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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 05:25:38 -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/t1259929615orktg1w753iyn6y.htm/, Retrieved Fri, 04 Dec 2009 13:27:02 +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/t1259929615orktg1w753iyn6y.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 «

1,4816 1,4562 1,4268 1,4088 1,4016 1,3650 1,3190 1,3050 1,2785 1,3239 1,3449 1,2732 1,3322 1,4369 1,4975 1,5770 1,5553 1,5557 1,5750 1,5527 1,4748 1,4718 1,4570 1,4684 1,4227 1,3896 1,3622 1,3716 1,3419 1,3511 1,3516 1,3242 1,3074 1,2999 1,3213 1,2881 1,2611 1,2727 1,2811 1,2684 1,2650 1,2770 1,2271 1,2020 1,1938 1,2103 1,1856 1,1786 1,2015 1,2256 1,2292 1,2037 1,2165 1,2694 1,2938 1,3201 1,3014 1,3119 1,3408 1,2991

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	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	1.4816	1.4816	0	0	0
2	1.4562	1.4575207999565	-0.00132079994551282	-0.00132079995650077	-0.426435187031089
3	1.4268	1.42823266926491	-0.00143266926490572	-0.00143266926490572	-0.826541506682138
4	1.4088	1.41029841263809	-0.00149841263808581	-0.00149841263808581	-0.487681100692778
5	1.4016	1.40312094855557	-0.00152094855557244	-0.00152094855557244	-0.167835020489262
6	1.365	1.36665905505158	-0.00165905505158485	-0.00165905505158485	-1.03261406592776
7	1.319	1.32083294110301	-0.00183294110301073	-0.00183294110301073	-1.30526443616929
8	1.305	1.30688046867487	-0.00188046867486810	-0.00188046867486810	-0.358164477712999
9	1.2785	1.28047626451267	-0.00197626451266697	-0.00197626451266697	-0.724736267722295
10	1.3239	1.32569263558796	-0.00179263558795749	-0.00179263558795749	1.39464706268916
11	1.3449	1.34660463313754	-0.00170463313753521	-0.00170463313753521	0.670967231770499
12	1.2732	1.27517384607608	-0.0019738460760805	-0.00197384607608049	-2.06053167576784
13	1.3322	1.29864567021683	-0.00305039361750168	0.0335543297831709	0.908524196673319
14	1.4369	1.43653836350162	0.000361636342605157	0.000361636498382501	3.54372588351020
15	1.4975	1.49702903812942	0.000470961870582468	0.000470961870582458	1.77511095853184
16	1.577	1.57638586958426	0.000614130415743534	0.000614130415743528	2.32884052408926
17	1.5553	1.55472622063322	0.000573779366778998	0.000573779366779008	-0.657557496272557
18	1.5557	1.55512653431438	0.000573465685616275	0.000573465685616264	-0.00512097536522936
19	1.575	1.57439279281162	0.000607207188375647	0.00060720718837565	0.551839259784684
20	1.5527	1.55213399282393	0.00056600717606827	0.000566007176068271	-0.67503770671021
21	1.4748	1.47437486536611	0.000425134633887282	0.000425134633887268	-2.31226787157924
22	1.4718	1.47138100360013	0.000418996399868614	0.00041899639986861	-0.100933408217086
23	1.457	1.45660822899579	0.000391771004212843	0.000391771004212837	-0.448480952493273
24	1.4684	1.46798857144430	0.000411428555696687	0.000411428555696696	0.324396484186423
25	1.4227	1.43454155634921	0.00107650511441964	-0.0118415563492138	-1.10126877603234
26	1.3896	1.38924376466441	0.000356235284039582	0.000356235335589112	-1.24331648436759
27	1.3622	1.36187638074137	0.000323619258626418	0.000323619258626414	-0.818185982906271
28	1.3716	1.37126572771238	0.000334272287623892	0.000334272287623883	0.267549707947931
29	1.3419	1.34160093787905	0.000299062120953077	0.000299062120953085	-0.885338169794054
30	1.3511	1.3507905152352	0.000309484764798849	0.000309484764798838	0.262378438573609
31	1.3516	1.35129029241037	0.000309707589634473	0.000309707589634475	0.00561593900392191
32	1.3242	1.32392266356397	0.000277336436034375	0.000277336436034372	-0.816817268774445
33	1.3074	1.30714259044421	0.000257409555789821	0.000257409555789808	-0.503400217378331
34	1.2999	1.29965163171405	0.000248368285946419	0.000248368285946414	-0.228670573412785
35	1.3213	1.32102700816151	0.000272991838486511	0.000272991838486504	0.623501827896867
36	1.2881	1.28786593024490	0.000234069755104313	0.000234069755104321	-0.986708071547363
37	1.2611	1.26668746170399	0.000507951055583273	-0.00558746170399208	-0.674528374654215
38	1.2727	1.27213556513670	0.000564434767028054	0.000564434863304471	0.136116288107659
39	1.2811	1.28052875761665	0.00057124238334515	0.000571242383345147	0.231008727017761
40	1.2684	1.26784027779238	0.000559722207619165	0.000559722207619156	-0.391263915138439
41	1.265	1.26444371207011	0.000556287929888535	0.000556287929888545	-0.116740916394658
42	1.277	1.27643379550849	0.000566204491513947	0.000566204491513933	0.337384762474245
43	1.2271	1.22657748919220	0.000522510807797504	0.000522510807797505	-1.48785068199346
44	1.202	1.20149965399403	0.000500346005972461	0.000500346005972458	-0.755406213968388
45	1.1938	1.19330717373996	0.000492826260042849	0.000492826260042838	-0.256504834555903
46	1.2103	1.20979335061923	0.000506649380771294	0.000506649380771291	0.471925942101908
47	1.1856	1.18511509923828	0.000484900761719691	0.000484900761719684	-0.743146565720972
48	1.1786	1.17812155173896	0.00047844826103745	0.000478448261037457	-0.220671152371540
49	1.2015	1.20410273220399	0.000236612009283087	-0.00260273220398864	0.790458499377938
50	1.2256	1.22517489645123	0.000425103432418337	0.000425103548770822	0.582845713590406
51	1.2292	1.22877270849228	0.000427291507716962	0.000427291507716957	0.0936109569276325
52	1.2037	1.20329056475384	0.000409435246158402	0.000409435246158393	-0.764459252765785
53	1.2165	1.21608203717994	0.000417962820064336	0.000417962820064346	0.36533257307745
54	1.2694	1.26894594224339	0.000454057756609353	0.000454057756609327	1.54741955714384
55	1.2938	1.29332948455095	0.000470515449047248	0.000470515449047252	0.70604020149205
56	1.3201	1.31961174452017	0.000488255479833286	0.000488255479833283	0.761576161780302
57	1.3014	1.30092491422208	0.000475085777923276	0.000475085777923262	-0.565761247670541
58	1.3119	1.31141803842350	0.000481961576502212	0.000481961576502208	0.295582332635997
59	1.3408	1.34029856067249	0.000501439327512362	0.000501439327512355	0.837899644406836
60	1.2991	1.29862746576822	0.00047253423177731	0.000472534231777324	-1.24430049621198

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259929615orktg1w753iyn6y/1xayz1259929534.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259929615orktg1w753iyn6y/1xayz1259929534.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259929615orktg1w753iyn6y/2uikb1259929534.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259929615orktg1w753iyn6y/2uikb1259929534.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259929615orktg1w753iyn6y/3451r1259929534.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259929615orktg1w753iyn6y/3451r1259929534.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259929615orktg1w753iyn6y/4cjym1259929534.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259929615orktg1w753iyn6y/4cjym1259929534.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259929615orktg1w753iyn6y/53fxe1259929534.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259929615orktg1w753iyn6y/53fxe1259929534.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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