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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: Wed, 02 Dec 2009 13:16:44 -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/02/t1259785080pt1hpkhb3fe7qsi.htm/, Retrieved Wed, 02 Dec 2009 21:18:25 +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/02/t1259785080pt1hpkhb3fe7qsi.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 «

17409 11514 31514 27071 29462 26105 22397 23843 21705 18089 20764 25316 17704 15548 28029 29383 36438 32034 22679 24319 18004 17537 20366 22782 19169 13807 29743 25591 29096 26482 22405 27044 17970 18730 19684 19785 18479 10698 31956 29506 34506 27165 26736 23691 18157 17328 18205 20995 17382 9367

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	17409	17409	0	0	0
2	11514	12506.2913059122	-244.387739386135	-992.291305912165	-1.02575576745848
3	31514	25092.0483989720	263.455919320672	6421.95160102797	3.76129702035886
4	27071	27652.2129060086	302.462594822305	-581.212906008617	0.741875577877264
5	29462	29050.3180734758	311.562729471478	411.681926524172	0.355364829596963
6	26105	27110.5237053057	295.116204126061	-1005.52370530575	-0.729445538109279
7	22397	23562.9421303995	264.372364381204	-1165.94213039951	-1.24419095901657
8	23843	23171.2353446991	258.794670874886	671.764655300916	-0.212356228078968
9	21705	22014.8067871875	246.482159104604	-309.806787187482	-0.458005659444351
10	18089	19115.2362452726	218.841494314162	-1026.23624527259	-1.01803450880119
11	20764	19741.6170308696	222.451435515269	1022.38296913042	0.131859719083486
12	25316	23451.9675313528	253.62258362137	1864.03246864717	1.12836445405244
13	17704	20987.7645475884	339.995907711357	-3283.76454758839	-0.976674646361794
14	15548	21350.3355673948	340.221565663245	-5802.3355673948	0.00699642041598322
15	28029	22150.6916096930	350.707267440226	5878.30839030697	0.138600590819406
16	29383	27461.3429708618	439.151274821344	1921.65702913815	1.57609701786548
17	36438	32980.9961770256	495.525735769707	3457.00382297441	1.64104499550511
18	32034	32995.2004504311	491.70721780234	-961.200450431071	-0.155627092140527
19	22679	27228.8152803244	445.706650485012	-4549.81528032437	-2.02217823630513
20	24319	23951.9360236159	416.94240254346	367.063976384116	-1.20227708216880
21	18004	19245.3871065936	374.523783314291	-1241.38710659358	-1.65448116236522
22	17537	18338.7646718214	363.548564422382	-801.764671821442	-0.413763642385118
23	20366	19417.4341971657	368.880213836674	948.565802834328	0.230803776638622
24	22782	19857.9552832287	369.077368601661	2924.0447167713	0.0231366955959056
25	19169	21581.0356239563	362.788673990991	-2412.03562395634	0.448329681305185
26	13807	20963.9299932715	356.229060112604	-7156.92999327152	-0.312401526011202
27	29743	24394.844008536	404.36950849435	5348.15599146397	0.95332870143285
28	25591	25753.5233548705	419.710702964736	-162.523354870471	0.301844145863279
29	29096	25789.8036672149	414.829476951876	3306.19633278512	-0.123231459848063
30	26482	25505.0202581335	407.88740658539	976.97974186654	-0.225707514196883
31	22405	25465.3240553517	403.974609611703	-3060.32405535166	-0.144413026627387
32	27044	25071.3118895142	397.065687832675	1972.68811048584	-0.257400474720513
33	17970	21178.021495698	358.987482530739	-3208.02149569799	-1.38367003912921
34	18730	19966.7604933765	345.493809491176	-1236.76049337648	-0.50618789646751
35	19684	19136.3917322311	337.246330197892	547.608267768923	-0.378656367123165
36	19785	17904.5314534989	330.706908092256	1880.46854650105	-0.506312571618937
37	18479	19608.7327298361	334.635187056392	-1129.73272983607	0.445890115329529
38	10698	19524.0990299617	331.391787168035	-8826.09902996174	-0.133945274356414
39	31956	24308.0969214647	389.264055020307	7647.90307853527	1.39988119559272
40	29506	28166.3317945716	439.631256086559	1339.66820542836	1.09826822047231
41	34506	30461.5796827833	464.120334104424	4044.42031721667	0.594305123307022
42	27165	28128.7238796734	432.466524820806	-963.723879673433	-0.900295610737329
43	26736	28755.7281315107	434.435342018757	-2019.72813151070	0.0626797013560997
44	23691	23498.5204122548	379.494343463104	192.479587745232	-1.83369999111623
45	18157	21292.4082253792	355.157143192920	-3135.40822537921	-0.832689979903131
46	17328	18991.8576227201	331.757250943064	-1663.85762272014	-0.85453855715057
47	18205	17557.7686653879	318.433972507718	647.231334612083	-0.56779656990192
48	20995	18658.8026655763	323.244276365139	2336.19733442366	0.252016929465789
49	17382	18869.7802341722	322.543282116104	-1487.78023417223	-0.0361841810728551
50	9367	19849.1267170278	328.428850430367	-10482.1267170278	0.209801690485282

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259785080pt1hpkhb3fe7qsi/15p2c1259785002.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259785080pt1hpkhb3fe7qsi/15p2c1259785002.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259785080pt1hpkhb3fe7qsi/2x7lo1259785002.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259785080pt1hpkhb3fe7qsi/2x7lo1259785002.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259785080pt1hpkhb3fe7qsi/3tjhi1259785002.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259785080pt1hpkhb3fe7qsi/3tjhi1259785002.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259785080pt1hpkhb3fe7qsi/43ac71259785002.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259785080pt1hpkhb3fe7qsi/43ac71259785002.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259785080pt1hpkhb3fe7qsi/51giy1259785002.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259785080pt1hpkhb3fe7qsi/51giy1259785002.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = 0 ; par3 = 1 ; par4 = 1 ;

Parameters (R input):

par1 = 12 ; par2 = 0 ; par3 = 1 ; par4 = 1 ;

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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