742	0.0352052074693835	-0.00608827599741574	-0.798228167377785
44	6.4	6.44443838014493	-0.338123841981909	-0.0444383801449323	-1.15528735084653
45	6.1	6.08321905330234	-0.35985009921521	0.0167809466976619	-0.0672330974337153
46	5.8	5.75831892912312	-0.326972000353692	0.0416810708768786	0.101743081994066
47	6.1	6.14758226120233	0.346809114373828	-0.0475822612023337	2.08505650834347
48	7.2	7.12567700265876	0.940648154446028	0.0743229973412384	1.83767299461869
49	7.3	7.34575538971294	0.262895392745059	-0.0457553897129378	-2.09813128064469
50	6.9	6.92888049085359	-0.37661523213112	-0.0288804908535856	-1.97945586579179
51	6.1	6.09037159746416	-0.809210615874872	0.00962840253584268	-1.34095569420808
52	5.8	5.80630513631187	-0.316903597736691	-0.0063051363118675	1.52319813244369
53	6.2	6.1754103140594	0.32577362947497	0.0245896859406047	1.98873885773683
54	7.1	7.06452695546595	0.853623162880105	0.0354730445340464	1.63348204105457
55	7.7	7.69952635570056	0.648766877760303	0.000473644299443214	-0.633938179025671
56	7.9	7.95928111000714	0.284256019334568	-0.0592811100071382	-1.12799918071472
57	7.7	7.68073704880277	-0.243093421202412	0.0192629511972343	-1.63191183021578
58	7.4	7.38031644492034	-0.296809909567934	0.0196835550796612	-0.166228641584115
59	7.5	7.5848011468465	0.172913430160318	-0.0848011468465008	1.45358846577102
60	8	7.90177211893404	0.307889335304279	0.0982278810659624	0.417693835744486

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/06/t1260130179lhurq7av1gecypf/1z8rs1260130008.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/06/t1260130179lhurq7av1gecypf/1z8rs1260130008.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/06/t1260130179lhurq7av1gecypf/2fehi1260130008.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/06/t1260130179lhurq7av1gecypf/2fehi1260130008.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/06/t1260130179lhurq7av1gecypf/35ijw1260130008.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/06/t1260130179lhurq7av1gecypf/35ijw1260130008.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/06/t1260130179lhurq7av1gecypf/4cnvw1260130008.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/06/t1260130179lhurq7av1gecypf/4cnvw1260130008.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/06/t1260130179lhurq7av1gecypf/5xs701260130008.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/06/t1260130179lhurq7av1gecypf/5xs701260130008.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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