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Structural Time Series Models

*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 06:30:37 -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/t1259847084469jh93unecrlla.htm/, Retrieved Thu, 03 Dec 2009 14:31:32 +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/t1259847084469jh93unecrlla.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:

JSSHWWS9P9

Dataseries X:

» Textbox « » Textfile « » CSV «

11.1 10.9 10 9.2 9.2 9.5 9.6 9.5 9.1 8.9 9 10.1 10.3 10.2 9.6 9.2 9.3 9.4 9.4 9.2 9 9 9 9.8 10 9.8 9.3 9 9 9.1 9.1 9.1 9.2 8.8 8.3 8.4 8.1 7.7 7.9 7.9 8 7.9 7.6 7.1 6.8 6.5 6.9 8.2 8.7 8.3 7.9 7.5 7.8 8.3 8.4 8.2 7.7 7.2 7.3 8.1

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	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	11.1	11.1	0	0	0
2	10.9	10.9023139605178	-0.197877275849182	-0.00231396051779417	-0.519268296715333
3	10	10.0192310725768	-0.860783815387878	-0.0192310725767628	-1.75760425368065
4	9.2	9.19482653488939	-0.82585397281315	0.0051734651106082	0.0910733826338701
5	9.2	9.17898470917852	-0.0476795308534081	0.0210152908214749	2.03083000302882
6	9.5	9.49661345703842	0.303317255381226	0.00338654296158203	0.91596087871694
7	9.6	9.60875181786168	0.119631753029153	-0.00875181786168083	-0.479345721896692
8	9.5	9.50570325546266	-0.094319524744667	-0.00570325546266232	-0.558327255182972
9	9.1	9.10770352363868	-0.386095916729550	-0.00770352363868439	-0.761419673784439
10	8.9	8.89407385611935	-0.220390061266825	0.00592614388065247	0.432426001083685
11	9	8.9933828003002	0.0867772470261645	0.00661719969979558	0.801583808956906
12	10.1	10.0758754350773	1.04346215693063	0.0241245649227205	2.49656494473471
13	10.3	10.3272435728530	0.282609815447896	-0.0272435728530215	-1.98625483889208
14	10.2	10.1930624323175	-0.118014591763028	0.0069375676824756	-1.04965212704135
15	9.6	9.61906717509268	-0.54608704578929	-0.0190671750926754	-1.12797678282709
16	9.2	9.20693966770739	-0.420475494555885	-0.00693966770739241	0.327427338297058
17	9.3	9.27623099198064	0.0385678849194214	0.0237690080193650	1.19806338758620
18	9.4	9.3951428305527	0.113891418959475	0.00485716944730701	0.196563696564963
19	9.4	9.4137804575969	0.0245898482455449	-0.0137804575968885	-0.233041580372739
20	9.2	9.20218397826148	-0.196833786966918	-0.00218397826147587	-0.577827100212828
21	9	9.00686393673775	-0.195414658049320	-0.00686393673774641	0.00370335885872557
22	9	8.97362998957414	-0.043370781896141	0.0263700104258586	0.396773703549157
23	9	9.04562202770204	0.0647823568253091	-0.0456220277020432	0.282236524362768
24	9.8	9.7281184322382	0.643878572129655	0.0718815677617899	1.51121218099864
25	10	10.041196682057	0.333836916004252	-0.0411966820570087	-0.809447417810787
26	9.8	9.78715326990133	-0.21757811345966	0.0128467300986743	-1.44159878044086
27	9.3	9.31726595248606	-0.451057299275273	-0.0172659524860579	-0.612360284747078
28	9	9.02276410745842	-0.305990234073916	-0.0227641074584214	0.37832176822637
29	9	8.97216330472896	-0.0696017530144864	0.0278366952710432	0.616906127733932
30	9.1	9.09053237841946	0.104439149326523	0.00946762158053677	0.454181547716595
31	9.1	9.10646325849621	0.0224874125032467	-0.00646325849621339	-0.213861223369617
32	9.1	9.10065244854538	-0.00371398418596567	-0.00065244854538207	-0.068375180528351
33	9.2	9.20621399566544	0.0974637128296588	-0.00621399566544226	0.264033327056016
34	8.8	8.78512717529671	-0.382662661252907	0.0148728247032879	-1.25293782103530
35	8.3	8.39135189386244	-0.392951970598074	-0.0913518938624389	-0.0268510404219564
36	8.4	8.31038932075387	-0.104095018862924	0.089610679246131	0.753803795253862
37	8.1	8.11910483601663	-0.184804100431604	-0.0191048360166275	-0.210734473624561
38	7.7	7.67597026841	-0.4240435509058	0.0240297315899946	-0.624685550084273
39	7.9	7.8829429751547	0.155900567848270	0.0170570248452985	1.51741587970476
40	7.9	7.94196471718982	0.0667057965112374	-0.0419647171898167	-0.232720465944251
41	8	7.99133725222027	0.0507662602148135	0.00866274777973165	-0.0415924660434171
42	7.9	7.89005066671207	-0.0890973122770287	0.00994933328792953	-0.364999188609893
43	7.6	7.61133181373123	-0.263529391031732	-0.0113318137312261	-0.455196598605809
44	7.1	7.13751958385879	-0.456964842218547	-0.0375195838587898	-0.504789479440009
45	6.8	6.75989621165295	-0.383980961370971	0.0401037883470502	0.190458739553836
46	6.5	6.46750805438957	-0.299726700524345	0.0324919456104339	0.219869964197356
47	6.9	6.97862588811384	0.446157526532614	-0.078625888113835	1.94646696161207
48	8.2	8.08007035604198	1.04888610852419	0.119929643958015	1.57289977650452
49	8.7	8.70836764820517	0.662062153029747	-0.00836764820516827	-1.01002821703670
50	8.3	8.38313990557518	-0.246030202978635	-0.0831399055751773	-2.36991742040616
51	7.9	7.88394172020598	-0.477839828699888	0.0160582797940225	-0.605824340497071
52	7.5	7.53419178862317	-0.360374393246054	-0.0341917886231732	0.306566532113275
53	7.8	7.7550985094328	0.172159058238768	0.0449014905671963	1.38946734900905
54	8.3	8.26797059748581	0.484346706484005	0.0320294025141878	0.814719274910062
55	8.4	8.41728627752001	0.177335316925176	-0.0172862775200103	-0.80117379363102
56	8.2	8.25656920572426	-0.132443127222985	-0.0565692057242573	-0.808398084804553
57	7.7	7.65360277760855	-0.563607653855369	0.0463972223914529	-1.12516697671528
58	7.2	7.1987688812449	-0.463931917987239	0.00123111875509691	0.260114049663913
59	7.3	7.41441270640327	0.158801166112815	-0.114412706403273	1.62508881005397
60	8.1	7.96575695144862	0.518465224937282	0.134243048551383	0.938609053421418

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259847084469jh93unecrlla/1fnv51259847034.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259847084469jh93unecrlla/1fnv51259847034.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259847084469jh93unecrlla/207f21259847034.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259847084469jh93unecrlla/207f21259847034.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259847084469jh93unecrlla/3wxfn1259847034.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259847084469jh93unecrlla/3wxfn1259847034.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259847084469jh93unecrlla/4dmpz1259847034.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259847084469jh93unecrlla/4dmpz1259847034.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259847084469jh93unecrlla/5q4pe1259847034.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259847084469jh93unecrlla/5q4pe1259847034.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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