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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: Thu, 03 Dec 2009 10:39:51 -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/03/t1259862056lm289erx5ptthsi.htm/, Retrieved Thu, 03 Dec 2009 18:41:03 +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/03/t1259862056lm289erx5ptthsi.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 «

115.6 111.9 107 107.1 100.6 99.2 108.4 103 99.8 115 90.8 95.9 114.4 108.2 112.6 109.1 105 105 118.5 103.7 112.5 116.6 96.6 101.9 116.5 119.3 115.4 108.5 111.5 108.8 121.8 109.6 112.2 119.6 104.1 105.3 115 124.1 116.8 107.5 115.6 116.2 116.3 119 111.9 118.6 106.9 103.2 118.6 118.7 102.8 100.6 94.9 94.5 102.9 95.3 92.5 102.7 91.5 89.5

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	115.6	115.6	0	0	0
2	111.9	113.687741698322	-0.0471880947713023	-1.78774169832153	-0.694616887019448
3	107	109.650650696342	-0.300420268999158	-2.65065069634248	-1.17986137036417
4	107.1	107.814489771174	-0.385595156621494	-0.714489771174473	-0.566908339019792
5	100.6	104.419200030583	-0.496982609736158	-3.81920003058255	-1.23743256303235
6	99.2	101.419839936339	-0.555269108731592	-2.21983993633902	-1.05663906033247
7	108.4	103.566241016991	-0.510382525763502	4.83375898300889	1.14565084555901
8	103	103.965582784848	-0.497212433639811	-0.96558278484805	0.385656753962141
9	99.8	102.390220127020	-0.512656541279543	-2.59022012702034	-0.456517879969998
10	115	107.274609641902	-0.433547339392617	7.72539035809793	2.28293493881863
11	90.8	101.772904482027	-0.508966894946389	-10.9729044820271	-2.14266125805436
12	95.9	97.8872412315243	-0.559236776159608	-1.98724123152428	-1.42734437175178
13	114.4	101.586003629562	-0.644494991047387	12.8139963704379	1.89998440734161
14	108.2	104.014112406986	-0.663732843833576	4.18588759301389	1.34566828907464
15	112.6	108.473969780654	-0.579723799837616	4.12603021934577	2.03765011748638
16	109.1	109.091962759106	-0.547802928386314	0.00803724089400593	0.467741863725307
17	105	108.696170420485	-0.543763716981717	-3.69617042048533	0.0614092171368355
18	105	108.610425413051	-0.533763963761378	-3.61042541305061	0.190500847750431
19	118.5	110.708530927764	-0.489342793652931	7.79146907223635	1.10937591968876
20	103.7	108.723510441766	-0.509550736680363	-5.02351044176596	-0.633337479110186
21	112.5	111.240773259540	-0.474549797153029	1.25922674045984	1.28309305009180
22	116.6	109.208001436983	-0.490083608045464	7.39199856301667	-0.66028082431665
23	96.6	107.514220213086	-0.499127164182574	-10.9142202130862	-0.509582683146522
24	101.9	106.906780162968	-0.499520615158058	-5.00678016296778	-0.04591202920547
25	116.5	106.616023582576	-0.499542033705390	9.88397641742383	0.0890426185936181
26	119.3	111.167437954341	-0.485961594362135	8.13256204565931	2.13501455937932
27	115.4	112.460169168803	-0.468526006664414	2.93983083119735	0.732356600130681
28	108.5	111.149181881861	-0.481860703171466	-2.64918188186052	-0.34176275406857
29	111.5	112.735400796103	-0.444007120938674	-1.23540079610252	0.844620551513454
30	108.8	113.365961531754	-0.425049793984041	-4.56596153175362	0.445604412221594
31	121.8	113.468199095062	-0.416957288587322	8.33180090493808	0.221313615354056
32	109.6	114.228788658551	-0.40201038768555	-4.62878865855079	0.497382907054865
33	112.2	112.356940498885	-0.417020417771914	-0.156940498884516	-0.622230937044485
34	119.6	111.394492866566	-0.421321308586175	8.2055071334341	-0.230922661251823
35	104.1	112.604607148882	-0.412128282963062	-8.50460714888187	0.690472793856605
36	105.3	112.430824121390	-0.411222634577728	-7.13082412138977	0.100889960881476
37	115	110.706514287640	-0.415547478620462	4.29348571235951	-0.555210311432967
38	124.1	112.716362589507	-0.403462274070319	11.3836374104934	1.01863608328307
39	116.8	113.573622595872	-0.393015451158836	3.2263774041275	0.523525100593334
40	107.5	112.883286111940	-0.396463177848309	-5.38328611194034	-0.122521932774575
41	115.6	114.524937754335	-0.36871405444321	1.07506224566542	0.840941179444782
42	116.2	117.417426362713	-0.323190776880803	-1.21742636271277	1.35571372482436
43	116.3	114.219682076951	-0.360424445039231	2.08031792304885	-1.20471851411286
44	119	116.731999858988	-0.328316434607079	2.26800014101163	1.21057249830677
45	111.9	115.315896545428	-0.33824442662793	-3.41589654542791	-0.459554304134722
46	118.6	113.269026546096	-0.350432278436624	5.33097345390403	-0.722327441597483
47	106.9	113.543308157550	-0.347016451361964	-6.6433081575504	0.264088344838222
48	103.2	112.195956954700	-0.351478738505313	-8.99595695469985	-0.422650512881255
49	118.6	113.340949444540	-0.344807623523081	5.25905055545963	0.630972541030574
50	118.7	111.444858783450	-0.353459097999474	7.2551412165505	-0.65103651598311
51	102.8	106.394057355863	-0.388552057390045	-3.5940573558635	-1.95933030901455
52	100.6	105.77669223239	-0.390713289251661	-5.17669223239005	-0.095040005492601
53	94.9	101.307677568354	-0.434911326123989	-6.40767756835446	-1.69421194787425
54	94.5	97.5523946791226	-0.472422598881949	-3.05239467912265	-1.38471498365671
55	102.9	98.448287977431	-0.457598387395081	4.45171202256897	0.573525871408617
56	95.3	95.9559531014323	-0.477327684353014	-0.655953101432312	-0.856299223544018
57	92.5	94.9026439899448	-0.482063745010377	-2.40264398994485	-0.242951611824349
58	102.7	95.5966404765	-0.474132088250357	7.10335952349996	0.496520236397815
59	91.5	96.4089929797308	-0.466983318817869	-4.90899297973084	0.543191702966212
60	89.5	97.2059100330946	-0.46077845252541	-7.70591003309457	0.533312661209458

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259862056lm289erx5ptthsi/10ku41259861988.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259862056lm289erx5ptthsi/10ku41259861988.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259862056lm289erx5ptthsi/2pii41259861988.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259862056lm289erx5ptthsi/2pii41259861988.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259862056lm289erx5ptthsi/32itg1259861988.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259862056lm289erx5ptthsi/32itg1259861988.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259862056lm289erx5ptthsi/40r8n1259861988.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259862056lm289erx5ptthsi/40r8n1259861988.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259862056lm289erx5ptthsi/52pst1259861988.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259862056lm289erx5ptthsi/52pst1259861988.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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