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Paper Statistiek

*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: Mon, 27 Dec 2010 13:51:50 +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/27/t12934578340y0ql727gzdkz4w.htm/, Retrieved Mon, 27 Dec 2010 14:50:40 +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/27/t12934578340y0ql727gzdkz4w.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:

STSM - Handelsbalans België (1995-2009)

Dataseries X:

» Textbox « » Textfile « » CSV «

2540,9 2370,3 1807,5 1834,8 786,8 1561,4 1347,2 1549,8 1553,8 1822,5 3078,7 1589,1 1791,5 2558,1 2111,8 2083,1 2052,1 2243,5 2622 1952,6 808,9 1709,8 1582,1 865,6 1116,1 1119,4 2350 1975,6 2536,5 2785 2819,7 1829,5 758,3 2921,6 2482 1892,7 1855,1 2151,3 1642,2 1640,5 1366,1 1532,8 824,4 -518,7 -978,5 1162,5 1243,4 1199,5 883,1 1437,2 534,5 -1901,9 -2521,1 -1721,1 -3094,5 -3694,8 -2492,1 -464,6 -626,1 -1711,4

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	'George Udny Yule' @ 72.249.76.132

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	2540.9	2540.9	0	0	0
2	2370.3	2403.24924220022	-33.0262994931002	-32.8106022456320	-0.0515760048945985
3	1807.5	1899.08565213502	-60.1141201628654	-82.2348547681139	-0.74644362976417
4	1834.8	1882.64971758962	-58.3161433188035	-48.7315746149965	0.0691987457464548
5	786.8	951.72914141744	29.4836641318971	-147.250014763606	-1.54486561578287
6	1561.4	1434.80877129596	69.3114047653	120.44137654359	0.596275212152444
7	1347.2	1332.38017698497	62.9511849408438	18.1019577113344	-0.268448903470677
8	1549.8	1432.84395008494	63.67029822502	116.223871151149	0.0586189578570718
9	1553.8	1761.99215161447	54.7134148070017	-213.408599611800	0.433626576690118
10	1822.5	1717.42247406297	49.3708619782162	106.679397072275	-0.141938122958428
11	3078.7	2902.70124212115	86.8374933633061	154.83576192816	1.76428976802993
12	1589.1	1679.05023825321	67.1945710549171	-64.958398785773	-2.03750832693580
13	1791.5	1949.63708045745	64.7650578145714	-162.043352650802	0.323219937913877
14	2558.1	2506.84682244767	84.263318888183	42.8163233388957	0.726993770255664
15	2111.8	1944.29561110069	64.329629166144	179.386023662537	-1.00026155177559
16	2083.1	2134.63018165642	66.1984410650525	-53.8972415275152	0.195339259616548
17	2052.1	2263.79552755699	66.174771687948	-212.885107513344	0.0987019302256869
18	2243.5	2159.90254881728	60.6533214443497	86.5909073839647	-0.255137574025964
19	2622	2424.04473580615	66.5839093529423	194.243876256577	0.313747641755618
20	1952.6	2076.86018284819	59.9630996849717	-116.564294830252	-0.640085582793468
21	808.9	1144.75520068021	53.1024230173618	-317.330581530955	-1.54300529308708
22	1709.8	1574.99310673692	63.9033070902898	128.077679713886	0.570837091286128
23	1582.1	1380.14961731873	56.7032657933839	206.653722283612	-0.398163486321655
24	865.6	941.39826291358	48.0198461424117	-66.6457330207683	-0.765112410724549
25	1116.1	1405.96021672508	52.9702601735526	-297.574231676639	0.644797905478254
26	1119.4	1029.35720633031	41.5657790094912	97.763903426313	-0.653569597301523
27	2350	1951.68899559281	65.2044682151926	382.324558022941	1.35362415591016
28	1975.6	2087.12084008529	66.5397906997679	-112.811878217570	0.108288350326667
29	2536.5	2710.54450694367	75.1200372660775	-184.297455293075	0.859445697977624
30	2785	2794.43918763284	75.3431442489767	-9.59754576186648	0.0133910501349597
31	2819.7	2504.94149934109	65.8072491733637	321.376837369521	-0.560261724028455
32	1829.5	2077.35815975666	55.7813904742582	-238.819698975269	-0.759839684374817
33	758.3	1089.74874544031	37.0415259598888	-312.318146003386	-1.60708060136847
34	2921.6	2647.77453200980	74.8521220679837	246.312313123360	2.32546493039416
35	2482	2189.94070844713	61.180622788213	301.720827202298	-0.817586433318246
36	1892.7	2044.76059764758	56.7627624581198	-148.290042907563	-0.317475004096619
37	1855.1	2310.74201058281	60.9126764785346	-459.466679830692	0.321814560881375
38	2151.3	1912.34408154991	49.6082982037528	247.275398265569	-0.703030177765467
39	1642.2	1401.29836656822	35.3859631650194	251.070392891113	-0.860219024490696
40	1640.5	1756.82692524019	42.5217123000626	-122.165239699443	0.492111698744722
41	1366.1	1772.74907989586	41.9571434471202	-406.163857432573	-0.0408763740474573
42	1532.8	1299.40519986005	29.3090398873362	242.735406085996	-0.789256053377551
43	824.4	702.576761551008	13.5330939003320	133.180143958761	-0.9604665336808
44	-518.7	-259.91797349528	-8.90646526517968	-241.008012500901	-1.49932162240393
45	-978.5	-599.261100829277	-16.2626176017902	-373.220480693438	-0.507453521652441
46	1162.5	645.302571722459	14.7253768909594	494.33373259316	1.93189342701042
47	1243.4	958.480116986247	22.2199668951932	279.506350167183	0.457735295304846
48	1199.5	1356.02310821577	31.0565994374538	-163.350665869844	0.576251741741529
49	883.1	1408.60912704329	31.5526558117382	-525.900810237818	0.0330468449702881
50	1437.2	1041.37404078267	21.7185000690529	403.059029505694	-0.611178060320598
51	534.5	397.422796403572	5.01968152845378	149.151787224210	-1.02080702000920
52	-1901.9	-1461.04183172475	-39.6640626649202	-406.986280739806	-2.85994318013708
53	-2521.1	-1991.11924917610	-51.2521024069567	-521.066134070186	-0.75249704565682
54	-1721.1	-2197.50832982783	-55.0939319890017	479.222395490493	-0.237790496988483
55	-3094.5	-3305.76705295137	-81.5250695603381	230.370331104769	-1.61487216135076
56	-3694.8	-3359.74803760573	-80.8552193909207	-335.552321681858	0.0422595034494663
57	-2492.1	-2187.74927976893	-50.691880992268	-327.110697861798	1.92188280508946
58	-464.6	-1212.04089779946	-25.1622688718237	728.822442179367	1.57333724598374
59	-626.1	-888.620432616458	-16.4024760290047	256.197649187543	0.534457103630498
60	-1711.4	-1176.84040422838	-23.0854439324801	-529.624050185194	-0.416935505309733

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/27/t12934578340y0ql727gzdkz4w/1cgfk1293457907.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t12934578340y0ql727gzdkz4w/1cgfk1293457907.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t12934578340y0ql727gzdkz4w/2npfn1293457907.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t12934578340y0ql727gzdkz4w/2npfn1293457907.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t12934578340y0ql727gzdkz4w/3yheq1293457907.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t12934578340y0ql727gzdkz4w/3yheq1293457907.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t12934578340y0ql727gzdkz4w/4yheq1293457907.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t12934578340y0ql727gzdkz4w/4yheq1293457907.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t12934578340y0ql727gzdkz4w/5yheq1293457907.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t12934578340y0ql727gzdkz4w/5yheq1293457907.ps (open in new window)

Parameters (Session):

par1 = 4 ; par2 = periodic ; par3 = 0 ; par5 = 1 ; par7 = 1 ; par8 = FALSE ;

Parameters (R input):

par1 = 4 ; par2 = periodic ; par3 = 0 ; par5 = 1 ; par7 = 1 ; par8 = FALSE ;

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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