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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: Tue, 01 Dec 2009 05:57:06 -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/01/t1259672261b01yyua39rsv6kk.htm/, Retrieved Tue, 01 Dec 2009 13:57:55 +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/01/t1259672261b01yyua39rsv6kk.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 «

149 139 135 130 127 122 117 112 113 149 157 157 147 137 132 125 123 117 114 111 112 144 150 149 134 123 116 117 111 105 102 95 93 124 130 124 115 106 105 105 101 95 93 84 87 116 120 117 109 105 107 109 109 108 107 99 103 131 137 135

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	149	149	0	0	0
2	139	140.642680576515	-8.49307815026848	-1.64268057651493	-1.53765266125616
3	135	133.500074333951	-7.48479596270134	1.49992566604908	0.179646588980101
4	130	129.283276243248	-4.92518488309534	0.716723756752483	0.429256154743507
5	127	126.651382555049	-3.16631001843137	0.348617444950974	0.291079352906523
6	122	122.311849936321	-4.06655159085912	-0.311849936321065	-0.149789544700316
7	117	117.091867312654	-4.95319531857533	-0.0918673126539773	-0.147350847235532
8	112	111.898546268554	-5.13780074827845	0.101453731446092	-0.030678983366815
9	113	111.824958833281	-1.24511431262927	1.17504116671907	0.646919143568898
10	149	142.446719252551	23.2474238085275	6.55328074744891	4.07033839229334
11	157	160.104218695606	18.9510630761748	-3.10421869560569	-0.713999477056228
12	157	160.519666867978	4.70448911649624	-3.51966686797777	-2.36759559411703
13	147	149.423130932804	-7.41655389196125	-2.42313093280427	-2.01924575973931
14	137	138.651364472095	-9.99854288348633	-1.65136447209467	-0.435433688410373
15	132	130.534993534140	-8.61043184634518	1.46500646586046	0.230491923985758
16	125	124.486759690037	-6.7092464825685	0.513240309963174	0.320020400182524
17	123	121.875694581931	-3.66906382684766	1.12430541806935	0.503847616814496
18	117	117.154745667397	-4.44511553052076	-0.154745667396741	-0.128904542228427
19	114	112.241921807902	-4.79063040828097	1.75807819209767	-0.0574491052755323
20	111	109.914705067346	-2.96936429543693	1.08529493265401	0.302662382626359
21	112	116.976242299824	4.44713746808584	-4.97624229982413	1.23251262198667
22	144	135.039765069888	14.5141101045557	8.96023493011166	1.67305690975416
23	150	150.237117393657	15.0191564854999	-0.237117393656592	0.0839323489125045
24	149	152.117735497448	5.3147578699753	-3.11773549744823	-1.61305750864612
25	134	139.248256960133	-8.11523536092009	-5.24825696013339	-2.2378636708975
26	123	125.537574114383	-12.2528618936276	-2.53757411438341	-0.68856124472217
27	116	114.622774908123	-11.2751993877573	1.37722509187697	0.162261823446907
28	117	114.934190035589	-2.80887045221621	2.06580996441128	1.41518045008513
29	111	110.122835175705	-4.27666918402211	0.877164824294993	-0.24393608941861
30	105	104.312497403644	-5.39670563159406	0.687502596355746	-0.185893147778276
31	102	99.421513904895	-5.02752634984793	2.57848609510502	0.0613714544182754
32	95	95.7214539580626	-4.05752352454881	-0.721453958062608	0.161219869519527
33	93	100.414362189554	2.33841008833955	-7.4143621895544	1.06288312950126
34	124	114.355181575426	10.8185210445949	9.64481842457443	1.40936625470719
35	130	127.555301236208	12.5585016763959	2.44469876379205	0.289158446775954
36	124	125.734579232927	2.06014739807857	-1.73457923292679	-1.74557285435788
37	115	119.776311469382	-3.79779900091381	-4.77631146938185	-0.975257794511677
38	106	110.058781352843	-8.12081463749695	-4.05878135284279	-0.718291414599892
39	105	105.904108687892	-5.24063090231314	-0.904108687892376	0.478301449981572
40	105	102.157704601022	-4.15587498894287	2.84229539897826	0.180798076324648
41	101	99.0789740558476	-3.37194082832595	1.92102594415243	0.130375755907062
42	95	93.937052234357	-4.65785530229202	1.06294776564306	-0.213476291706792
43	93	89.62050641417	-4.41014266812671	3.37949358583002	0.0411638873681076
44	84	86.587003679845	-3.41035569721649	-2.58700367984496	0.166174772278906
45	87	95.6373444638323	5.64313017181864	-8.63734446383228	1.50454521176173
46	116	106.975877331137	9.78108234959173	9.02412266886324	0.687688851854283
47	120	114.692232025580	8.28158483850222	5.3077679744197	-0.249204179611138
48	117	117.675976326169	4.43523333482768	-0.675976326169283	-0.639585710530923
49	109	113.874904078211	-1.54813087197722	-4.87490407821138	-0.995393229057181
50	105	110.472914701071	-2.89384823860998	-5.47291470107083	-0.223548606989907
51	107	108.300245479617	-2.37204396861045	-1.30024547961667	0.0866803898783519
52	109	106.305202687956	-2.09933141825618	2.69479731204412	0.0453975352294533
53	109	105.741816728978	-0.98629899255522	3.25818327102178	0.185116680497438
54	108	105.870806544331	-0.178682118569657	2.12919345566875	0.134123914864716
55	107	103.829194688776	-1.52632852533577	3.17080531122411	-0.223899932731448
56	99	104.546454530491	0.0971454867296635	-5.5464545304908	0.269819606800327
57	103	112.131042314681	5.51737273017742	-9.13104231468078	0.900777278002992
58	131	121.366370110087	8.20885579141082	9.63362988991344	0.447291391219030
59	137	130.380943106825	8.7919556953649	6.61905689317495	0.0969124558026854
60	135	134.498138531539	5.40894923658199	0.50186146846088	-0.562506573840623

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259672261b01yyua39rsv6kk/12n6r1259672224.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259672261b01yyua39rsv6kk/12n6r1259672224.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259672261b01yyua39rsv6kk/2sj961259672224.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259672261b01yyua39rsv6kk/2sj961259672224.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259672261b01yyua39rsv6kk/3euda1259672224.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259672261b01yyua39rsv6kk/3euda1259672224.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259672261b01yyua39rsv6kk/4vr171259672224.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259672261b01yyua39rsv6kk/4vr171259672224.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259672261b01yyua39rsv6kk/5aqay1259672224.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259672261b01yyua39rsv6kk/5aqay1259672224.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = periodic ; par3 = 0 ; par5 = 1 ; par7 = 1 ; par8 = FALSE ;

Parameters (R input):

par1 = 12 ; 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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