Blog & Share Statistical Computations at FreeStatistics.org

Home » date » 2009 » Dec » 01 »

*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, 01 Dec 2009 11:53:41 -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/01/t1259693682902t41val1f8nj6.htm/, Retrieved Tue, 01 Dec 2009 19:54:49 +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/01/t1259693682902t41val1f8nj6.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 «

785.8 819.3 849.4 880.4 900.1 937.2 948.9 952.6 947.3 974.2 1000.8 1032.8 1050.7 1057.3 1075.4 1118.4 1179.8 1227 1257.8 1251.5 1236.3 1170.6 1213.1 1265.5 1300.8 1348.4 1371.9 1403.3 1451.8 1474.2 1438.2 1513.6 1562.2 1546.2 1527.5 1418.7 1448.5 1492.1 1395.4 1403.7 1316.6 1274.5 1264.4 1323.9 1332.1 1250.2 1096.7 1080.8 1039.2 792 746.6 688.8 715.8 672.9 629.5 681.2 755.4 760.6 765.9 836.8 904.9

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	785.8	785.8	0	0	0
2	819.3	817.609282416434	2.67691669634891	1.69071758356565	0.39719223433328
3	849.4	847.720422441074	6.8457719559912	1.67957755892550	0.533925998333214
4	880.4	878.728299666824	11.6089242081624	1.67170033317598	0.457582594189363
5	900.1	898.430343864027	13.4318026707852	1.66965613597312	0.150572765794228
6	937.2	935.534877703158	19.1547469770608	1.66512229684247	0.435741924222337
7	948.9	947.233808359028	17.2823436060088	1.66619164097247	-0.136394450123664
8	952.6	950.93235956639	13.8000063715200	1.66764043360883	-0.247639628313144
9	947.3	945.630850424226	8.84811679642649	1.66914957577367	-0.347566601463131
10	974.2	972.531904715653	13.5566759407004	1.66809528434752	0.3281445814981
11	1000.8	999.13246713868	16.9700300135244	1.66753286132071	0.236961926540982
12	1032.8	1031.13294532186	20.91030792724	1.66705467814030	0.272967387597524
13	1050.7	1064.19528093053	23.9861078329843	-13.4952809305295	0.256142096431306
14	1057.3	1056.77482598595	16.140104236904	0.525174014053045	-0.476856585731127
15	1075.4	1074.87717814867	16.6562750391262	0.522821851332131	0.0355656476534347
16	1118.4	1117.90047570500	23.5865448498081	0.499524295004611	0.478147592285431
17	1179.8	1179.32512473132	33.5280995815171	0.474875268683573	0.686401833691654
18	1227	1226.53169455762	37.1213936863546	0.468305442379223	0.248191353229814
19	1257.8	1257.32945512834	35.4602836533393	0.470544871660763	-0.114758419392082
20	1251.5	1251.01854819546	24.4877623896678	0.481451804534982	-0.758128365479101
21	1236.3	1235.81090598933	14.0603520655634	0.489094010668068	-0.720510051317063
22	1170.6	1170.09958259550	-6.89496964288594	0.500417404495105	-1.44801390892128
23	1213.1	1212.60475273339	6.08229481863566	0.495247266608715	0.896746339175407
24	1265.5	1265.00832708782	18.2509826282907	0.491672912180066	0.840881089688386
25	1300.8	1302.58843568902	23.2522482701005	-1.78843568902327	0.378965520562840
26	1348.4	1347.92035387033	28.8668834649575	0.479646129670325	0.360460365295743
27	1371.9	1371.41608794063	27.4542262841326	0.483912059369256	-0.0974010858232042
28	1403.3	1402.81839950051	28.4919255256697	0.481600499488614	0.0716210713320114
29	1451.8	1451.32703971248	33.7513787005342	0.472960287518644	0.363203749207738
30	1474.2	1473.72342600172	30.7682430707837	0.4765739982753	-0.206069355466187
31	1438.2	1437.70775553654	13.2240239121624	0.49224446345753	-1.21211965582312
32	1513.6	1513.11851407799	29.5603326892345	0.481485922008465	1.12876620314203
33	1562.2	1561.72094300987	34.5626687168323	0.4790569901292	0.345655853288744
34	1546.2	1545.71618730810	21.2785175141530	0.483812691902991	-0.917944182211116
35	1527.5	1527.01341499785	10.7752302529652	0.486585002153875	-0.725794894781744
36	1418.7	1418.20730152607	-20.6397594865404	0.492698473930562	-2.17084571764114
37	1448.5	1447.77614094509	-7.57910563285872	0.72385905490675	0.960074783422643
38	1492.1	1491.6213716054	5.61123607123262	0.47862839460027	0.865517533559587
39	1395.4	1394.86114539285	-21.3056704956263	0.538854607147992	-1.85696181010308
40	1403.7	1403.17399088462	-13.521747457278	0.526009115377599	0.537408060928477
41	1316.6	1316.05045698711	-32.8602069476179	0.549543012891735	-1.33569010807091
42	1274.5	1273.94827825169	-35.2882279703313	0.551721748310102	-0.167738647801777
43	1264.4	1263.85265703700	-28.6699786105155	0.547342962996684	0.457273961923214
44	1323.9	1323.36395757756	-5.50446386409072	0.536042422442138	1.60067779808003
45	1332.1	1331.56525257134	-1.90390376092505	0.534747428658438	0.248798403139152
46	1250.2	1249.65967937765	-22.9208508660966	0.540320622345836	-1.45229757317388
47	1096.7	1096.15297219280	-57.2269050840887	0.547027807197017	-2.37061674091869
48	1080.8	1080.25453725348	-46.369458607251	0.545462746522689	0.750275514409668
49	1039.2	1044.25763222343	-43.6643470865065	-5.05763222342639	0.195832418939757
50	792	793.278437919647	-97.1088401705711	-1.27843791964651	-3.54866067243658
51	746.6	747.902599241084	-83.5087750771732	-1.30259924108436	0.938570404677832
52	688.8	690.111454041365	-76.750486622232	-1.31145404136497	0.466683921680099
53	715.8	717.137797289207	-49.4842359072828	-1.33779728920699	1.88344525119048
54	672.9	674.239029796824	-47.7541191975249	-1.33902979682444	0.119530812847165
55	629.5	630.839630696876	-46.6100959362039	-1.33963069687565	0.0790462235088793
56	681.2	682.549633566706	-20.7807519469652	-1.34963356670612	1.78477045555338
57	755.4	756.756758657565	4.17325989438115	-1.35675865756537	1.72433530226900
58	760.6	761.956815444139	4.44300874407886	-1.35681544413915	0.0186400750996998
59	765.9	767.256850389777	4.66815896021728	-1.35685038977692	0.0155583692333735
60	836.8	838.158841592364	22.0686346454974	-1.35884159236399	1.20241617704689
61	904.9	887.949577141857	29.3093455405917	16.9504228581431	0.519368014977001

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259693682902t41val1f8nj6/10y1f1259693618.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259693682902t41val1f8nj6/10y1f1259693618.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259693682902t41val1f8nj6/24fsv1259693618.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259693682902t41val1f8nj6/24fsv1259693618.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259693682902t41val1f8nj6/30pvs1259693618.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259693682902t41val1f8nj6/30pvs1259693618.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259693682902t41val1f8nj6/4d7ya1259693618.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259693682902t41val1f8nj6/4d7ya1259693618.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259693682902t41val1f8nj6/52uys1259693618.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259693682902t41val1f8nj6/52uys1259693618.ps (open in new window)

Parameters (Session):

par1 = FALSE ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 2 ; par7 = 1 ; par8 = 0 ; par9 = 0 ;

Parameters (R input):

par1 = 12 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 2 ; par7 = 1 ; par8 = 0 ; par9 = 0 ;

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

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

We may request personal information to be submitted to our servers in order to be able to:

personalize online software applications according to your needs
enforce strict security rules with respect to the data that you upload (e.g. statistical data)
manage user sessions of online applications
alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

FreeStatistics.org is powered by