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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, 08 Dec 2010 15:36:36 +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/08/t1291823326wfggamqjz75l0z7.htm/, Retrieved Wed, 08 Dec 2010 16:48:48 +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/08/t1291823326wfggamqjz75l0z7.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 «

9700 9081 9084 9743 8587 9731 9563 9998 9437 10038 9918 9252 9737 9035 9133 9487 8700 9627 8947 9283 8829 9947 9628 9318 9605 8640 9214 9567 8547 9185 9470 9123 9278 10170 9434 9655 9429 8739 9552 9687 9019 9672 9206 9069 9788 10312 10105 9863 9656 9295 9946 9701 9049 10190 9706 9765 9893 9994 10433 10073 10112 9266 9820 10097 9115 10411 9678 10408 10153 10368 10581 10597 10680 9738 9556

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	9700	9700	0	0	0
2	9081	9420.75450143316	-4.57323719029182	-334.807899115417	-1.94834013632446
3	9084	9148.23690533508	-22.2229146322506	-61.4760003105638	-1.35940558228141
4	9743	9343.3410893296	-8.81350400055626	396.802512755963	1.35792880524648
5	8587	9095.71792616632	-19.3898286098834	-504.931356723109	-1.70068400570002
6	9731	9271.8098096163	-13.6789709574988	455.875165586204	1.44995580907109
7	9563	9434.3419938712	-10.0335857183998	125.612554401045	1.31903750930236
8	9998	9698.05321184868	-5.3287449179581	295.19507000796	2.05149393903093
9	9437	9674.89339629866	-5.61986801785221	-237.5839449585	-0.133514733832356
10	10038	9807.9599625221	-3.34218991531362	227.636519697675	1.03724816845382
11	9918	9889.1118146233	-1.93650787035048	27.4255473642788	0.6314277490997
12	9252	9667.92152658138	-5.59569782119897	-412.128213795466	-1.63791142714891
13	9737	9552.09646360713	-3.60297502605207	186.867956364579	-0.867993514739218
14	9035	9409.60408920573	-2.67806138231115	-372.145429557391	-1.07958564974153
15	9133	9311.8670562481	-4.16396481957125	-177.363252235036	-0.67266590846052
16	9487	9154.7049266868	-8.33657128828147	334.584414763756	-1.05065058009594
17	8700	9193.58255742851	-6.97670755254194	-494.30617022458	0.333375757119034
18	9627	9253.45661914782	-5.30619486369144	372.47736536272	0.487314530858606
19	8947	9171.22218329847	-6.8489039452291	-222.963887319412	-0.570816284511288
20	9283	9097.5437699252	-7.92764326966444	186.562643494913	-0.499537504676475
21	8829	9104.99880734835	-7.72006152946614	-276.254767306947	0.115256870510946
22	9947	9330.401327745	-5.08068646725834	612.71196511763	1.74690752842199
23	9628	9424.0075377992	-4.23375213024213	202.345169841292	0.739029481362515
24	9318	9518.233353789	-3.76373048259059	-201.881264385133	0.738235804272518
25	9605	9459.67914841382	-3.82810473375604	146.243003672187	-0.412983398291401
26	8640	9244.05520062057	-4.5614664474363	-600.521714378761	-1.58335108754847
27	9214	9214.62719890013	-4.81019516280528	-0.22464114649487	-0.181371770740218
28	9567	9224.516761558	-4.57400113307158	342.251417518535	0.105411069767361
29	8547	9155.49379595095	-5.80539090009781	-607.480281767522	-0.463548212929267
30	9185	8982.94359899634	-8.98969150139358	204.715084781184	-1.21612242545158
31	9470	9195.95005020216	-5.17614871686062	270.452461626172	1.64058433173774
32	9123	9183.67764068775	-5.27922954825366	-60.5613089813522	-0.0528669508714306
33	9278	9382.19726346708	-2.87328272037568	-107.559720361746	1.5236769346327
34	10170	9524.09469487191	-1.54036934419529	643.509448971725	1.08334525580578
35	9434	9459.83031998424	-1.96703685693058	-24.7907015091494	-0.469402423735074
36	9655	9554.2111387519	-1.49176664531097	99.1904466203823	0.721117644780371
37	9429	9426.44024351576	-2.04143743527976	4.65246249873495	-0.94390669372978
38	8739	9354.04484078152	-2.44741155897752	-613.887181820166	-0.52257735361842
39	9552	9400.49104181577	-2.02045921379527	150.715049174559	0.359346060548004
40	9687	9364.46944021814	-2.42468218856774	323.075912981341	-0.247865446690069
41	9019	9439.2406026585	-1.34112591070702	-421.473969794341	0.562504440206011
42	9672	9526.31204832682	-0.0428513508651429	144.268435267398	0.64814736397209
43	9206	9354.37026517756	-2.44559839392539	-145.585843110317	-1.2701001625453
44	9069	9291.78863492691	-3.18985192897205	-221.806596474209	-0.4470367361601
45	9788	9527.2691993719	-0.71589068617328	256.811673152004	1.78023707522975
46	10312	9624.42082805441	0.100170390095405	685.967142746008	0.730999398129028
47	10105	9836.12068994242	1.50193541449598	265.388717012408	1.58105311970829
48	9863	9824.44272464268	1.42873328858631	38.7747351140736	-0.0984385370787065
49	9656	9747.28648110487	1.00259473583613	-89.9922998100579	-0.585806296407066
50	9295	9801.81326763457	1.34088482098732	-507.69042163976	0.397302840410875
51	9946	9816.20255551631	1.44476309446794	129.585144443431	0.0963122419887453
52	9701	9677.00316972274	0.0714613300482087	26.270297346684	-1.0336560688549
53	9049	9569.03808422818	-1.13203119590869	-518.296349569519	-0.793453922902278
54	10190	9686.25380915568	0.255628143352628	501.834536365409	0.87166070665636
55	9706	9795.08371932902	1.49968239644785	-90.8459012856327	0.803256547155335
56	9765	9964.8495425342	3.26806929279488	-202.594791905987	1.24994318954811
57	9893	9928.3794111347	2.90356737883564	-34.728420318324	-0.295988750252327
58	9994	9736.87356064694	1.39315731484946	260.319591394797	-1.45005227890209
59	10433	9841.16984845244	2.07211549502545	590.137780993964	0.76785759012792
60	10073	9924.9231069369	2.55428630773501	146.733500356274	0.609236964687423
61	10112	10052.7997058889	3.28499710432706	57.1422558867383	0.93330041507913
62	9266	9964.62348979044	2.70209668546316	-697.126316059047	-0.67926581475193
63	9820	9805.68357171138	1.51495021034942	16.9512711711893	-1.19658207327127
64	10097	9863.91284314564	1.99306605262294	232.16612168332	0.418809574824304
65	9115	9841.34154179606	1.76455060490202	-725.94329780538	-0.181296573386226
66	10411	9901.66119152187	2.33417542623351	508.388716623748	0.432784215057325
67	9678	9895.0958122416	2.24852864652447	-216.951027647743	-0.0659462390872501
68	10408	10131.518557488	4.36911179243316	272.659302302699	1.73978933267392
69	10153	10180.004637344	4.73063532414807	-27.7267648139687	0.328412380568315
70	10368	10200.9383803914	4.84828292513222	166.79586815495	0.120757261637749
71	10581	10156.2675107526	4.52786575459365	425.545517013987	-0.369203429549534
72	10597	10266.9790642662	5.16437023326159	328.277479977141	0.791437348961157
73	10680	10388.5765997519	5.85381681877687	289.513630460247	0.866899581061993
74	9738	10404.3992444693	5.91598737040549	-666.562423290676	0.0740933883024219
75	9556	10104.9944128139	3.83319949892939	-544.009399803566	-2.26486452572958

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291823326wfggamqjz75l0z7/1xbig1291822592.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291823326wfggamqjz75l0z7/1xbig1291822592.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291823326wfggamqjz75l0z7/2qk0j1291822592.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291823326wfggamqjz75l0z7/2qk0j1291822592.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291823326wfggamqjz75l0z7/30tzm1291822592.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291823326wfggamqjz75l0z7/30tzm1291822592.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291823326wfggamqjz75l0z7/40tzm1291822592.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291823326wfggamqjz75l0z7/40tzm1291822592.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291823326wfggamqjz75l0z7/5b3y71291822592.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291823326wfggamqjz75l0z7/5b3y71291822592.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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