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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 05:35:38 -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/t12599302292fxlbnfvq1dcq16.htm/, Retrieved Fri, 04 Dec 2009 13:37:16 +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/t12599302292fxlbnfvq1dcq16.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 «

111,5 108,1 124,5 106,3 111,1 121,3 116,5 117,4 123,6 98,4 107,2 118,9 111,9 115,2 124,4 104,6 117 126,2 117,5 122,2 124,1 105,8 107,5 125,6 112,1 120,1 130,6 109,8 122,1 129,5 132,1 133,3 128,4 114,7 114,1 136,9 123,4 134 137 127,8 140,1 140,4 157,8 151,8 141,1 138,8 141,1 139,5 150,7 144,4 146 143,6 143,1 156,4 164,8 145,1 153,4 133,2 131,4 145,9

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	111.5	111.5	0	0	0
2	108.1	111.694333593543	0.127013872581406	-3.59433359354289	-0.63308613142944
3	124.5	113.859502216785	0.352529422801186	10.6404977832149	1.85061668043858
4	106.3	113.807832829266	0.293628585121169	-7.50783282926601	-0.191021354181433
5	111.1	113.087948163715	0.143816037535123	-1.98794816371468	-0.504153550667496
6	121.3	114.722976280664	0.368338849070413	6.57702371933586	0.901036140166431
7	116.5	115.851379159976	0.487060858249145	0.64862084002418	0.519111210471918
8	117.4	116.799698725208	0.561716669660962	0.600301274791685	0.325578326389754
9	123.6	118.803392908098	0.799995773334033	4.79660709190239	0.999850840559043
10	98.4	115.57993132403	0.130765004234486	-17.1799313240299	-2.7057330315737
11	107.2	111.993331465076	-0.48687766624061	-4.79333146507598	-2.44171696709596
12	118.9	111.475457858815	-0.492012222694210	7.42454214118519	-0.0201158081528456
13	111.9	111.454087945391	-0.415781152703632	0.445912054608922	0.299070875450645
14	115.2	113.278967216213	-0.0543670674190671	1.92103278378733	1.47045151018923
15	124.4	114.259467673784	0.114409852553765	10.1405323262155	0.692414475799659
16	104.6	114.440010483647	0.125290776566171	-9.8400104836468	0.0434177310168511
17	117	115.966565692806	0.355452056634784	1.03343430719439	0.891823827221471
18	126.2	117.713992477134	0.582382095715809	8.48600752286584	0.872737737015678
19	117.5	118.313872440647	0.58521781400367	-0.81387244064678	0.0110270777487032
20	122.2	118.994024986290	0.600585479790961	3.20597501371031	0.0605905716932384
21	124.1	118.489258689075	0.421250234146354	5.61074131092486	-0.710783979844778
22	105.8	118.866061861438	0.414021999495885	-13.066061861438	-0.0285278147017121
23	107.5	117.984967343967	0.203348946180801	-10.4849673439667	-0.825035231188455
24	125.6	118.150939764585	0.197280086094968	7.44906023541487	-0.0236515649307427
25	112.1	117.469205828784	0.0548923065535816	-5.36920582878395	-0.555339070831884
26	120.1	117.707777120867	0.084608061675689	2.39222287913331	0.116406154096969
27	130.6	118.767105447630	0.242348322626825	11.8328945523698	0.620056876784354
28	109.8	119.932518262879	0.391877855355108	-10.1325182628786	0.58767018920538
29	122.1	121.031639096761	0.506502456534344	1.06836090323894	0.449224608095414
30	129.5	121.570245393277	0.511703416730382	7.92975460672282	0.0203314054282976
31	132.1	124.287029365935	0.868626168018364	7.81297063406452	1.39468847291033
32	133.3	126.757900824207	1.12781205394757	6.54209917579263	1.01412924641963
33	128.4	127.117079105104	1.00348141049854	1.28292089489587	-0.48718982844723
34	114.7	127.419354371964	0.890023051481278	-12.7193543719638	-0.444757558497701
35	114.1	127.144122016322	0.701431273256025	-13.0441220163224	-0.73875355369403
36	136.9	127.751611064037	0.68622762135459	9.1483889359626	-0.059498039007574
37	123.4	128.770886648316	0.740114177803186	-5.37088664831644	0.210789168182076
38	134	130.525284817586	0.904180517052674	3.47471518241371	0.641954145409312
39	137	130.813714030525	0.804588438771652	6.18628596947451	-0.389891912572933
40	127.8	133.121440533992	1.04772437602999	-5.32144053399152	0.952133263165548
41	140.1	136.163399020403	1.37033106822392	3.93660097959717	1.2631897626605
42	140.4	137.601040140969	1.38122011508573	2.79895985903136	0.0426224261677001
43	157.8	141.473449378368	1.78420376296158	16.3265506216321	1.57700346908746
44	151.8	144.309229266042	1.95429376598789	7.49077073395762	0.665623970757335
45	141.1	144.920902193170	1.73714014273204	-3.82090219317019	-0.8499474175402
46	138.8	147.012174290943	1.79441735235743	-8.21217429094274	0.224217992581392
47	141.1	150.225508833553	2.02392126796341	-9.12550883355313	0.898426826833146
48	139.5	148.156788934433	1.36193873750189	-8.65678893443319	-2.59116961149216
49	150.7	149.709317586389	1.39276618670942	0.990682413610866	0.120654114863056
50	144.4	149.261057329514	1.09499437839259	-4.86105732951403	-1.16540230402029
51	146	147.983871713231	0.711322689297049	-1.98387171323054	-1.50165922444738
52	143.6	148.475235857224	0.675747215515352	-4.87523585722414	-0.139247746956525
53	143.1	147.287822078214	0.374401596630297	-4.18782207821431	-1.17953801087730
54	156.4	148.806334686166	0.55945089157139	7.59366531383427	0.72430981888555
55	164.8	149.701892837557	0.613813128607809	15.0981071624431	0.212773460217785
56	145.1	147.376780444894	0.1384736042569	-2.27678044489416	-1.86043771151726
57	153.4	148.418149398770	0.284505642071951	4.98185060123034	0.57156099990177
58	133.2	147.097512756849	0.0248951325389817	-13.8975127568485	-1.01612175251219
59	131.4	144.112644160618	-0.461895332698342	-12.7126441606177	-1.90533519273149
60	145.9	144.547294532076	-0.316890006788326	1.35270546792415	0.567560377545531

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599302292fxlbnfvq1dcq16/14pq11259930133.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599302292fxlbnfvq1dcq16/14pq11259930133.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599302292fxlbnfvq1dcq16/22p5n1259930133.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599302292fxlbnfvq1dcq16/22p5n1259930133.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599302292fxlbnfvq1dcq16/31mtj1259930133.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599302292fxlbnfvq1dcq16/31mtj1259930133.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599302292fxlbnfvq1dcq16/4y4b11259930133.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599302292fxlbnfvq1dcq16/4y4b11259930133.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599302292fxlbnfvq1dcq16/5p74m1259930133.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599302292fxlbnfvq1dcq16/5p74m1259930133.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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