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review WS 9 structural time series models

*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: Sun, 06 Dec 2009 13:39:30 -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/06/t1260132157g4t24votr7y8bs6.htm/, Retrieved Sun, 06 Dec 2009 21:42:44 +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/06/t1260132157g4t24votr7y8bs6.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 «

2360 2214 2825 2355 2333 3016 2155 2172 2150 2533 2058 2160 2260 2498 2695 2799 2947 2930 2318 2540 2570 2669 2450 2842 3440 2678 2981 2260 2844 2546 2456 2295 2379 2479 2057 2280 2351 2276 2548 2311 2201 2725 2408 2139 1898 2537 2069 2063 2524 2437 2189 2793 2074 2622 2278 2144 2427 2139 1828 2072 1800 1758 2246 1987 1868 2514 2121

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	2360	2360	0	0	0
2	2214	2312.07185528361	-6.09728971493757	-10.4814504587985	-0.503823320444186
3	2825	2486.47953830121	12.0298992713060	37.9844806231517	1.76515815669492
4	2355	2448.68099141428	8.04694318022202	-8.2138867659148	-0.497455912616607
5	2333	2411.58392912464	5.04968559230386	1.66131960561733	-0.462897298598276
6	3016	2611.95835180597	16.2099399533660	45.9922776583717	2.05073021813675
7	2155	2472.5468542077	8.33551524132652	-25.2704786803007	-1.6650203457865
8	2172	2375.62053625177	3.51007807127923	-2.24116510491916	-1.14262590815467
9	2150	2302.67893970694	0.278209027686111	-4.37049592090061	-0.839005633276679
10	2533	2374.45984410445	3.10342126472291	18.3699404846487	0.791198574481487
11	2058	2276.91686153069	-0.651484681150949	-20.0272748430463	-1.12072730933494
12	2160	2237.80471816400	-2.01665279708150	-1.32577296413176	-0.430376487549795
13	2260	2234.98380115384	-1.92582074510822	27.2212796857331	-0.0135582763221846
14	2498	2333.39902867889	2.14357352462572	1.68857856205111	0.963772746803275
15	2695	2448.39352890708	6.60333541709837	54.5411504367443	1.13358629261098
16	2799	2571.24799158952	10.5345252771927	16.1797954639417	1.23318890829615
17	2947	2703.16189965531	14.1008190706457	13.8205788412401	1.33046031264561
18	2930	2769.56663719848	15.4713768493359	58.8928155109394	0.584648547189137
19	2318	2646.98062479641	12.1681906169619	-56.9107432447787	-1.56206758493857
20	2540	2614.02714043294	11.1633548086852	15.7596577450187	-0.514552001978047
21	2570	2606.64828368113	10.7732538097629	0.488353433914017	-0.212558377597882
22	2669	2621.63838203486	10.8580068128171	38.8780815353053	0.0485147752708763
23	2450	2579.13410007489	9.8274210650839	-21.4206433738035	-0.615559654652054
24	2842	2660.94798309561	11.0589618394814	34.8257232887654	0.833855510537335
25	3440	2886.32413460303	1.67381757988094	51.188122997334	2.97836615147476
26	2678	2839.51877723206	0.562390348888481	-73.4366766160979	-0.517168659177117
27	2981	2873.16210475039	1.41774286298317	47.9168249464882	0.35405989640968
28	2260	2691.71310925119	-2.75118549557304	-87.9583997277819	-2.01893954347535
29	2844	2730.57594456748	-1.92002499899366	33.152173063534	0.469256678942312
30	2546	2656.79381526752	-3.20641032641517	30.049394039541	-0.820940676054125
31	2456	2610.984367479	-3.9061159190136	-70.65184050281	-0.490649390332296
32	2295	2511.75830313100	-5.3707336568113	-26.8606337874650	-1.1035133652903
33	2379	2468.93353149858	-5.91732909600921	-14.9989100389308	-0.435104908455723
34	2479	2456.85838204709	-6.00357924213021	34.4979595261797	-0.0717062016589342
35	2057	2349.75968351681	-7.3552746871455	-89.3865954923687	-1.17950114685758
36	2280	2322.58955430596	-7.56062708489063	-2.41419156589651	-0.232359517512022
37	2351	2287.53802422025	-6.91536097947537	124.168319463426	-0.357766165566186
38	2276	2299.77167985541	-6.63001852927053	-60.0269472844922	0.213490258175437
39	2548	2348.08905197103	-5.57060707324941	97.8600751150478	0.605719354125933
40	2311	2365.36307795246	-5.16722818613402	-97.7607440938145	0.256817895904591
41	2201	2301.40705814395	-6.08581067232341	13.4272814764400	-0.671434143825295
42	2725	2407.08488840604	-4.51673537665382	98.8074098714247	1.28949247609095
43	2408	2424.60731875143	-4.23249209061842	-60.1534905269351	0.255911638474619
44	2139	2345.53963502971	-5.13679192547475	-57.9302577934933	-0.872537064377107
45	1898	2211.79820162133	-6.61512455961682	-57.5591676010272	-1.50353655325922
46	2537	2277.96735580523	-5.81304532325085	113.668530809122	0.852553327350742
47	2069	2240.82572657119	-6.13564051572941	-109.098359702545	-0.367629344962183
48	2063	2182.91872516131	-6.49488393213439	-15.3831744507752	-0.610944330033546
49	2524	2235.98447140751	-7.31405058614799	160.882757380108	0.749725942233221
50	2437	2314.76552887464	-6.4056679745918	-43.9362476092444	0.98213554386673
51	2189	2250.30058657887	-7.29257303698016	48.1170304956805	-0.65160067825887
52	2793	2428.3741042231	-4.58928485656759	10.4986850466005	2.10641698339533
53	2074	2335.30614196911	-5.74716880791852	-89.7567989202613	-1.01798149709272
54	2622	2382.82207958888	-5.11866050924947	134.838902451937	0.618033780480188
55	2278	2362.96009068093	-5.27856545732531	-55.8860781174464	-0.172007948654729
56	2144	2304.28415280321	-5.82119236018597	-54.5299604488134	-0.625171885663563
57	2427	2353.07773814699	-5.29364767372799	-34.5538516704371	0.64091858745992
58	2139	2255.44894550371	-6.14344126463155	67.3433823392528	-1.08541249282018
59	1828	2152.31441886992	-6.95320847066517	-130.736536972702	-1.14223313958602
60	2072	2127.95099970961	-7.04066723065633	-20.9175276022442	-0.206202918854760
61	1800	1994.25102727495	-5.99999288657584	70.3221695240682	-1.56346128657037
62	1758	1924.42350806582	-6.51009920322493	-41.9747155219494	-0.737738361564623
63	2246	2007.67258776075	-5.38470692570339	67.4185642386299	1.01983569746544
64	1987	1993.53473924339	-5.49379822584723	10.2607411200347	-0.10021392832232
65	1868	1983.01384121028	-5.55098586876803	-105.255784181258	-0.058124904806395
66	2514	2091.10432427825	-4.37882657175151	200.363202041606	1.32356497331593
67	2121	2115.25863604306	-4.10806931066608	-50.4613355973748	0.333929708904055

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/06/t1260132157g4t24votr7y8bs6/1h3fi1260131967.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/06/t1260132157g4t24votr7y8bs6/1h3fi1260131967.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/06/t1260132157g4t24votr7y8bs6/2i4071260131967.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/06/t1260132157g4t24votr7y8bs6/2i4071260131967.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/06/t1260132157g4t24votr7y8bs6/3w9or1260131967.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/06/t1260132157g4t24votr7y8bs6/3w9or1260131967.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/06/t1260132157g4t24votr7y8bs6/4riky1260131967.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/06/t1260132157g4t24votr7y8bs6/4riky1260131967.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/06/t1260132157g4t24votr7y8bs6/51r251260131967.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/06/t1260132157g4t24votr7y8bs6/51r251260131967.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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