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decomposition 3

*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 02:08:52 -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/t1259917787hzdwioeejadtyrf.htm/, Retrieved Fri, 04 Dec 2009 10:09:53 +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/t1259917787hzdwioeejadtyrf.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 «

5.7 6.1 6 5.9 5.8 5.7 5.6 5.4 5.4 5.5 5.6 5.7 5.9 6.1 6 5.8 5.8 5.7 5.5 5.3 5.2 5.2 5 5.1 5.1 5.2 4.9 4.8 4.5 4.5 4.4 4.4 4.2 4.1 3.9 3.8 3.9 4.2 4.1 3.8 3.6 3.7 3.5 3.4 3.1 3.1 3.1 3.2 3.3 3.5 3.6 3.5 3.3 3.2 3.1 3.2 3 3 3.1 3.4

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	11 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	5.7	5.7	0	0	0
2	6.1	6.07884880815518	0.021506092449984	0.0211511918448191	1.52963603821458
3	6	5.98081389252993	0.0196210034839888	0.0191861074700705	-0.801081630437777
4	5.9	5.8806974440651	0.0171237270371641	0.0193025559349021	-0.799935278947233
5	5.8	5.78108815167059	0.0140527026745525	0.0189118483294073	-0.777645075668014
6	5.7	5.68146257095776	0.0104867702924174	0.0185374290422363	-0.75523168838216
7	5.6	5.5818085261228	0.00651170061781887	0.0181914738772051	-0.729844260706367
8	5.4	5.38304916150118	-0.00179307611904878	0.0169508384988162	-1.35693753496063
9	5.4	5.38158935004924	-0.00177825899900189	0.0184106499507612	0.00219809645207262
10	5.5	5.48109825571713	0.00309370584769649	0.018901744282871	0.666675182117168
11	5.6	5.58106636186441	0.00807173407984241	0.0189336381355904	0.636426540786974
12	5.7	5.68085312693168	0.0130549010288591	0.0191468730683169	0.601498343837729
13	5.9	5.9773419778874	0.0209125052151983	-0.0773419778873993	2.21508419190292
14	6.1	6.08917510333549	0.0273773709266605	0.0108248966645065	0.507280713144852
15	6	5.99351037283877	0.0198867847500754	0.0064896271612301	-0.802957580818163
16	5.8	5.79328481101275	0.00616177418513105	0.006715188987245	-1.43433420819565
17	5.8	5.79040339739136	0.00558228993531618	0.0095966026086434	-0.0588758815277227
18	5.7	5.69260724985264	-0.00119305111860298	0.00739275014736436	-0.672481894469816
19	5.5	5.4924861031196	-0.0144831339901178	0.00751389688039589	-1.29307690457191
20	5.3	5.29372235341134	-0.0269980557961081	0.00627764658865619	-1.19708640493505
21	5.2	5.19170791706359	-0.0321644311217447	0.00829208293641082	-0.48702920834903
22	5.2	5.19063437628873	-0.0299974103452812	0.00936562371127295	0.201751549253228
23	5	4.99328022398454	-0.0417843741092933	0.00671977601545689	-1.08556691450785
24	5.1	5.09056384911272	-0.0319153865619695	0.009436150887284	0.901520025084876
25	5.1	5.16914873806469	-0.0246871781444536	-0.0691487380646942	0.781885054008576
26	5.2	5.19018446917844	-0.0212497538881903	0.00981553082155947	0.271193288844019
27	4.9	4.89828077600158	-0.0408759769876554	0.00171922399842354	-1.75352693601003
28	4.8	4.79539959618549	-0.0453808676869526	0.00460040381450809	-0.401373510111418
29	4.5	4.49613858087191	-0.0639085674474407	0.00386141912809288	-1.64331607786774
30	4.5	4.49072297243223	-0.0596246536884174	0.00927702756776707	0.378560208904886
31	4.4	4.39349943229872	-0.0623866139156848	0.006500567701279	-0.243303499934338
32	4.4	4.3933599153963	-0.0578022539319941	0.00664008460370301	0.402756441979409
33	4.2	4.19724190768549	-0.0680113421442882	0.00275809231451025	-0.894853206835917
34	4.1	4.08988793987476	-0.0709207211864103	0.0101120601252424	-0.254511840152121
35	3.9	3.89815198280308	-0.0798706248766471	0.00184801719691903	-0.78156431551142
36	3.8	3.79322121014328	-0.0817278823740084	0.0067787898567181	-0.162036599737284
37	3.9	3.9401539810759	-0.0651558348692222	-0.0401539810759024	1.56651754070755
38	4.2	4.18187184769333	-0.0421247978703715	0.0181281523066671	1.87004402768307
39	4.1	4.10109719577813	-0.0450017564418658	-0.00109719577812907	-0.250035773377558
40	3.8	3.79598262698776	-0.0643580364420527	0.00401737301224230	-1.68135936194194
41	3.6	3.59820658684057	-0.0742937758376488	0.00179341315942727	-0.862497209824643
42	3.7	3.68509853743323	-0.0622832402415998	0.0149014625667696	1.04200965505825
43	3.5	3.49879582636976	-0.0715287399007832	0.00120417363024326	-0.801727117250042
44	3.4	3.39102150805701	-0.0742318929348198	0.00897849194299096	-0.234306505665383
45	3.1	3.10135690759451	-0.090304158839998	-0.00135690759450704	-1.39262646837832
46	3.1	3.08457632567703	-0.0848172873631888	0.0154236743229741	0.47527926407406
47	3.1	3.09429375033841	-0.0777600725696301	0.00570624966159481	0.611148465526161
48	3.2	3.19298645835192	-0.0645930659443174	0.00701354164807784	1.14009233794824
49	3.3	3.35273618860181	-0.0479862437124517	-0.0527361886018095	1.51226097657081
50	3.5	3.48072067290545	-0.0348315493139966	0.0192793270945480	1.08868800693393
51	3.6	3.59440210036854	-0.0237389574813225	0.00559789963145971	0.960308896214668
52	3.5	3.49585695527987	-0.0293260501325651	0.00414304472012664	-0.483341446501009
53	3.3	3.30672158577066	-0.0412631631007524	-0.00672158577066073	-1.03268373535159
54	3.2	3.18419733750798	-0.0473336081685154	0.0158026624920215	-0.525128986295893
55	3.1	3.10017755206214	-0.0500743730394271	-0.000177552062141973	-0.237075410837949
56	3.2	3.18270208583513	-0.0401675160373335	0.0172979141648653	0.856887313562906
57	3	3.00727807172696	-0.0502734642826878	-0.00727807172695857	-0.874061653703504
58	3	2.98431228219589	-0.0482330071032828	0.0156877178041127	0.176472542310693
59	3.1	3.09323284994450	-0.0364893619244272	0.00676715005550279	1.01567524940561
60	3.4	3.39004921441626	-0.0115931649931183	0.0099507855837353	2.15284544647217

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259917787hzdwioeejadtyrf/1saqz1259917721.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259917787hzdwioeejadtyrf/1saqz1259917721.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259917787hzdwioeejadtyrf/2jnhf1259917721.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259917787hzdwioeejadtyrf/2jnhf1259917721.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259917787hzdwioeejadtyrf/3ge7e1259917721.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259917787hzdwioeejadtyrf/3ge7e1259917721.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259917787hzdwioeejadtyrf/4h4ym1259917721.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259917787hzdwioeejadtyrf/4h4ym1259917721.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259917787hzdwioeejadtyrf/5nlbs1259917721.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259917787hzdwioeejadtyrf/5nlbs1259917721.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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