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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: Tue, 01 Dec 2009 12:03:49 -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/t1259694259ybdss1uo14wfyj6.htm/, Retrieved Tue, 01 Dec 2009 20:04:26 +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/t1259694259ybdss1uo14wfyj6.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 «

8.9 8.8 8.3 7.5 7.2 7.4 8.8 9.3 9.3 8.7 8.2 8.3 8.5 8.6 8.5 8.2 8.1 7.9 8.6 8.7 8.7 8.5 8.4 8.5 8.7 8.7 8.6 8.5 8.3 8 8.2 8.1 8.1 8 7.9 7.9 8 8 7.9 8 7.7 7.2 7.5 7.3 7 7 7 7.2 7.3 7.1 6.8 6.4 6.1 6.5 7.7 7.9 7.5 6.9 6.6 6.9

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	8.9	8.9	0	0	0
2	8.8	8.80116511062432	-0.0989311795123792	-0.00116511062431548	-0.282751620481151
3	8.3	8.3111650143321	-0.477189480934895	-0.0111650143321000	-1.09234441260947
4	7.5	7.50640511938206	-0.791631310115204	-0.00640511938205747	-0.892873240433318
5	7.2	7.18503514599877	-0.339964678960045	0.0149648540012271	1.28373061268300
6	7.4	7.38863829204952	0.182180591798653	0.0113617079504795	1.48396631035935
7	8.8	8.77102959225823	1.33506658076245	0.0289704077417715	3.27656850899902
8	9.3	9.33021728964243	0.589784159016862	-0.0302172896424309	-2.11813549261455
9	9.3	9.31161259681123	0.00538604414095833	-0.0116125968112328	-1.6608930432081
10	8.7	8.71268521128293	-0.575097457634592	-0.0126852112829362	-1.64976748750803
11	8.2	8.1944642782976	-0.520463752234779	0.00553572170239226	0.155272131963560
12	8.3	8.28387886134105	0.0653651703181595	0.0161211386589456	1.66495948069117
13	8.5	8.4994732046533	0.209633542448509	0.000526795346705918	0.410171625509456
14	8.6	8.60302724287449	0.10769334662923	-0.00302724287448834	-0.290885332876739
15	8.5	8.49939254551501	-0.0906308482338243	0.000607454484992285	-0.56915629633319
16	8.2	8.22114002512543	-0.266503472689155	-0.0211400251254290	-0.499275050458061
17	8.1	8.06859506650381	-0.159729499455314	0.0314049334961882	0.303494460607542
18	7.9	7.9504542607466	-0.120752516451051	-0.0504542607465975	0.110774490408360
19	8.6	8.52301694939901	0.529022662180614	0.0769830506009897	1.84670003104847
20	8.7	8.74171634371209	0.238192770378631	-0.0417163437120898	-0.826555246652197
21	8.7	8.69897726508716	-0.0250918156324362	0.00102273491284020	-0.748269937356021
22	8.5	8.50556690768398	-0.182837382859991	-0.00556690768397682	-0.448321976087315
23	8.4	8.4088918022782	-0.102086748566112	-0.0088918022781924	0.229498022688034
24	8.5	8.48440480837169	0.0643545088790036	0.0155951916283108	0.47303647532219
25	8.7	8.6947721195464	0.201158835189445	0.0052278804536009	0.388981265434598
26	8.7	8.70717941319444	0.0241738054931103	-0.00717941319444131	-0.503921089884762
27	8.6	8.59185891650277	-0.104863339065838	0.00814108349722883	-0.368581482019345
28	8.5	8.52267464327635	-0.0718135929079912	-0.0226746432763477	0.0938686093731788
29	8.3	8.256898445496	-0.251282773698354	0.0431015545040007	-0.510083273041614
30	8	8.09768740595025	-0.166063730839384	-0.0976874059502524	0.242199854442588
31	8.2	8.10462034736826	-0.0059377504203659	0.0953796526317395	0.455087165429725
32	8.1	8.13036200215647	0.0233841422091786	-0.0303620021564676	0.0833345244824027
33	8.1	8.09014705982349	-0.0354815638235687	0.0098529401765114	-0.167299726482142
34	8	8.00655886836528	-0.0800081143337638	-0.00655886836527993	-0.126547020089523
35	7.9	7.9148843387258	-0.090806451314017	-0.0148843387257907	-0.0306895626239415
36	7.9	7.8960375512163	-0.0242053365183239	0.00396244878370423	0.189284883186909
37	8	7.9813592280208	0.0771458592453621	0.0186407719792000	0.288205654434986
38	8	8.00060964775332	0.0235476075564089	-0.000609647753322567	-0.152418334971885
39	7.9	7.90799502759682	-0.0831752697023524	-0.00799502759681478	-0.304111733842731
40	8	7.99479706720854	0.0732671557566858	0.00520293279145892	0.444540005722395
41	7.7	7.67793272093754	-0.28537064321275	0.0220672790624626	-1.01918476015459
42	7.2	7.31235165181671	-0.359125510900463	-0.112351651816708	-0.209622129067310
43	7.5	7.38514215681945	0.0380552893580257	0.114857843180549	1.12880724109671
44	7.3	7.3338869911354	-0.0440714939602683	-0.0338869911353984	-0.233409192515345
45	7	7.00332994115018	-0.307510243260277	-0.00332994115017805	-0.748708086482017
46	7	6.98591465417594	-0.040750106309603	0.0140853458240569	0.758147806048401
47	7	7.01293555706717	0.0215699729508071	-0.0129355570671717	0.177117933216027
48	7.2	7.19920910614585	0.173010844470607	0.00079089385415466	0.430409039622866
49	7.3	7.28469687495622	0.0925418831471268	0.0153031250437844	-0.228827733082672
50	7.1	7.1033193555692	-0.159316911146325	-0.00331935556920586	-0.715843643918503
51	6.8	6.84155945681376	-0.253084869175999	-0.0415594568137613	-0.266886673704591
52	6.4	6.3722661816598	-0.451292429441536	0.0277338183402029	-0.563372996812719
53	6.1	6.04811626816333	-0.33485233658452	0.0518837318366739	0.330873375589449
54	6.5	6.60579968606385	0.482676445456254	-0.105799686063849	2.32356290755763
55	7.7	7.56406066544086	0.91833694420958	0.135939334559141	1.23816733332057
56	7.9	7.93429932424964	0.416252565729041	-0.0342993242496419	-1.42695310587975
57	7.5	7.56597644032848	-0.302447461947194	-0.0659764403284789	-2.04258685254906
58	6.9	6.90093570241678	-0.63459888729584	-0.000935702416784052	-0.943994372545665
59	6.6	6.60725402942677	-0.322304655662228	-0.00725402942676914	0.88756062858964
60	6.9	6.86927917180645	0.212898058094026	0.0307208281935522	1.52112584256506

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259694259ybdss1uo14wfyj6/1q2421259694227.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259694259ybdss1uo14wfyj6/1q2421259694227.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259694259ybdss1uo14wfyj6/2bj9t1259694227.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259694259ybdss1uo14wfyj6/2bj9t1259694227.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259694259ybdss1uo14wfyj6/3homh1259694227.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259694259ybdss1uo14wfyj6/3homh1259694227.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259694259ybdss1uo14wfyj6/427u31259694227.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259694259ybdss1uo14wfyj6/427u31259694227.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259694259ybdss1uo14wfyj6/5w8wc1259694227.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259694259ybdss1uo14wfyj6/5w8wc1259694227.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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