Home » date » 2010 » Dec » 29 »

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: Wed, 29 Dec 2010 18:14:33 +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/29/t1293646379ys8asd0zlvjt3xg.htm/, Retrieved Wed, 29 Dec 2010 19:13:03 +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/29/t1293646379ys8asd0zlvjt3xg.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 «

16 17 23 24 27 31 40 47 43 60 64 65 65 55 57 57 57 65 69 70 71 71 73 68 65 57 41 21 21 17 9 11 6 -2 0 5 3 7 4 8 9 14 12 12 7 15 14 19 39 12 11 17 16 25 24 28 25 31 24 24

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' @ www.wessa.org

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	16	16	0	0	0
2	17	16.8189041196543	0.0912076185806569	0.0480403621867126	0.117992263574249
3	23	21.5751478045096	1.02599281784352	0.11538603093639	0.909848580676293
4	24	23.6194042612875	1.28719275188899	0.117119412526921	0.188105422110507
5	27	26.4973673964988	1.7375309530466	0.115354984624336	0.282991191503654
6	31	30.3800047722248	2.37028419874244	0.11243083439311	0.375132627188318
7	40	38.540368715094	4.10849204466902	0.106210306034056	1.00535608939563
8	47	46.0949416343831	5.15093603675348	0.10360976196454	0.596636938761412
9	43	44.4663977739943	3.09325927144279	0.107054102086662	-1.17244837068779
10	60	57.5739710581868	6.13729349116615	0.103687965203531	1.73116925896938
11	64	63.8615128754061	6.18299516106835	0.103654800615645	0.0259698778553742
12	65	65.8646626405841	4.91119254403798	0.104258694594049	-0.722449482914933
13	65	68.139149397587	4.14661781976435	-2.55830288271316	-0.530410140956923
14	55	57.5451793700634	-0.114004135155964	-0.141234495521304	-2.09916133299504
15	57	57.1964219408155	-0.184868926136985	-0.142301638816791	-0.0405202187611567
16	57	57.1177682356777	-0.152518332986102	-0.142369528191314	0.0183457137820035
17	57	57.1092747757382	-0.108654699718851	-0.142578557200022	0.0248437530770836
18	65	63.6195535475588	1.90581574295869	-0.15082136958017	1.14216042302572
19	69	68.4714259509022	2.80220113563265	-0.153470002565439	0.508656249576685
20	70	70.3636809249428	2.5253421825755	-0.152913281285965	-0.157173209799402
21	71	71.479031702085	2.09631308653295	-0.152339942262533	-0.243609811216449
22	71	71.6077784041141	1.49758031723914	-0.151813516278726	-0.340000792342195
23	73	73.143078049246	1.50905910396626	-0.151820127573323	0.00651868068407722
24	68	69.3744835495099	-0.0971211170214097	-0.151215285885445	-0.91214779112687
25	65	65.2919885711796	-1.28239107221911	0.608828631088303	-0.748299318746499
26	57	58.22915268166	-2.98265052330271	-0.152620059753036	-0.885066327473196
27	41	43.8248388009016	-6.44028247467356	-0.186649890230214	-1.97244702926666
28	21	24.2289479034855	-10.4462776800871	-0.181046398014057	-2.272830217249
29	21	19.795307133977	-8.61546673875535	-0.186813129955735	1.03788164914021
30	17	16.0608539691079	-7.12989700995922	-0.190827042634025	0.842750395790024
31	9	9.14205855758652	-7.06565853006861	-0.190952331891495	0.0364621280715375
32	11	9.47887055140683	-4.81311589615717	-0.19394163495184	1.27892718998514
33	6	5.90670233125862	-4.43548478216535	-0.194274660704912	0.214436585222105
34	-2	-1.18952893172386	-5.2452138956526	-0.193804858334996	-0.459829256519875
35	0	-1.05296855994787	-3.60734000719007	-0.194427353506894	0.930140250807293
36	5	3.34050644059383	-1.17231576352817	-0.195032433872419	1.38285309273212
37	3	1.23239427867053	-1.45281625712956	1.98094158300677	-0.171234749324379
38	7	5.89421481848356	0.361468866114299	-0.103065891057654	0.967507279110624
39	4	4.51042887305639	-0.167596486403253	-0.106938319913765	-0.301465234863315
40	8	7.39961071118244	0.763109439668594	-0.107908611134671	0.528172740598879
41	9	8.9306589939601	0.996917553368051	-0.108457633818503	0.132605186292304
42	14	13.3239915402587	2.03064954488711	-0.110539733066509	0.586588661427802
43	12	12.7197749022712	1.22881149074013	-0.109374008098244	-0.455189122175689
44	12	12.4550147919313	0.774296060044767	-0.108924413360004	-0.258076102779455
45	7	8.25966973152868	-0.738084218890249	-0.107930291588654	-0.858822925557773
46	15	13.6811100820932	1.13647661048924	-0.108740954589365	1.06453842257497
47	14	14.2420860313697	0.961325808988462	-0.108691337458263	-0.0994677355647124
48	19	18.373949436112	1.92628668104321	-0.108870061458832	0.548003542704071
49	39	33.1652785110815	5.79747994253969	2.88942688706379	2.32245707002914
50	12	16.9804615567605	-0.758747847409714	-0.483924526763226	-3.54431638502212
51	11	12.3794930158989	-1.92445380156352	-0.490716145837041	-0.663775662082355
52	17	16.1682247915084	-0.185065311944782	-0.492161363222622	0.987241996228739
53	16	16.3966410167668	-0.0591837925492021	-0.492396984531823	0.0714133994709363
54	25	23.7736076840126	2.2040939785777	-0.496030601682609	1.28450183974847
55	24	24.7744022260201	1.83789570724547	-0.495606258250371	-0.207900833698034
56	28	28.1415798714023	2.30329502351782	-0.495973186555613	0.264265555816127
57	25	26.426627075754	1.08041014358021	-0.495332504045457	-0.69444049401996
58	31	30.745135554309	2.06589949796219	-0.495672183760553	0.559650229594412
59	24	26.0600432927072	0.0112364730245047	-0.495208271144148	-1.16684177434916
60	24	24.7917462124555	-0.37819681453236	-0.495150782514451	-0.221160351795789

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293646379ys8asd0zlvjt3xg/1x6ib1293646471.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293646379ys8asd0zlvjt3xg/1x6ib1293646471.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293646379ys8asd0zlvjt3xg/2pxiw1293646471.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293646379ys8asd0zlvjt3xg/2pxiw1293646471.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293646379ys8asd0zlvjt3xg/3pxiw1293646471.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293646379ys8asd0zlvjt3xg/3pxiw1293646471.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293646379ys8asd0zlvjt3xg/40ohh1293646471.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293646379ys8asd0zlvjt3xg/40ohh1293646471.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293646379ys8asd0zlvjt3xg/5tygk1293646471.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293646379ys8asd0zlvjt3xg/5tygk1293646471.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

bitmap(file='test1.png')

plot(as.numeric(m$resid),main='Standardized Residuals',ylab='Residuals',xlab='time')

grid()

dev.off()

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='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