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Paper

*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, 28 Dec 2010 19:35:27 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/28/t1293564807jcur2lex67a98l4.htm/, Retrieved Tue, 28 Dec 2010 20:33:27 +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/2010/Dec/28/t1293564807jcur2lex67a98l4.htm/},
    year = {2010},
}
@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 = {2010},
    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 «

961 935 956 951 986 980 1031 1059 1036 1023 1030 1075 1151 1220 1290 1330 1419 1443 1516 1546 1579 1591 1603 1606 1616 1628 1594 1596 1526 1535 1581 1611 1571 1535 1498 1493 1480 1448 1462 1428 1315 1186 1230 1271 1243 1220 1214 1227 1262 1274 1272 1249 1266 1307 1345 1369 1374 1400 1425 1465 1510 1508 1512 1539 1569 1571 1650 1736 1700 1731 1752

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	961	961	0	0	0
2	935	936.438293083233	-2.27637477957655	-1.43829308323263	-0.499108215241076
3	956	956.520905336905	1.88090707857587	-0.52090533690505	0.692943432588317
4	951	952.62439327153	0.522303979089565	-1.62439327153079	-0.172794216955631
5	986	986.336340520499	9.23595056033624	-0.336340520498809	0.974877953007878
6	980	981.923231619693	5.4538208472925	-1.92323161969277	-0.396897826292056
7	1031	1031.02233513208	17.8752955290597	-0.0223351320779017	1.26251599520245
8	1059	1060.35502114715	21.1797372184675	-1.35502114715345	0.330552661263599
9	1036	1038.52283621066	8.69191806663708	-2.52283621065761	-1.23930631232365
10	1023	1024.53605972045	2.08557974162984	-1.53605972044556	-0.653029879979702
11	1030	1030.98710657750	3.35937377700362	-0.987106577502066	0.125665013576204
12	1075	1075.24452117220	15.3030159167281	-0.244521172197851	1.17713119431908
13	1151	1123.52541406011	24.6160355697118	27.4745859398925	1.09031624085282
14	1220	1220.19354289373	44.5601500537191	-0.193542893734683	1.74420887730978
15	1290	1289.17566036024	51.642889286124	0.824339639756534	0.700164244363578
16	1330	1333.02471229712	49.3735462597942	-3.02471229712164	-0.222575238569513
17	1419	1416.38243190095	59.2583501811928	2.61756809905171	0.97174755754607
18	1443	1447.50119311164	51.0761606487051	-4.50119311164243	-0.80509743647965
19	1516	1515.20797787227	55.9114470427712	0.792022127728652	0.475932948220083
20	1546	1547.27848444499	48.9798502867707	-1.27848444498643	-0.682380584106402
21	1579	1580.80053769127	44.4854994607685	-1.80053769126774	-0.442481985966224
22	1591	1593.11151778853	35.1303677775772	-2.11151778853419	-0.92108114172083
23	1603	1604.86392016411	28.3320520125587	-1.86392016410777	-0.669373640446721
24	1606	1607.60460275141	20.8967134286134	-1.60460275140648	-0.732125689047544
25	1616	1610.14080858481	15.6247659436142	5.85919141518533	-0.561064670792634
26	1628	1629.02120640121	16.5433281641576	-1.02120640121451	0.0850458557114716
27	1594	1595.20689190256	2.01487705230139	-1.20689190256321	-1.43764506684695
28	1596	1599.91729362584	2.79662476399651	-3.91729362584116	0.0767551914209629
29	1526	1526.13634724695	-19.3957822855772	-0.136347246953412	-2.18190432396939
30	1535	1537.31240326809	-10.5385872992571	-2.31240326809260	0.871616335450915
31	1581	1576.33515244992	3.81921211585667	4.66484755007803	1.41333220373628
32	1611	1610.75888768924	12.6851757217994	0.241112310756465	0.872841590170346
33	1571	1574.92809426307	-1.36985704441351	-3.92809426307030	-1.38378555078528
34	1535	1537.57609053635	-11.7945013977784	-2.57609053635208	-1.02640195154334
35	1498	1499.49920631234	-19.4097065379955	-1.49920631233638	-0.749814275253908
36	1493	1492.37303268138	-15.855811990299	0.626967318621819	0.350092537472794
37	1480	1475.05430200280	-16.2770744479791	4.94569799719625	-0.0433772342277661
38	1448	1446.67049618222	-19.7205308454165	1.32950381777925	-0.326431159583033
39	1462	1461.85270255144	-9.68272586078546	0.147297448555404	0.992772385235179
40	1428	1428.28978373195	-16.5890962198329	-0.289783731945483	-0.678791871948481
41	1315	1322.11398647155	-42.4875884672512	-7.11398647154654	-2.54628934253845
42	1186	1195.57292617751	-66.7794317357355	-9.57292617750833	-2.39054537875425
43	1230	1220.13881620159	-40.3816795349727	9.86118379840554	2.59859029667091
44	1271	1263.54006076648	-16.1695228150910	7.45993923351947	2.38370025756123
45	1243	1246.58987670696	-16.395128349875	-3.58987670695951	-0.0222122520143006
46	1220	1221.47681180011	-18.91475317103	-1.47681180010925	-0.248084376934295
47	1214	1215.24296723906	-15.2498243490977	-1.24296723905904	0.36084984568892
48	1227	1224.68496850432	-8.12574450385479	2.31503149568248	0.702234398576933
49	1262	1252.25337181628	2.15801760879647	9.74662818371508	1.04144267450171
50	1274	1275.68234002454	8.23213147249949	-1.68234002454475	0.583172495751679
51	1272	1273.45375975580	5.22911195984318	-1.45375975579564	-0.296713112341198
52	1249	1245.81723425674	-4.25719587133692	3.18276574326016	-0.933210584713405
53	1266	1262.79930650963	1.87261729535962	3.20069349036747	0.602682430644237
54	1307	1318.35975883673	17.3627980171068	-11.3597588367340	1.52433229881749
55	1345	1342.06124999012	19.1915632081027	2.93875000987607	0.180024785351115
56	1369	1362.00640925850	19.4089823732107	6.99359074150351	0.0214053063621615
57	1374	1377.12632270666	18.1715075646823	-3.12632270665660	-0.121838533672427
58	1400	1401.41947794047	19.9378559517536	-1.41947794046984	0.17391803019349
59	1425	1427.17647305111	21.6166500044912	-2.17647305110964	0.165287869637088
60	1465	1464.06304293403	26.0145369108756	0.936957065966978	0.433764151234548
61	1510	1501.65740889875	29.3501814380784	8.34259110124787	0.334575383573677
62	1508	1510.43968048571	23.4642753438675	-2.43968048571409	-0.56942788806412
63	1512	1511.81724594255	17.1299224367108	0.182754057446914	-0.625238911494709
64	1539	1536.07232183158	19.1835479477738	2.92767816842037	0.202173286452353
65	1569	1569.17657654332	23.1964785388394	-0.176576543323348	0.394579951374799
66	1571	1583.99019666247	20.7806479673288	-12.9901966624666	-0.237722109364262
67	1650	1644.25004188389	32.1574227473424	5.74995811610639	1.11992954661253
68	1736	1725.41934260191	46.2814335518937	10.5806573980932	1.39054652026512
69	1700	1709.38080465618	28.3215536995056	-9.38080465618261	-1.76830337762832
70	1731	1732.73824915606	26.8908706126999	-1.73824915605955	-0.140867939939903
71	1752	1755.68756866500	25.7552284609808	-3.68756866499811	-0.111808362882112

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293564807jcur2lex67a98l4/15lft1293564923.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293564807jcur2lex67a98l4/15lft1293564923.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293564807jcur2lex67a98l4/25lft1293564923.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293564807jcur2lex67a98l4/25lft1293564923.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293564807jcur2lex67a98l4/35lft1293564923.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293564807jcur2lex67a98l4/35lft1293564923.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293564807jcur2lex67a98l4/4yuww1293564923.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293564807jcur2lex67a98l4/4yuww1293564923.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293564807jcur2lex67a98l4/5yuww1293564923.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293564807jcur2lex67a98l4/5yuww1293564923.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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