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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 05:25:21 -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/t12599295669pe316r4bwcd34g.htm/, Retrieved Fri, 04 Dec 2009 13:26:13 +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/t12599295669pe316r4bwcd34g.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 «

20366 22782 19169 13807 29743 25591 29096 26482 22405 27044 17970 18730 19684 19785 18479 10698 31956 29506 34506 27165 26736 23691 18157 17328 18205 20995 17382 9367 31124 26551 30651 25859 25100 25778 20418 18688 20424 24776 19814 12738 31566 30111 30019 31934 25826 26835 20205 17789 20520 22518 15572 11509 25447 24090 27786 26195 20516 22759 19028 16971 20036

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	20366	20366	0	0	0
2	22782	21193.6675851375	958.934718175826	1588.33241486253	0.997276983536058
3	19169	20924.4843277242	237.385385001715	-1755.48432772419	-0.437492457784884
4	13807	16727.0517507557	-2218.62355168664	-2920.05175075572	-1.73937110654325
5	29743	23291.2289923925	2908.04817164494	6451.77100760747	3.32856330234781
6	25591	27164.6786710660	3456.87449877651	-1573.67867106597	0.342895434537874
7	29096	29875.3873479631	3038.29426951669	-779.387347963149	-0.265218197482212
8	26482	28863.1183195991	756.640596866757	-2381.11831959906	-1.45026658659479
9	22405	24643.7348440921	-2055.24970013090	-2238.73484409214	-1.78290175841877
10	27044	24815.3412892653	-796.287084798538	2228.65871073466	0.79788885643197
11	17970	20594.9333592384	-2731.72090378324	-2624.93335923837	-1.22685550331592
12	18730	18041.7786043577	-2630.82113190869	688.221395642296	0.0639589718187483
13	19684	17941.3226596808	-1209.02972084024	1742.67734031916	0.905671678121439
14	19785	16976.2896379384	-1071.19204282220	2808.71036206163	0.0888683917718068
15	18479	17684.2722047980	-79.0737090463728	794.727795202044	0.623777469104689
16	10698	17853.9857610657	56.0249926095691	-7155.98576106568	0.0858650176625413
17	31956	23170.3734751062	2935.28301840299	8785.6265248938	1.85693005783753
18	29506	29557.8391270713	4837.45981268984	-51.8391270712555	1.20767469639308
19	34506	34023.3214664879	4634.14817202373	482.678533512138	-0.128233395283186
20	27165	31726.0347443636	861.489801120861	-4561.03474436356	-2.38993447130127
21	26736	29994.2967587512	-552.503505558864	-3258.29675875124	-0.89706647400581
22	23691	23175.8384658944	-3974.65822862368	515.161534105587	-2.16959438384515
23	18157	19624.5008052785	-3743.49813450407	-1467.50080527852	0.146545424076826
24	17328	16921.9628292914	-3175.53144022084	406.037170708649	0.360368606101136
25	18205	15390.1210921186	-2278.08332606694	2814.87890788138	0.57058953523941
26	20995	16664.0275548978	-335.952374164951	4330.97244510216	1.23324769979221
27	17382	17277.0723363253	180.334664438083	104.92766367472	0.326236378340560
28	9367	19047.4081185976	1038.85127371424	-9680.40811859762	0.544118254525539
29	31124	23112.6001683402	2674.76342462685	8011.39983165984	1.04324384771461
30	26551	26437.6981621657	3027.88550077186	113.301837834284	0.224605054653344
31	30651	27996.1686766081	2230.95820209727	2654.83132339190	-0.504303814073434
32	25859	29000.1920539628	1567.90792866891	-3141.19205396277	-0.419449319291681
33	25100	27138.4299432095	-283.372743220674	-2038.42994320953	-1.17310080388471
34	25778	25487.9281381442	-1021.70396643237	290.071861855767	-0.468241959680586
35	20418	22909.0547076613	-1863.04916896555	-2491.05470766127	-0.533785528846109
36	18688	19652.4171276587	-2616.40031000041	-964.417127658702	-0.478219081961303
37	20424	18145.9972831992	-2015.79183667570	2278.00271680082	0.381239880619699
38	24776	19263.6610800866	-320.680116834597	5512.33891991341	1.07411934126550
39	19814	20470.2232877218	502.928463061592	-656.223287721751	0.521086914453038
40	12738	23113.3756728051	1653.24787540263	-10375.3756728051	0.729162304600828
41	31566	24521.7565982733	1521.58062198078	7044.24340172667	-0.0837175067358104
42	30111	28220.2326340707	2695.13436206932	1890.76736592929	0.745879219348724
43	30019	28457.9984903607	1369.96958604314	1561.00150963933	-0.839814572746483
44	31934	31875.2524919213	2471.55407167145	58.747508078736	0.697118496416605
45	25826	29872.1748298281	68.7404363168002	-4046.17482982809	-1.52170871095426
46	26835	26574.1301062608	-1738.24410910148	260.8698937392	-1.14590188775832
47	20205	22653.0960196170	-2910.44967679836	-2448.09601961695	-0.74404159149443
48	17789	19330.2173855243	-3132.16343074005	-1541.21738552429	-0.140755866161784
49	20520	18392.0812694051	-1951.85278984319	2127.91873059490	0.74870643142129
50	22518	17551.1059180449	-1354.67934364851	4966.8940819551	0.378241476645152
51	15572	16924.2473486072	-964.332482578171	-1352.2473486072	0.247097371033234
52	11509	19977.6813568358	1186.26399857658	-8468.6813568358	1.3633303884715
53	25447	20501.4710065703	831.544472568955	4945.52899342968	-0.225304814152327
54	24090	21504.4456840479	923.494132849033	2585.55431595209	0.0584038432930896
55	27786	25317.5863452870	2474.25325173195	2468.41365471304	0.983207468070805
56	26195	25493.7429511298	1242.73860389668	701.25704887024	-0.779676939134254
57	20516	23839.9217403962	-306.431655162060	-3323.92174039622	-0.98100859084074
58	22759	21787.7739812756	-1239.25411424985	971.226018724396	-0.591467686998088
59	19028	20893.5151327091	-1054.81738691758	-1865.51513270911	0.117072143999097
60	16971	19615.3722642040	-1174.34133904716	-2644.37226420395	-0.0758740948010906
61	20036	18351.9763427279	-1222.03046285902	1684.02365727214	-0.0302428817436366

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599295669pe316r4bwcd34g/1ghsj1259929518.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599295669pe316r4bwcd34g/1ghsj1259929518.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599295669pe316r4bwcd34g/2wss31259929518.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599295669pe316r4bwcd34g/2wss31259929518.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599295669pe316r4bwcd34g/3pu5t1259929518.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599295669pe316r4bwcd34g/3pu5t1259929518.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599295669pe316r4bwcd34g/42mpr1259929518.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599295669pe316r4bwcd34g/42mpr1259929518.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599295669pe316r4bwcd34g/55wlw1259929518.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599295669pe316r4bwcd34g/55wlw1259929518.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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