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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: Wed, 16 Dec 2009 13:58:04 -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/16/t1260997121pxibbzt75icxzpf.htm/, Retrieved Wed, 16 Dec 2009 21:58:49 +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/16/t1260997121pxibbzt75icxzpf.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 «

519 517 510 509 501 507 569 580 578 565 547 555 562 561 555 544 537 543 594 611 613 611 594 595 591 589 584 573 567 569 621 629 628 612 595 597 593 590 580 574 573 573 620 626 620 588 566 557 561 549 532 526 511 499 555 565 542 527 510 514 517 508 493 490 469 478 528 534 518 506 502 516

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	519	519	0	0	0
2	517	517.53488576319	-1.50931967068352	-0.534885763190245	-0.195917433969918
3	510	511.16081785952	-4.83640438677179	-1.16081785951987	-0.392237856250045
4	509	508.037137786154	-3.59297681257972	0.962862213845823	0.144093393598201
5	501	501.931210878454	-5.38261979234418	-0.931210878453754	-0.198503448653565
6	507	504.481454351377	0.225291191827157	2.5185456486234	0.62847050025145
7	569	554.95164228436	35.867331872617	14.0483577156393	3.99269021633074
8	580	586.062027693306	32.4901132096203	-6.06202769330635	-0.378037598250256
9	578	586.988624471589	10.0833547031088	-8.98862447158926	-2.50841293522469
10	565	570.172230981533	-9.00870670356781	-5.1722309815326	-2.13730328845535
11	547	548.41501673278	-18.0560584872628	-1.41501673278001	-1.01281832390928
12	555	548.559512126371	-5.13937789484071	6.4404878736286	1.44597793857026
13	562	558.837841072575	5.77274633040281	3.16215892742494	1.22544629398114
14	561	562.308458906698	4.13702027413221	-1.30845890669831	-0.186017119087309
15	555	557.687050697457	-1.87267524876861	-2.68705069745723	-0.668685054456384
16	544	542.403886365893	-11.0334912457731	1.59611363410696	-1.04188732497722
17	537	536.684457281772	-7.37502441697304	0.315542718228301	0.4098364124012
18	543	551.268255807669	7.6204892170364	-8.26825580766865	1.67404698884967
19	594	577.463147782637	20.2926889639789	16.5368522173628	1.41962649034373
20	611	607.760346136581	27.1302151031926	3.23965386341893	0.765654019379351
21	613	619.073585930938	16.3148820785158	-6.07358593093843	-1.21064162342642
22	611	616.16090698309	3.16786824404775	-5.16090698308993	-1.47186502087566
23	594	604.156010494937	-7.20248277329205	-10.1560104949366	-1.16094206889327
24	595	593.894944914613	-9.29072115986202	1.10505508538653	-0.233853818426585
25	591	586.786106270801	-7.80084535688394	4.21389372919851	0.167298240048712
26	589	584.679424821553	-3.9076773595721	4.32057517844665	0.436478595201897
27	584	580.491453784252	-4.09741968659976	3.50854621574841	-0.0211877937283579
28	573	572.376381552077	-6.80792453391357	0.623618447923053	-0.305025292554735
29	567	571.275527873055	-2.93767135303228	-4.2755278730546	0.434380592348358
30	569	581.139807467815	5.72276901437693	-12.1398074678145	0.967631686718844
31	621	604.783455390935	17.8162552110648	16.2165446090654	1.35334777357137
32	629	622.914321794534	18.0287501436880	6.085678205466	0.0237963385170933
33	628	631.273185881033	11.4919827271705	-3.27318588103264	-0.731760462375117
34	612	619.034372715256	-4.55084459529663	-7.034372715256	-1.79597672442147
35	595	605.602642402641	-10.5515908366955	-10.6026424026414	-0.671780986634648
36	597	596.117984864524	-9.83110419756276	0.882015135476252	0.0807106975335485
37	593	589.505590051469	-7.65594162463881	3.49440994853093	0.243935906296182
38	590	583.826580184859	-6.32036795774515	6.17341981514053	0.149496513561709
39	580	574.370230788928	-8.42874262687417	5.62976921107169	-0.235737801836184
40	574	571.936294220964	-4.40530367621779	2.06370577903589	0.451462185397122
41	573	578.775270023456	3.16303817899002	-5.77527002345611	0.848969328353827
42	573	590.423616178246	8.87255658476506	-17.4236161782464	0.638620028477297
43	620	604.478954183038	12.3531944414395	15.5210458169624	0.389364730856851
44	626	617.413377632499	12.7435337701036	8.58662236750144	0.0437003858891592
45	620	618.948409424444	5.2109568683047	1.05159057555633	-0.84329004262027
46	588	599.128070785592	-11.6137169992138	-11.1280707855923	-1.88348049229621
47	566	578.635295529771	-17.5798043371606	-12.6352955297715	-0.667966338555024
48	557	557.86847801415	-19.7210446513701	-0.868478014149465	-0.239866377758354
49	561	552.673817483451	-9.95541515873275	8.32618251654923	1.09422816963352
50	549	541.487802219984	-10.7821493913125	7.51219778001625	-0.0925134172564313
51	532	527.86983573287	-12.6818517297867	4.13016426713028	-0.212518265865295
52	526	524.353760526945	-6.54767085350996	1.64623947305465	0.687590183337382
53	511	520.026577030717	-5.05903817220852	-9.02657703071652	0.166892365403853
54	499	518.76078483126	-2.51522676542611	-19.7607848312599	0.284698009363485
55	555	535.884644676667	10.6385500832129	19.1153553233334	1.47152213130353
56	565	552.41137851768	14.5805359889659	12.5886214823201	0.441223277411353
57	542	540.482672361279	-3.17263792438587	1.51732763872071	-1.98749946266108
58	527	534.192382851342	-5.26087479406452	-7.19238285134166	-0.233788317873157
59	510	523.701322028714	-8.76379582719401	-13.7013220287140	-0.392233342365311
60	514	518.376693631045	-6.46002578594065	-4.37669363104481	0.258046937760827
61	517	508.663803878302	-8.6398232894806	8.33619612169845	-0.244128210074671
62	508	498.971407597004	-9.3446543170203	9.02859240299631	-0.0788689212302369
63	493	490.464523405607	-8.78471794516405	2.5354765943928	0.0626554170019082
64	490	486.563474934858	-5.52257960050777	3.43652506514171	0.365491028832501
65	469	480.416519265422	-5.94012292608596	-11.4165192654216	-0.0467943279911121
66	478	498.690151024325	10.260040052035	-20.6901510243251	1.81360380907420
67	528	511.418310545811	11.9100070657757	16.5816894541889	0.184608971279338
68	534	515.141021350741	6.44011800242520	18.8589786492590	-0.612165182048206
69	518	516.533998204122	3.06812512897663	1.4660017958784	-0.377486923997789
70	506	513.587580086199	-0.950712848649473	-7.58758008619888	-0.449964271024861
71	502	515.853248502042	1.19863293710772	-13.8532485020418	0.240690861429298
72	516	518.818108391217	2.37924407106951	-2.81810839121707	0.132227795184545

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260997121pxibbzt75icxzpf/1z7jo1260997081.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260997121pxibbzt75icxzpf/1z7jo1260997081.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260997121pxibbzt75icxzpf/28f3p1260997081.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260997121pxibbzt75icxzpf/28f3p1260997081.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260997121pxibbzt75icxzpf/36cka1260997081.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260997121pxibbzt75icxzpf/36cka1260997081.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260997121pxibbzt75icxzpf/47r821260997081.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260997121pxibbzt75icxzpf/47r821260997081.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260997121pxibbzt75icxzpf/5ycvi1260997081.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260997121pxibbzt75icxzpf/5ycvi1260997081.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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