ws9 Structural Time Series

*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, 04 Dec 2009 08:38:11 -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/04/t1259941160prd4mse9qhm2pvx.htm/, Retrieved Fri, 04 Dec 2009 16:39:27 +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/04/t1259941160prd4mse9qhm2pvx.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 «

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 7,7 8 8 7,7 7,3 7,4 8,1 8,3

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 'Gwilym Jenkins' @ 72.249.127.135 Structural Time Series Model t Observed Level Slope Seasonal Stand. Residuals 1 9.3 9.3 0 0 0 2 9.3 9.3 0 0 0 3 8.7 8.77525230598956 -0.0076745553976964 -0.0752523059895582 -1.97088465287498 4 8.2 8.25227981210922 -0.00993735738546997 -0.052279812109215 -1.94953585912716 5 8.3 8.28214163216692 -0.00976178289552904 0.0178583678330857 0.150511606241261 6 8.5 8.48399129646074 -0.00874923325063979 0.0160087035392632 0.800213212939008 7 8.6 8.60159861615121 -0.00814027592986616 -0.00159861615121014 0.477817965309843 8 8.5 8.52286633642054 -0.00847838428486613 -0.0228663364205374 -0.266942509635764 9 8.2 8.2409379298869 -0.00978098535056802 -0.0409379298869055 -1.03403735512353 10 8.1 8.11312599318411 -0.0103405433559001 -0.0131259931841093 -0.446323798175294 11 7.9 7.92789423457948 -0.0111657666971488 -0.0278942345794744 -0.661329766165156 12 8.6 8.524502767595 -0.00831144125436691 0.0754972324049972 2.29820304191118 13 8.7 8.61233532731105 -0.012167484684343 0.0876646726889449 0.426479468888753 14 8.7 8.64697890568697 -0.0112364642374091 0.053021094313027 0.156250978450350 15 8.5 8.5414998315855 -0.0123895402946268 -0.0414998315854959 -0.35019598916982 16 8.4 8.46170941023772 -0.0126545537920266 -0.0617094102377202 -0.254804525035108 17 8.5 8.4932025633073 -0.0125500502235609 0.00679743669269767 0.166823768911631 18 8.7 8.67075545093492 -0.0120542832336588 0.0292445490650771 0.718216130902494 19 8.7 8.70713914010227 -0.0119189153143273 -0.00713914010226971 0.182991857196360 20 8.6 8.61864935694136 -0.012134911536214 -0.0186493569413626 -0.289273523363328 21 8.5 8.53834411827887 -0.0123275704592064 -0.0383441182788657 -0.257541197498903 22 8.3 8.31741955181045 -0.012943739849171 -0.0174195518104463 -0.78816999941086 23 8 8.11865880983634 -0.0135061293569174 -0.118658809836342 -0.702266477523946 24 8.2 8.12305790757048 -0.0135103088672294 0.0769420924295213 0.0675869056758669 25 8.1 8.03590561762649 -0.0123969428762549 0.064094382373513 -0.295275808183713 26 8.1 8.02453126597765 -0.0123866328200543 0.0754687340223495 0.00366062845961385 27 8 8.02335656546262 -0.0122723147413111 -0.0233565654626200 0.0415232736116278 28 7.9 7.97356668589169 -0.0124421967098636 -0.0735666858916876 -0.141689227325010 29 7.9 7.9294054700144 -0.0125125259591850 -0.0294054700143992 -0.119854608939092 30 8 7.9684984754914 -0.0124084863298355 0.031501524508603 0.194940090506568 31 8 7.99431405307434 -0.0123241433193786 0.00568594692565916 0.144373966838509 32 7.9 7.92856970049737 -0.0124480476790977 -0.0285697004973683 -0.201766120028321 33 8 7.98919102969673 -0.0122709626530984 0.0108089703032685 0.276004804148458 34 7.7 7.74282660249692 -0.0128739875002979 -0.0428266024969196 -0.88447287872128 35 7.2 7.38545840629785 -0.0135799508315851 -0.185458406297851 -1.30129562410372 36 7.5 7.38506995222871 -0.0136012899151014 0.114930047771286 0.0498450948200217 37 7.3 7.25700557979932 -0.0127453413194778 0.0429944202006818 -0.444270438266987 38 7 6.97393055634415 -0.0143657446755038 0.0260694436558471 -0.992453666237136 39 7 6.99392138534081 -0.0140791708184529 0.00607861465918763 0.127358032673715 40 7 7.05009140078826 -0.0137416967681016 -0.0500914007882632 0.264930560610493 41 7.2 7.2041689772245 -0.0133346411833875 -0.00416897722449316 0.634115094862683 42 7.3 7.26878015878369 -0.0131915724319570 0.0312198412163093 0.294440074528764 43 7.1 7.12777865036264 -0.0134366216164051 -0.0277786503626356 -0.482720136809865 44 6.8 6.89613654726884 -0.0138933880354078 -0.0961365472688436 -0.824109094208999 45 6.4 6.44159726325472 -0.0148917002820362 -0.0415972632547197 -1.66446254292099 46 6.1 6.13019169630231 -0.0155658547521039 -0.0301916963023118 -1.12024668920766 47 6.5 6.56784204306559 -0.0149794427572034 -0.0678420430655875 1.71118825389689 48 7.7 7.38388762251882 -0.0164708802091240 0.316112377481180 3.14249305286777 49 7.9 7.73901752778758 -0.0179678727048104 0.160982472212419 1.42236376118628 50 7.5 7.53985705828932 -0.0187061261454646 -0.039857058289324 -0.672434601146582 51 6.9 7.02530961969086 -0.0221005128758527 -0.125309619690864 -1.84228285775196 52 6.6 6.73933288466165 -0.0233604449147042 -0.139332884661648 -0.993893188274412 53 6.9 6.88126093732315 -0.0229222509090924 0.0187390626768471 0.624450050849338 54 7.7 7.51025364709912 -0.0217273056181553 0.189746352900883 2.46267021661483 55 8 7.92012530155855 -0.0209587591221130 0.0798746984414455 1.63012339275497 56 8 8.00804481067862 -0.0207455461472738 -0.0080448106786205 0.411219467997272 57 7.7 7.74922543206893 -0.0212502099453783 -0.0492254320689253 -0.899308834759664 58 7.3 7.47439277422635 -0.0217454481387501 -0.174392774226348 -0.957896051554856 59 7.4 7.58921952411478 -0.0216367556764171 -0.189219524114784 0.515519067666413 60 8.1 7.79947334592646 -0.0219982787698112 0.300526654073542 0.877003018098422 61 8.3 8.03382385406515 -0.0225663073694065 0.266176145934855 0.974579542652016

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259941160prd4mse9qhm2pvx/1nd6x1259941088.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259941160prd4mse9qhm2pvx/1nd6x1259941088.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259941160prd4mse9qhm2pvx/2oc3c1259941088.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259941160prd4mse9qhm2pvx/2oc3c1259941088.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259941160prd4mse9qhm2pvx/3s7v91259941088.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259941160prd4mse9qhm2pvx/3s7v91259941088.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259941160prd4mse9qhm2pvx/4jz9p1259941088.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259941160prd4mse9qhm2pvx/4jz9p1259941088.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259941160prd4mse9qhm2pvx/57r311259941088.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259941160prd4mse9qhm2pvx/57r311259941088.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = periodic ; par3 = 0 ; par5 = 1 ; par7 = 1 ; par8 = FALSE ;

Parameters (R input):

par1 = 12 ; par2 = periodic ; par3 = 0 ; par5 = 1 ; par7 = 1 ; par8 = FALSE ;

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')

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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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