Home » date » 2010 » Dec » 17 »

Model 1: Classical decomposition van tijdreeksen

*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: Fri, 17 Dec 2010 10:48:09 +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/17/t1292582825v7ufrnvuoue6r1s.htm/, Retrieved Fri, 17 Dec 2010 11:47:06 +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/17/t1292582825v7ufrnvuoue6r1s.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 «

101.76 102.37 102.38 102.86 102.87 102.92 102.95 103.02 104.08 104.16 104.24 104.33 104.73 104.86 105.03 105.62 105.63 105.63 105.94 106.61 107.69 107.78 107.93 108.48 108.14 108.48 108.48 108.89 108.93 109.21 109.47 109.80 111.73 111.85 112.12 112.15 112.17 112.67 112.80 113.44 113.53 114.53 114.51 115.05 116.67 117.07 116.92 117.00 117.02 117.35 117.36 117.82 117.88 118.24 118.50 118.80 119.76 120.09

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	101.76	101.76	0	0	0
2	102.37	102.317472718342	0.0347185971257529	0.0525272816582338	1.21653408394008
3	102.38	102.363096703179	0.0353709973016911	0.0169032968206521	0.0374807288615759
4	102.86	102.766012138015	0.0618267673722994	0.093987861984837	1.26006628543763
5	102.87	102.856525994415	0.0643938166690492	0.0134740055851707	0.0970614551395525
6	102.92	102.895144192622	0.0617022027953932	0.0248558073779502	-0.0863355542135141
7	102.95	102.923266405444	0.0578077936652806	0.0267335945557088	-0.111558917578599
8	103.02	102.98636077963	0.0584674245139674	0.0336392203703432	0.017449553371332
9	104.08	103.90638400872	0.171686564439623	0.173615991279555	2.82958576258916
10	104.16	104.162351654142	0.183178957970156	-0.00235165414204881	0.275755218128024
11	104.24	104.231111063131	0.167159739228873	0.00888893686904191	-0.373300151584694
12	104.33	104.306402225416	0.154052684611207	0.0235977745844905	-0.299090948647967
13	104.73	104.860469594302	0.207117411890546	-0.130469594302274	1.47412309781891
14	104.86	104.856636596468	0.176237437183658	0.00336340353179794	-0.61391938697607
15	105.03	105.069025950853	0.181514555098871	-0.0390259508527905	0.114470266103365
16	105.62	105.494732795342	0.217288646307836	0.125267204657531	0.786668310554586
17	105.63	105.657563137021	0.209287094648009	-0.0275631370206787	-0.174805076269677
18	105.63	105.652031424569	0.17763982941347	-0.0220314245687912	-0.689462488532367
19	105.94	105.881191492709	0.185245872012312	0.0588085072913497	0.165392890227162
20	106.61	106.598075402621	0.263849096227719	0.0119245973789498	1.70670020285572
21	107.69	107.450004125231	0.350889138940555	0.23999587476921	1.88783100840636
22	107.78	107.820014813184	0.353721699690585	-0.0400148131839514	0.0613901764090433
23	107.93	107.97153810996	0.323756401892095	-0.0415381099602706	-0.649034296102
24	108.48	108.474179945054	0.350196044238844	0.00582005494615399	0.573277064926967
25	108.14	108.36983568475	0.283469851836746	-0.229835684750324	-1.52703398147439
26	108.48	108.502559420456	0.261203837856906	-0.0225594204562057	-0.466573400302342
27	108.48	108.595840947402	0.2365189597646	-0.115840947401956	-0.528806541071097
28	108.89	108.754077483945	0.224963005931033	0.135922516054989	-0.250963502594185
29	108.93	108.906008556163	0.214161926608119	0.023991443836591	-0.233533413380494
30	109.21	109.195067450371	0.225238948215228	0.0149325496287804	0.239287207581077
31	109.47	109.491641959238	0.235788138049671	-0.02164195923787	0.228009899219974
32	109.8	109.87249692127	0.257240968772351	-0.0724969212698966	0.463856853136858
33	111.73	111.227936559647	0.419656202253994	0.50206344035269	3.51250250747222
34	111.85	111.867074625992	0.452117757985171	-0.0170746259920647	0.702089726930494
35	112.12	112.249011290207	0.441743034536639	-0.129011290206952	-0.224285673307821
36	112.15	112.188971200621	0.367730337746188	-0.0389712006213954	-1.60540473445718
37	112.17	112.390198530512	0.343180227978755	-0.22019853051239	-0.544259583429246
38	112.67	112.663055464534	0.33280179995353	0.00694453546573659	-0.221512032443065
39	112.8	112.908784344847	0.320004833533807	-0.108784344847394	-0.274447825358123
40	113.44	113.263023114046	0.325047947686811	0.176976885954167	0.109440013056598
41	113.53	113.519325206873	0.314899108820857	0.010674793126677	-0.219640800811456
42	114.53	114.362028613653	0.39283913660256	0.167971386347278	1.68370953206525
43	114.51	114.617911585248	0.372618191763011	-0.107911585248089	-0.436936613034195
44	115.05	115.284914564748	0.416080409316406	-0.234914564747862	0.939601821048872
45	116.67	116.131466885196	0.479636530689533	0.538533114803861	1.37440659450527
46	117.07	117.000315957138	0.537097267294933	0.0696840428617493	1.24250556479722
47	116.92	117.08559372415	0.470440601665885	-0.165593724150122	-1.44086873152366
48	117	117.108378747357	0.404494399090913	-0.108378747357085	-1.43164644904341
49	117.02	117.270661657809	0.368784058769506	-0.250661657809041	-0.782605866684855
50	117.35	117.372915778327	0.329478226036952	-0.022915778327269	-0.844391729488189
51	117.36	117.497660005016	0.299379264506053	-0.137660005016105	-0.646510140041732
52	117.82	117.649255399568	0.277631536147089	0.170744600431516	-0.471422125078926
53	117.88	117.950340427491	0.281089309001206	-0.0703404274913736	0.0748875130991198
54	118.24	118.070387404351	0.257335350069455	0.169612595649055	-0.513390879686081
55	118.5	118.596688309704	0.297004046873483	-0.0966883097041517	0.857194639883577
56	118.8	119.10287751444	0.327853732568275	-0.302877514440261	0.666895154373479
57	119.76	119.348102585206	0.315668020619073	0.411897414793714	-0.263489131274974
58	120.09	119.873375327828	0.346574409910598	0.216624672172457	0.668167654188408

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/17/t1292582825v7ufrnvuoue6r1s/1x2o11292582885.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/17/t1292582825v7ufrnvuoue6r1s/1x2o11292582885.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/17/t1292582825v7ufrnvuoue6r1s/28bnn1292582885.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/17/t1292582825v7ufrnvuoue6r1s/28bnn1292582885.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/17/t1292582825v7ufrnvuoue6r1s/38bnn1292582885.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/17/t1292582825v7ufrnvuoue6r1s/38bnn1292582885.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/17/t1292582825v7ufrnvuoue6r1s/40km71292582885.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/17/t1292582825v7ufrnvuoue6r1s/40km71292582885.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/17/t1292582825v7ufrnvuoue6r1s/50km71292582885.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/17/t1292582825v7ufrnvuoue6r1s/50km71292582885.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

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