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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 10:56:50 -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/t1259949547b00hdvseiqlxmxi.htm/, Retrieved Fri, 04 Dec 2009 18:59:16 +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/t1259949547b00hdvseiqlxmxi.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 «

2849,27 2921,44 2981,85 3080,58 3106,22 3119,31 3061,26 3097,31 3161,69 3257,16 3277,01 3295,32 3363,99 3494,17 3667,03 3813,06 3917,96 3895,51 3801,06 3570,12 3701,61 3862,27 3970,1 4138,52 4199,75 4290,89 4443,91 4502,64 4356,98 4591,27 4696,96 4621,4 4562,84 4202,52 4296,49 4435,23 4105,18 4116,68 3844,49 3720,98 3674,4 3857,62 3801,06 3504,37 3032,6 3047,03 2962,34 2197,82 2014,45 1862,83 1905,41 1810,99 1670,07 1864,44 2052,02 2029,6 2070,83 2293,41 2443,27 2513,17

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	2849.27	2849.27	0	0	0
2	2921.44	2917.76313399115	5.13790583480385	3.67686600884535	0.264174667852236
3	2981.85	2978.12789803119	11.2323616630119	3.72210196881298	0.338719245348942
4	3080.58	3076.79690322809	24.2028219139144	3.78309677191355	0.524636601294583
5	3106.22	3102.43607661879	24.454220929067	3.7839233812064	0.0084812578178234
6	3119.31	3115.53135333181	22.2643177599525	3.77864666818843	-0.0663376075692007
7	3061.26	3057.51103325591	5.87032567891759	3.74896674408907	-0.465499328144555
8	3097.31	3093.55223694707	12.2470569381727	3.75776305293064	0.174130835969007
9	3161.69	3157.92031998754	23.4935368361806	3.76968001245783	0.299950075187489
10	3257.16	3253.37746110682	39.2164484815003	3.78253889318345	0.413402697369485
11	3277.01	3273.23015947018	34.9538535510738	3.77984052981891	-0.111114812339812
12	3295.32	3291.54196573444	31.2737557750883	3.77803426556331	-0.0954323118956617
13	3363.99	3381.42695333392	43.7382114887806	-17.4369533339194	0.391778289159546
14	3494.17	3491.10200524756	57.8518638462192	3.06799475243978	0.317896052319807
15	3667.03	3664.06178187676	83.464393067397	2.96821812323714	0.658757311629081
16	3813.06	3810.13397441251	97.3966639944196	2.92602558749436	0.358375195739271
17	3917.96	3915.03790773248	99.0674386948443	2.92209226752185	0.0429793591223882
18	3895.51	3892.53839095819	72.0098959654047	2.97160904181063	-0.696059101657574
19	3801.06	3798.03566377233	34.9460010059936	3.02433622767383	-0.953494777019992
20	3570.12	3567.03019516236	-24.2553870110425	3.08980483764101	-1.52301749022897
21	3701.61	3698.55000546485	10.4221764763242	3.059994535151	0.892123635120283
22	3862.27	3859.23235891387	43.8733095859944	3.03764108613488	0.860576334564032
23	3970.1	3967.06975608431	58.1135205871739	3.03024391569038	0.366350051019184
24	4138.52	4135.49967342526	82.6736582433226	3.02032657473887	0.631846223109648
25	4199.75	4230.56405684713	85.3916521685081	-30.8140568471254	0.0768490048576036
26	4290.89	4288.48540385612	79.4342060359086	2.4045961438822	-0.142027442385313
27	4443.91	4441.5499837752	95.8398464478655	2.36001622479537	0.421427346514012
28	4502.64	4500.26251066665	87.5706628099617	2.37748933335368	-0.212544699497747
29	4356.98	4354.51715706549	35.6162178098846	2.46284293451407	-1.33587653254883
30	4591.27	4588.86367100342	79.8643750302113	2.4063289965789	1.13797584921890
31	4696.96	4694.5593813035	85.6155377524236	2.40061869650293	0.147928025980703
32	4621.4	4618.97167944399	49.7255060131889	2.42832055600669	-0.923215444774458
33	4562.84	4560.39721215894	25.6138601920837	2.44278784106401	-0.620264419110675
34	4202.52	4200.03713105689	-60.3188318868336	2.48286894311003	-2.21065512929778
35	4296.49	4294.01958690279	-25.9651425903545	2.47041309721281	0.883778750285135
36	4435.23	4432.76992305769	10.7074858624405	2.46007694231146	0.94344545845217
37	4105.18	4167.37148713995	-50.1819026991242	-62.1914871399531	-1.66893610767262
38	4116.68	4111.09118841473	-51.5135800812206	5.58881158527523	-0.0324681561925759
39	3844.49	3838.8018394913	-100.696153305120	5.6881605086983	-1.26387849756210
40	3720.98	3715.28385723677	-105.778742767923	5.69614276323134	-0.130668861223294
41	3674.4	3668.71995664016	-92.5932308977474	5.68004335983704	0.339078839393447
42	3857.62	3851.99826090203	-31.1692488309829	5.6217390979733	1.57983645428615
43	3801.06	3795.43408875761	-36.8233187553788	5.625911242391	-0.145438008795883
44	3504.37	3498.71089630002	-94.688020471979	5.6591036999766	-1.48852521020575
45	3032.6	3026.90345650104	-178.650507951500	5.69654349895634	-2.15994812306076
46	3047.03	3041.34835859982	-135.659291616836	5.68164140017621	1.10597969054765
47	2962.34	2956.66141654926	-124.310622559588	5.67858345073642	0.291956419034426
48	2197.82	2192.11155878457	-266.856730598819	5.708441215433	-3.66717716307664
49	2014.45	2064.11497959758	-236.158079925354	-49.6649795975794	0.828389947333573
50	1862.83	1858.06098260740	-229.557600717804	4.76901739259809	0.162901085914849
51	1905.41	1900.73827178121	-168.918027281417	4.67172821878572	1.55865684837942
52	1810.99	1806.33897240724	-152.322988289243	4.65102759276265	0.426703256060083
53	1670.07	1665.4214352507	-149.783354148778	4.6485647492991	0.065314780566455
54	1864.44	1859.84921339512	-73.1433494724781	4.59078660488022	1.97129588133215
55	2052.02	2047.46323802728	-15.0864476722291	4.55676197271762	1.49342691045499
56	2029.6	2025.04249409234	-16.7193884936204	4.55750590765862	-0.0420069356825406
57	2070.83	2066.27706370684	-3.81628725433422	4.552936293159	0.331938029389666
58	2293.41	2288.87094123193	46.5927054907584	4.53905876806952	1.29681608710483
59	2443.27	2438.73586183875	69.5858078936419	4.53413816124997	0.591524112987543
60	2513.17	2508.63587347639	69.6557643271715	4.53412652360881	0.00179972133477979

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259949547b00hdvseiqlxmxi/16w131259949408.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259949547b00hdvseiqlxmxi/16w131259949408.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259949547b00hdvseiqlxmxi/21eyj1259949408.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259949547b00hdvseiqlxmxi/21eyj1259949408.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259949547b00hdvseiqlxmxi/36xlo1259949408.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259949547b00hdvseiqlxmxi/36xlo1259949408.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259949547b00hdvseiqlxmxi/4hdwd1259949408.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259949547b00hdvseiqlxmxi/4hdwd1259949408.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259949547b00hdvseiqlxmxi/5h5xs1259949408.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259949547b00hdvseiqlxmxi/5h5xs1259949408.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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