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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: Fri, 04 Dec 2009 12:05:11 -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/t1259953542lbcne2lg2kfz3oe.htm/, Retrieved Fri, 04 Dec 2009 20:05:48 +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/t1259953542lbcne2lg2kfz3oe.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 «

14.9 18.6 19.1 18.8 18.2 18 19 20.7 21.2 20.7 19.6 18.6 18.7 23.8 24.9 24.8 23.8 22.3 21.7 20.7 19.7 18.4 17.4 17 18 23.8 25.5 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

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	6 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	14.9	14.9	0	0	0
2	18.6	18.4963663363712	1.95952200894963	0.103633663628848	2.67574541083026
3	19.1	19.0017999365895	0.789189066721225	0.0982000634105242	-1.09926465742992
4	18.8	18.6893326054695	-0.0819720301077848	0.110667394530525	-0.88351553292114
5	18.2	18.0852634657129	-0.495402408713859	0.114736534287079	-0.421087081668346
6	18	17.8804873802303	-0.265180392917277	0.119512619769678	0.234513407124899
7	19	18.8750395746505	0.732805723110806	0.124960425349499	1.01659379848851
8	20.7	20.5790040450088	1.50219178423542	0.120995954991207	0.783731637440376
9	21.2	21.0926828747593	0.719053988075138	0.107317125240685	-0.797739789429887
10	20.7	20.5906039300775	-0.248375069964352	0.109396069922484	-0.985467253946108
11	19.6	19.4874950900653	-0.92552856489005	0.112504909934693	-0.689779358614831
12	18.6	18.4825677346654	-0.988431391960232	0.117432265334611	-0.0640756815651315
13	18.7	19.5802450329432	0.63599789298586	-0.880245032943204	1.81717330558587
14	23.8	23.6336704662259	2.96176953273286	0.166329533774143	2.25596283857556
15	24.9	24.7899553301526	1.53109006944619	0.110044669847427	-1.4191781479967
16	24.8	24.6672342767233	0.230695431852504	0.132765723276674	-1.32112552682345
17	23.8	23.6597219728002	-0.743869702391468	0.140278027199789	-0.992692153068098
18	22.3	22.1596515174833	-1.33916482229958	0.140348482516665	-0.606393989794981
19	21.7	21.5433064816194	-0.770136650338426	0.156693518380579	0.579637914084658
20	20.7	20.5478414789925	-0.947524077101723	0.152158521007479	-0.180694901995688
21	19.7	19.5526192416813	-0.985074014522	0.147380758318688	-0.0382500747013373
22	18.4	18.2556005298177	-1.23065006115613	0.144399470182251	-0.250154934121929
23	17.4	17.2348323352030	-1.06541243520625	0.165167664797027	0.168318936995219
24	17	16.8570602808589	-0.524230497044236	0.142939719141127	0.551288476205146
25	18	19.3546424097877	1.83813004492188	-1.35464240978769	2.52028624841156
26	23.8	23.5906128565651	3.56245780446402	0.209387143434875	1.71548337349918
27	25.5	25.4034666323282	2.18612132555086	0.0965333676718153	-1.38271892324709
28	25.6	25.4761548945288	0.532695890603911	0.123845105471156	-1.67984582071548
29	23.7	23.5659805432428	-1.38012050787108	0.134019456757183	-1.94841302878142
30	22	21.8612771969591	-1.63432120665732	0.138722803040948	-0.258940390083650
31	21.3	21.1122099702114	-0.941026774520532	0.187790029788623	0.706221206934525
32	20.7	20.5393365378003	-0.65270379144625	0.160663462199673	0.293698904322016
33	20.4	20.2341127210846	-0.380571342852756	0.165887278915445	0.277206496272518
34	20.3	20.1436842126631	-0.153340335203859	0.156315787336867	0.231467846116482
35	20.4	20.2030317799140	0.0132444059073885	0.196968220086033	0.169692280945363
36	19.8	19.7046967814650	-0.387176308674755	0.0953032185349647	-0.407945161905656
37	19.5	21.1297265954815	1.02794309669007	-1.62972659548154	1.48271640034508
38	23.1	22.8684619366577	1.55189471247967	0.231538063342316	0.52597406976628
39	23.5	23.4066347629893	0.758802522538638	0.0933652370107018	-0.80197510590265
40	23.5	23.3331567444107	0.110218177337289	0.166843255589294	-0.658890555859676
41	22.9	22.7583142710786	-0.42402720431889	0.141685728921434	-0.54418400017232
42	21.9	21.7890760967952	-0.849307098078393	0.110923903204748	-0.433209393622026
43	21.5	21.3069770570496	-0.56287853957346	0.193022942950386	0.29176916548235
44	20.5	20.3555221305564	-0.865972774956012	0.144477869443552	-0.308745570150847
45	20.2	20.0275731302723	-0.44630778574107	0.172426869727690	0.427489865582739
46	19.4	19.2670945002758	-0.691371828148299	0.132905499724190	-0.249633473705347
47	19.2	18.9559171978162	-0.394785120192152	0.244082802183789	0.302121020156532
48	18.8	18.7431486512696	-0.252924954882053	0.0568513487303511	0.144553995138398
49	18.8	20.4309765259120	1.2595856319138	-1.63097652591196	1.56953414634139
50	22.6	22.3442638188545	1.74804911047923	0.255736181145520	0.492583844589775
51	23.3	23.2200128706681	1.06846113927952	0.0799871293318805	-0.689780782450303
52	23	22.8526861167906	-0.0471980932328169	0.147313883209369	-1.13333102016186
53	21.4	21.2679155967925	-1.24258392127100	0.132084403207512	-1.21760144990606
54	19.9	19.8029482758241	-1.41552605262346	0.0970517241758727	-0.176166552709623
55	18.8	18.5801599358129	-1.26564078420919	0.21984006418706	0.152679956194470
56	18.6	18.4499206974265	-0.382693695003875	0.150079302573451	0.899410046192465
57	18.4	18.2165947665365	-0.266537358924606	0.183405233463466	0.118322133278772
58	18.6	18.4651228591248	0.134023237565158	0.134877140875249	0.408029936691651
59	19.9	19.6074242264006	0.918177833591412	0.292575773599369	0.798786383587909
60	19.2	19.2338836305732	-0.085342739094769	-0.0338836305732321	-1.02281489359146
61	18.4	20.0825764786328	0.641142144687673	-1.68257647863281	0.749424269891704

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259953542lbcne2lg2kfz3oe/1m21n1259953504.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259953542lbcne2lg2kfz3oe/1m21n1259953504.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259953542lbcne2lg2kfz3oe/2dbij1259953504.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259953542lbcne2lg2kfz3oe/2dbij1259953504.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259953542lbcne2lg2kfz3oe/3aigr1259953504.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259953542lbcne2lg2kfz3oe/3aigr1259953504.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259953542lbcne2lg2kfz3oe/47qxz1259953504.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259953542lbcne2lg2kfz3oe/47qxz1259953504.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259953542lbcne2lg2kfz3oe/5ptz61259953505.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259953542lbcne2lg2kfz3oe/5ptz61259953505.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = -1.8 ; par3 = 2 ; par4 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 12 ; par2 = -1.8 ; par3 = 2 ; par4 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

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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