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WS9

*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, 11 Dec 2009 05:50:35 -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/11/t1260535889mobetfc7xscshky.htm/, Retrieved Fri, 11 Dec 2009 13:51:36 +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/11/t1260535889mobetfc7xscshky.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 «

7.55 7.55 7.59 7.59 7.59 7.57 7.57 7.59 7.6 7.64 7.64 7.76 7.76 7.76 7.77 7.83 7.94 7.94 7.94 8.09 8.18 8.26 8.28 8.28 8.28 8.29 8.3 8.3 8.31 8.33 8.33 8.34 8.48 8.59 8.67 8.67 8.67 8.71 8.72 8.72 8.72 8.74 8.74 8.74 8.74 8.79 8.85 8.86 8.87 8.92 8.96 8.97 8.99 8.98 8.98 9.01 9.01 9.03 9.05 9.05

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	7.55	7.55	0	0	0
2	7.55	7.55	0	0	0
3	7.59	7.58990771340992	0.0024007105550275	9.22865900841344e-05	1.06827691323131
4	7.59	7.58991278702805	0.00219907416585357	8.7212971953873e-05	-0.0632927357523968
5	7.59	7.58991695269382	0.00197108996449322	8.30473061849324e-05	-0.0573504975986414
6	7.57	7.56995361060425	-0.000648120067153568	4.63893957548886e-05	-0.568004021155119
7	7.57	7.56995267101184	-0.00056314909751527	4.73289881560325e-05	0.0166419211157233
8	7.59	7.58992703343113	0.00231549072444540	7.29665688688694e-05	0.52529751643838
9	7.6	7.59991885630896	0.00344137092073834	8.1143691039594e-05	0.195559371745820
10	7.64	7.63988583759632	0.00897042770434947	0.000114162403681912	0.92778399049776
11	7.64	7.63989268665707	0.0075833444568994	0.000107313342932199	-0.227196164587133
12	7.76	7.75982033421348	0.025237756223237	0.000179665786516509	2.84313202135591
13	7.76	7.76891938926894	0.0228611326116433	-0.00891938926893606	-0.479562959226583
14	7.76	7.75991451951649	0.0177995322003241	8.54804835116081e-05	-0.682317175534645
15	7.77	7.76991195949442	0.0165450313109139	8.80405055766801e-05	-0.196813177933444
16	7.83	7.82992391986315	0.0235602887687689	7.60801368530244e-05	1.09615309066543
17	7.94	7.93994386043161	0.0375509979587897	5.61395683930133e-05	2.17990158004761
18	7.94	7.93993660250133	0.0314621621198385	6.339749867429e-05	-0.946823552635257
19	7.94	7.93993150872076	0.0263541445485271	6.84912792434782e-05	-0.793200122860028
20	8.09	8.08994827422833	0.0464464389351056	5.17257716723804e-05	3.11699660771905
21	8.18	8.17995321954107	0.0535282486168987	4.67804589345699e-05	1.09787822891675
22	8.26	8.25995573634209	0.0578344357980684	4.42636579128188e-05	0.667259493580475
23	8.28	8.27995272455853	0.0516779852051912	4.72754414694701e-05	-0.953644339934985
24	8.28	8.2799492803118	0.0432670971055187	5.07196881949043e-05	-1.30255387275861
25	8.28	8.28781819076896	0.0375929514288642	-0.00781819076896485	-0.969939021343275
26	8.29	8.28980682994419	0.0318899566322585	0.000193170055808733	-0.81457050795472
27	8.3	8.29979910510404	0.0283238665065306	0.000200894895957535	-0.551689911682417
28	8.3	8.29979073802117	0.0237102420980077	0.000209261978827828	-0.713852183622498
29	8.31	8.30978734756625	0.0214772130535243	0.000212652433754479	-0.345545158482727
30	8.33	8.32978704175544	0.02123663055199	0.000212958244557618	-0.0372310755894764
31	8.33	8.32978336134716	0.0177781396026453	0.000216638652835544	-0.53524176071904
32	8.34	8.33978223287843	0.0165114714802538	0.000217767121566926	-0.196038543351975
33	8.48	8.47979723130562	0.0366210961203699	0.000202768694375998	3.11238488854689
34	8.59	8.58980469230427	0.048570375887871	0.000195307695725699	1.84943285114186
35	8.67	8.66980736760433	0.05368843035051	0.000192632395669920	0.792149223483837
36	8.67	8.66980354180451	0.044945780928337	0.000196458195488437	-1.35315905324315
37	8.67	8.67721558017537	0.0388864245590012	-0.00721558017537371	-1.00113850041526
38	8.71	8.709415722347	0.0378117009290267	0.000584277653006517	-0.157265106796134
39	8.72	8.71940810976931	0.0332806369663036	0.000591890230692181	-0.700930959637714
40	8.72	8.71940048464838	0.0278593923425237	0.000599515351616428	-0.838775358579526
41	8.72	8.71939514127338	0.0233217184965352	0.00060485872662086	-0.702150360107278
42	8.74	8.73939460793605	0.0227807245478065	0.000605392063954994	-0.0837190760111358
43	8.74	8.73939154592883	0.0190707182239226	0.000608454071174561	-0.574157866944926
44	8.74	8.73938940003462	0.0159650259501973	0.000610599965376414	-0.4806537862901
45	8.74	8.73938789614622	0.0133651659250915	0.00061210385378419	-0.402379661059021
46	8.79	8.7893907851389	0.0193309404188876	0.000609214861099462	0.923339410461482
47	8.85	8.84939347001116	0.0259535829546015	0.000606529988838693	1.02501872946052
48	8.86	8.85939258830118	0.0233556877965697	0.000607411698818161	-0.402092780351392
49	8.87	8.877234006816	0.022463385363615	-0.00723400681599721	-0.145071746740841
50	8.92	8.91917684266502	0.0256026177572776	0.00082315733498205	0.465227470300943
51	8.96	8.95917998885346	0.0279480019242307	0.000820011146539278	0.362856825217533
52	8.97	8.96917670474563	0.0250245635900004	0.000823295254371052	-0.452348355170663
53	8.99	8.98917593509685	0.0242062132295584	0.00082406490315245	-0.126636484180673
54	8.98	8.97917154880821	0.0186353811313104	0.000828451191791742	-0.862120579036046
55	8.98	8.97916954833848	0.0156005451401988	0.00083045166151505	-0.469681068759545
56	9.01	9.00917084236662	0.0179454773656467	0.00082915763337638	0.362920969542036
57	9.01	9.00916949229011	0.0150231399568251	0.00083050770989142	-0.452295110641569
58	9.03	9.02916980573825	0.0158335867924407	0.000830194261744637	0.125436206750590
59	9.05	9.04917002541313	0.0165120512004670	0.000829974586873763	0.105009900970198
60	9.05	9.04916929658114	0.0138232252403307	0.000830703418861457	-0.416168527928599

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260535889mobetfc7xscshky/1k61q1260535833.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260535889mobetfc7xscshky/1k61q1260535833.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260535889mobetfc7xscshky/29lp81260535833.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260535889mobetfc7xscshky/29lp81260535833.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260535889mobetfc7xscshky/3s7l61260535833.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260535889mobetfc7xscshky/3s7l61260535833.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260535889mobetfc7xscshky/4f2fv1260535833.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260535889mobetfc7xscshky/4f2fv1260535833.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260535889mobetfc7xscshky/5jrqy1260535833.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260535889mobetfc7xscshky/5jrqy1260535833.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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