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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: Thu, 03 Dec 2009 10:48:33 -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/03/t1259862545padc3lf1dbrnoye.htm/, Retrieved Thu, 03 Dec 2009 18:49:12 +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/03/t1259862545padc3lf1dbrnoye.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 «

115.47 103.34 102.60 100.69 105.67 123.61 113.08 106.46 123.38 109.87 95.74 123.06 123.39 120.28 115.33 110.4 114.49 132.03 123.16 118.82 128.32 112.24 104.53 132.57 122.52 131.8 124.55 120.96 122.6 145.52 118.57 134.25 136.7 121.37 111.63 134.42 137.65 137.86 119.77 130.69 128.28 147.45 128.42 136.9 143.95 135.64 122.48 136.83 153.04 142.71 123.46 144.37 146.15 147.61 158.51 147.4 165.05 154.64 126.2 157.36 154.15 123.21 113.07 110.45 113.57 122.44 114.93 111.85 126.04 121.34

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	115.47	115.47	0	0	0
2	103.34	107.327958564947	-0.325179553534179	-3.98795856494674	-1.31384091634919
3	102.6	103.335702428143	-0.531108494473806	-0.735702428143354	-0.626994004952887
4	100.69	101.477800279429	-0.582071727486263	-0.78780027942943	-0.277578314861533
5	105.67	103.358480085691	-0.530568820401064	2.31151991430892	0.54103236586135
6	123.61	114.176046780436	-0.386893349113194	9.43395321956443	2.50565761915007
7	113.08	115.999701237838	-0.363708685345868	-2.9197012378379	0.487784846962114
8	106.46	111.601457500004	-0.406517997994906	-5.14145750000427	-0.889343162668956
9	123.38	116.778244224018	-0.344680551818183	6.6017557759817	1.22986577501193
10	109.87	114.426950837446	-0.367363045269992	-4.55695083744614	-0.441883426953570
11	95.74	104.474675073961	-0.47567205218093	-8.73467507396095	-2.11065283575416
12	123.06	111.968804389118	-0.386522584471784	11.0911956108823	1.75506234544260
13	123.39	115.761408280578	-0.498189359351577	7.62859171942242	0.987641954012402
14	120.28	119.227540796823	-0.506199967616021	1.05245920317707	0.884476715828104
15	115.33	118.010039970474	-0.520238922243998	-2.68003997047408	-0.144853501871608
16	110.4	115.656618777612	-0.564656549838987	-5.25661877761206	-0.381198650923356
17	114.49	116.273380986845	-0.541489489472847	-1.78338098684487	0.255282991059217
18	132.03	119.676897405235	-0.487400342347508	12.3531025947649	0.866253538290777
19	123.16	122.752227021661	-0.451821974445156	0.407772978339069	0.785280587709519
20	118.82	124.872475979880	-0.429886337941507	-6.05247597988047	0.56717228913698
21	128.32	122.470496177201	-0.446161534524373	5.84950382279913	-0.434773043057902
22	112.24	117.393782083926	-0.482434263437948	-5.153782083926	-1.02038976027460
23	104.53	116.47949329434	-0.48496253223978	-11.9494932943399	-0.095073714820492
24	132.57	119.789924425355	-0.479783439094625	12.7800755746453	0.83685261990826
25	122.52	118.619278274337	-0.477247943817894	3.90072172566312	-0.154085010070662
26	131.8	123.770050157323	-0.468173836714676	8.02994984267697	1.23641175510898
27	124.55	125.958475991532	-0.440029360964334	-1.40847599153218	0.565287481436237
28	120.96	127.091100751783	-0.415541955356167	-6.1311007517826	0.333279162886685
29	122.6	127.257181742023	-0.406460463823326	-4.65718174202272	0.125298946680323
30	145.52	131.126861504700	-0.350456398656903	14.3931384953004	0.934480534758247
31	118.57	125.780747762463	-0.402289786662204	-7.210747762463	-1.09901390072755
32	134.25	130.762629209823	-0.3568825882647	3.48737079017685	1.18700408177217
33	136.7	130.254959961601	-0.357951047881837	6.44504003839928	-0.0332481632645142
34	121.37	128.303595820502	-0.366972286446859	-6.93359582050245	-0.351062524363421
35	111.63	126.473888893507	-0.372345045912592	-14.8438888935066	-0.32201849472247
36	134.42	124.058720669928	-0.375416327841318	10.3612793300721	-0.45012444939853
37	137.65	129.866061576178	-0.370301711064613	7.7839384238219	1.36299362686532
38	137.86	131.537550056016	-0.363209861709759	6.32244994398364	0.44618146357317
39	119.77	127.165199857200	-0.394911294055877	-7.39519985720027	-0.863858541840704
40	130.69	131.518977027508	-0.341231395126340	-0.828977027508219	1.01856100287634
41	128.28	133.561342767946	-0.311735769256841	-5.28134276794625	0.514873768675007
42	147.45	132.764725227951	-0.317325757141901	14.6852747720485	-0.105771942779876
43	128.42	135.154076773928	-0.290757182740712	-6.7340767739285	0.594353827488041
44	136.9	134.33399253471	-0.294998529839911	2.56600746529012	-0.116568172349279
45	143.95	134.995478364977	-0.288925961192967	8.95452163502331	0.210740649050774
46	135.64	138.190665341355	-0.272397667199056	-2.55066534135518	0.767201469201027
47	122.48	138.254498853333	-0.271316509184752	-15.7744988533332	0.0739973500996006
48	136.83	134.148506177838	-0.279668582818051	2.68149382216241	-0.843764540139479
49	153.04	139.038125773193	-0.267516581540994	14.0018742268066	1.13538098247071
50	142.71	137.994579852830	-0.270696474969341	4.71542014717033	-0.169431413360703
51	123.46	135.677102722450	-0.284477601915333	-12.2171027224504	-0.443468572362297
52	144.37	140.449551607447	-0.238881977944825	3.92044839255288	1.09224676117646
53	146.15	146.527074125742	-0.175029283663729	-0.377074125742317	1.36894574101198
54	147.61	141.454574985447	-0.223619489293693	6.15542501455256	-1.06825724005665
55	158.51	151.972920945210	-0.128474338226703	6.53707905479046	2.35575479203730
56	147.4	150.672578421736	-0.137142283222423	-3.27257842173574	-0.257732805261729
57	165.05	153.743011841665	-0.118352598903569	11.3069881583353	0.706005605617627
58	154.64	155.669447008316	-0.109317000949693	-1.02944700831632	0.449957575074511
59	126.2	148.838105752518	-0.131296583785884	-22.6381057525176	-1.47852021154116
60	157.36	151.710423859536	-0.12316487604108	5.6495761404642	0.66017908858174
61	154.15	146.374999541500	-0.13896620166243	7.77500045849982	-1.14322064543085
62	123.21	132.103879576503	-0.199355267159524	-8.8938795765034	-3.08655763456848
63	113.07	128.24269740184	-0.221396367090524	-15.1726974018401	-0.79601403941959
64	110.45	118.437305427123	-0.294314662373635	-7.98730542712287	-2.07908279108819
65	113.57	114.372258390693	-0.326413110977238	-0.802258390692765	-0.819523877149432
66	122.44	117.268916504714	-0.298839422008591	5.17108349528605	0.703454687289402
67	114.93	113.484551149028	-0.326286780023321	1.44544885097167	-0.763837738536676
68	111.85	114.51460613273	-0.317123253986082	-2.66460613273006	0.297982879869803
69	126.04	114.776303062257	-0.313948563807010	11.2636969377431	0.127282440685429
70	121.34	116.877827379219	-0.303557140838329	4.46217262078138	0.531164098880861

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259862545padc3lf1dbrnoye/1t91j1259862510.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259862545padc3lf1dbrnoye/1t91j1259862510.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259862545padc3lf1dbrnoye/2j05x1259862510.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259862545padc3lf1dbrnoye/2j05x1259862510.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259862545padc3lf1dbrnoye/330541259862510.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259862545padc3lf1dbrnoye/330541259862510.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259862545padc3lf1dbrnoye/4qoel1259862510.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259862545padc3lf1dbrnoye/4qoel1259862510.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259862545padc3lf1dbrnoye/5kqd51259862510.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259862545padc3lf1dbrnoye/5kqd51259862510.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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