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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 10:40:16 -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/t1259948467jmfr4yarxhc3ppx.htm/, Retrieved Fri, 04 Dec 2009 18:41:15 +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/t1259948467jmfr4yarxhc3ppx.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 «

92.9 107.7 103.5 91.1 79.8 71.9 82.9 90.1 100.7 90.7 108.8 44.1 93.6 107.4 96.5 93.6 76.5 76.7 84 103.3 88.5 99 105.9 44.7 94 107.1 104.8 102.5 77.7 85.2 91.3 106.5 92.4 97.5 107 51.1 98.6 102.2 114.3 99.4 72.5 92.3 99.4 85.9 109.4 97.6 104.7 56.9 86.7 108.5 103.4 86.2 71 75.9 87.1 102 88.5 87.8 100.8 50.6 85.9

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	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	92.9	92.9	0	0	0
2	107.7	92.6896588715088	-0.255408224587871	11.4862058095046	1.5666548067674
3	103.5	95.9571130213081	0.33873407102119	3.93328481542845	1.79029325294979
4	91.1	96.8349522021884	0.423485059763639	-6.05327517098392	0.181397495851078
5	79.8	93.2838337171227	-0.122637281959	-11.0959300621323	-1.39024174152871
6	71.9	87.7384773189906	-0.771104665389701	-12.0145288848744	-2.17351412427144
7	82.9	84.8266931604193	-0.994915865053252	-0.160115655525621	-0.977188508428675
8	90.1	84.4284428943173	-0.939933815930676	5.1128029966993	0.302467009589666
9	100.7	86.5977434347225	-0.684901445394613	10.8939113236001	1.70913723134016
10	90.7	87.7990789197332	-0.545721621551445	0.805231580307828	1.10332943982679
11	108.8	91.1591633714338	-0.28375898751813	13.0483755989312	2.39676117711606
12	44.1	85.6522090833307	-0.605278927103812	-35.1350798057273	-3.32701502292999
13	93.6	84.6350834063906	-0.615960443069126	9.5819190415182	-0.32363542878073
14	107.4	85.5008160701826	-0.570642640199136	19.8085167797505	1.10129764248051
15	96.5	86.1859164339805	-0.519351428534164	8.74245527183433	0.842663491769534
16	93.6	87.3065763966798	-0.442506555448933	4.38610410922142	1.03887150098209
17	76.5	86.8948407551352	-0.44099857588712	-10.4298706755120	0.0192374399233076
18	76.7	86.678979958388	-0.430026620876359	-10.2380129310181	0.142547550202579
19	84	86.3939921811031	-0.423195811427058	-2.56510218008255	0.0940317144533676
20	103.3	88.1654160327014	-0.324990884961405	12.4686131539189	1.46077392759870
21	88.5	87.6582452075743	-0.332650245544944	1.06949323662941	-0.124355187337928
22	99	88.8199850810234	-0.274225415054977	8.26176750670494	1.04369166108818
23	105.9	88.9565083929617	-0.259522140848873	16.4029679322993	0.293011771483107
24	44.7	87.9509488890128	-0.283202932912098	-42.2434226261589	-0.544123915405248
25	94	87.4804606057772	-0.288077321390526	6.7812964543588	-0.140928604769788
26	107.1	87.4854477285908	-0.280776508120438	19.2046130697403	0.220557366360404
27	104.8	88.6386829232844	-0.242948300591821	14.1961118975016	1.06015371103563
28	102.5	90.187212978114	-0.192354810314921	9.90923787994986	1.30167389162281
29	77.7	90.5945439357755	-0.174649392821282	-13.6894063279646	0.431823045761138
30	85.2	91.4780356024694	-0.142886443893557	-7.67740454751008	0.761526374812002
31	91.3	92.3839021929191	-0.111625447586399	-2.47772720870655	0.758796171771787
32	106.5	92.9663899001254	-0.0914593163880353	12.6026452216870	0.506528146446527
33	92.4	93.1821204289992	-0.082890093477477	-1.19873615161219	0.226414573086229
34	97.5	92.8154175798178	-0.09039312192698	5.07404912766853	-0.211347910648492
35	107	92.3636135731259	-0.0993371009743986	15.1382138548937	-0.271884604166801
36	51.1	92.4024274984616	-0.096170759646488	-41.4964541313314	0.104956503193787
37	98.6	92.5912284062815	-0.0901267100045483	5.60459455342621	0.218340692796258
38	102.2	91.9542646572515	-0.101305497071859	11.0234045807122	-0.419869473713256
39	114.3	92.9807456784587	-0.078182412054691	19.7211350814306	0.863179902415187
40	99.4	93.1534977447879	-0.0729285721180936	5.89293541372207	0.191159228555848
41	72.5	92.6504471578614	-0.082119141796351	-19.5470088167793	-0.326595268933698
42	92.3	93.468368769283	-0.0626884545257687	-2.42928831540983	0.682930848028511
43	99.4	94.8012246862116	-0.0326426917322024	2.64082456643265	1.06073296136916
44	85.9	92.8497014467416	-0.0733147859915818	-4.24769499770760	-1.46360157733441
45	109.4	94.0773542276447	-0.0464791764099767	13.4815357034655	0.996807334186805
46	97.6	94.3046864070464	-0.0410353827161918	2.90561020965797	0.210850861143600
47	104.7	93.8986426555385	-0.0479807496392532	11.3238851407079	-0.282503396091259
48	56.9	94.2988988694428	-0.0398403959701915	-38.0440392326514	0.348537428297218
49	86.7	92.9879798645008	-0.0619774904272617	-4.45084026349198	-0.99191234376584
50	108.5	93.1703345405175	-0.0578339251680406	14.9758184033050	0.190986099273943
51	103.4	92.2021495834002	-0.0731233370108304	12.5160834006845	-0.711500130759697
52	86.2	90.5149500256944	-0.100267479626643	-1.98051497421404	-1.26028062105924
53	71	90.0067661009445	-0.107158792933552	-18.4174689131130	-0.318242879042410
54	75.9	88.5346700753104	-0.130259213455715	-10.6634088344547	-1.06482595409878
55	87.1	87.2752388661739	-0.149285846332507	1.45682568825914	-0.881688871590838
56	102	88.9819829185483	-0.118379731313824	10.3305413985350	1.45174519427050
57	88.5	87.9447125816579	-0.133391162943477	1.88919545860889	-0.720401031225008
58	87.8	87.0453990008443	-0.145592609449186	1.86974513715388	-0.602056475077186
59	100.8	86.802390550314	-0.147099983250943	14.139875682295	-0.0767794008640793
60	50.6	86.5560765552507	-0.148589947577902	-35.8107748484401	-0.078388589618882
61	85.9	86.6456027697475	-0.145108503481557	-1.09511693794696	0.188500270170006

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259948467jmfr4yarxhc3ppx/1jznr1259948413.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259948467jmfr4yarxhc3ppx/1jznr1259948413.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259948467jmfr4yarxhc3ppx/27t9r1259948413.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259948467jmfr4yarxhc3ppx/27t9r1259948413.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259948467jmfr4yarxhc3ppx/325j81259948413.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259948467jmfr4yarxhc3ppx/325j81259948413.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259948467jmfr4yarxhc3ppx/40izq1259948413.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259948467jmfr4yarxhc3ppx/40izq1259948413.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259948467jmfr4yarxhc3ppx/5mbo21259948413.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259948467jmfr4yarxhc3ppx/5mbo21259948413.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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