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Paper: Structural Time Series Model

*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, 29 Dec 2010 16:22:57 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/29/t12936396535ulimsjzv1iy152.htm/, Retrieved Wed, 29 Dec 2010 17:20:58 +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/2010/Dec/29/t12936396535ulimsjzv1iy152.htm/},
    year = {2010},
}
@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 = {2010},
    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 «

31245 30951 30872 30752 30967 30781 30681 31356 31434 31594 31949 32396 32441 32447 32288 32418 32346 32091 31855 31683 31615 31840 31536 31383 31638 31626 31720 31472 31372 31419 31341 31171 31036 30532 30666 30571 30173 30032 29874 30018 29911 29963 30050 29901 29544 29451 29293 29334 29389 29563

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	1 seconds
R Server	'Gwilym Jenkins' @ www.wessa.org

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	31245	31245	0	0	0
2	30951	30966.2739415637	-15.5442801599388	-15.2739415637431	-0.791661176826256
3	30872	30887.5166084096	-16.1346586769645	-15.5166084096155	-0.29892365905723
4	30752	30767.9090426388	-17.380907596485	-15.9090426388181	-0.48861711586687
5	30967	30982.0438767587	-13.9829549850008	-15.0438767586947	1.09174463019894
6	30781	30796.6733130974	-16.9353257897189	-15.6733130973929	-0.807107610329334
7	30681	30696.9712984209	-18.5643540818563	-15.9712984208925	-0.389255466828759
8	31356	31369.5378493448	-3.33426269602627	-13.5378493448312	3.24626914594959
9	31434	31447.2593847371	-1.36600264825519	-13.2593847370721	0.380253557263629
10	31594	31606.7214605902	2.88249691480855	-12.7214605902434	0.75359423887647
11	31949	31960.5809221459	12.8623013850883	-11.5809221459309	1.64271996943008
12	32396	32406.2172369703	25.9905886651772	-10.2172369702792	2.02338682077191
13	32441	32361.2432220378	26.3057225577656	79.7567779622374	-0.398149163354623
14	32447	32452.6970545236	29.5342130970008	-5.69705452357042	0.258805926359441
15	32288	32293.9395769665	23.1125477764634	-5.93957696650549	-0.876969086273123
16	32418	32423.8069756149	26.9164976769195	-5.80697561486573	0.496794993291035
17	32346	32351.9251472244	23.2559089050994	-5.92514722443949	-0.459409099559962
18	32091	32097.2448299504	12.5930008502601	-6.24482995041355	-1.29145369042109
19	31855	31861.519142529	2.76515580695383	-6.51914252899029	-1.15305278087372
20	31683	31689.7041494154	-4.33937976419046	-6.70414941536826	-0.810144006477588
21	31615	31621.7687318731	-6.99273965837496	-6.76873187306778	-0.294948002278496
22	31840	31846.5434111315	2.8954429917442	-6.54341113153677	1.07432379848715
23	31536	31542.8285184522	-10.4503339895168	-6.82851845221873	-1.42054592977705
24	31383	31389.9550843462	-16.7618423480564	-6.95508434620576	-0.659556110132069
25	31638	31527.8345327213	-11.4293162628538	110.165467278704	0.785401175030913
26	31626	31634.2436891432	-5.28026573408549	-8.24368914322513	0.497025632650487
27	31720	31728.197021138	-0.702650629023177	-8.19702113796054	0.458914510848177
28	31472	31480.3078370393	-12.2426509901965	-8.30783703927386	-1.14277732721684
29	31372	31380.3453068556	-16.3821604570421	-8.3453068555836	-0.405424961254062
30	31419	31427.3195334722	-13.3633544754091	-8.31953347216264	0.292744987250647
31	31341	31349.3445541952	-16.4687894514474	-8.34455419519239	-0.298473926864508
32	31171	31179.4011080844	-23.902955353664	-8.40110808439705	-0.70882384263698
33	31036	31044.440035665	-29.3202906414276	-8.44003566500355	-0.512821616280683
34	30532	30540.5981982787	-52.6131252897033	-8.59819827865321	-2.19075626401384
35	30666	30674.539087559	-43.4038667268277	-8.53908755898293	0.861136304245901
36	30571	30579.5546202609	-45.9631068661237	-8.55462026087105	-0.238061582436233
37	30173	30136.4336583547	-64.209751319512	36.5663416453475	-1.95087065774321
38	30032	30035.7235296431	-66.1318608577058	-3.72352964305939	-0.157954438992422
39	29874	29877.7386827749	-70.7431144549682	-3.73868277487997	-0.423742064582086
40	30018	30021.7050470175	-59.9278244707317	-3.70504701754825	0.990414823373518
41	29911	29914.7120475897	-62.3057582247592	-3.71204758971698	-0.217083686027672
42	29963	29966.6959091468	-56.5156469474721	-3.69590914679706	0.527107870954779
43	30050	30053.6766755633	-49.2280954675697	-3.67667556331955	0.66176262275603
44	29901	29904.6893662596	-54.3055566941981	-3.68936625955319	-0.460029459230713
45	29544	29547.7259048464	-69.740394105798	-3.72590484639961	-1.39559295784481
46	29451	29454.7285691163	-70.9285469124179	-3.7285691163369	-0.107234838963537
47	29293	29296.7380324213	-75.3834673424578	-3.7380324213163	-0.401412269638809
48	29334	29337.7260314656	-69.4202663517712	-3.72603146555702	0.536524188056835
49	29389	29340.1757307954	-65.8489637750225	48.8242692045578	0.347375103767396
50	29563	29564.9375212838	-50.615856627008	-1.93752128381224	1.27568802192432

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/29/t12936396535ulimsjzv1iy152/1d08k1293639774.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t12936396535ulimsjzv1iy152/1d08k1293639774.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t12936396535ulimsjzv1iy152/2d08k1293639774.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t12936396535ulimsjzv1iy152/2d08k1293639774.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t12936396535ulimsjzv1iy152/3o9q51293639774.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t12936396535ulimsjzv1iy152/3o9q51293639774.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t12936396535ulimsjzv1iy152/4z0p81293639774.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t12936396535ulimsjzv1iy152/4z0p81293639774.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t12936396535ulimsjzv1iy152/5z0p81293639774.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t12936396535ulimsjzv1iy152/5z0p81293639774.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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