ws9: decomposition 3

*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 10:22:48 -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/t1259947466269v1fcs9fqls3e.htm/, Retrieved Fri, 04 Dec 2009 18:24:32 +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/t1259947466269v1fcs9fqls3e.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 «

6,3 6,2 6,1 6,3 6,5 6,6 6,5 6,2 6,2 5,9 6,1 6,1 6,1 6,1 6,1 6,4 6,7 6,9 7 7 6,8 6,4 5,9 5,5 5,5 5,6 5,8 5,9 6,1 6,1 6 6 5,9 5,5 5,6 5,4 5,2 5,2 5,2 5,5 5,8 5,8 5,5 5,3 5,1 5,2 5,8 5,8 5,5 5 4,9 5,3 6,1 6,5 6,8 6,6 6,4 6,4 6,6

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 6.3 6.3 0 0 0 2 6.2 6.20033875634969 -0.0996892400546821 -0.000338756349693864 -0.413526898000771 3 6.1 6.09976744827461 -0.100562515222695 0.000232551725384802 -0.00363474764207676 4 6.3 6.2974530563921 0.193771042443022 0.00254694360790351 1.21883612320128 5 6.5 6.50062828204771 0.203054049444421 -0.000628282047714086 0.0384449021976258 6 6.6 6.60097171365893 0.101665299403964 -0.000971713658931074 -0.419893279294913 7 6.5 6.50158266492297 -0.0968007826560898 -0.00158266492297389 -0.821931126823448 8 6.2 6.20138698065123 -0.2975773150637 -0.00138698065122801 -0.831499669577698 9 6.2 6.19705230530992 -0.0081096582559993 0.00294769469008469 1.19880674346806 10 5.9 5.90319097012336 -0.290182783260372 -0.00319097012336136 -1.16818289178009 11 6.1 6.09522394922025 0.185825295955012 0.00477605077974664 1.9713487220021 12 6.1 6.10267012692514 0.00974249630433024 -0.00267012692514542 -0.729232584938666 13 6.1 6.09961056619894 -0.00289373740588862 0.000389433801055103 -0.0523382102394348 14 6.1 6.09785093585783 -0.00177405910085651 0.00214906414216770 0.00464350935965628 15 6.1 6.10327734927333 0.00527074334871684 -0.00327734927332607 0.0292998277865995 16 6.4 6.39355779297442 0.283524727495623 0.00644220702558011 1.15208749848241 17 6.7 6.70141704898546 0.307286599264358 -0.00141704898545800 0.098409103018933 18 6.9 6.90239308024715 0.203474052341428 -0.00239308024714992 -0.429931209766651 19 7 6.99751842689687 0.0976719463955992 0.00248157310312842 -0.438170815007838 20 7 7.00932280684428 0.0138226543213788 -0.00932280684427659 -0.347255019452226 21 6.8 6.79247267854197 -0.211428359410104 0.00752732145802524 -0.932858742203005 22 6.4 6.41270405860088 -0.375811908003098 -0.0127040586008774 -0.680781089097793 23 5.9 5.89467502498198 -0.514686465598539 0.00532497501802364 -0.575137684607805 24 5.5 5.50016070165732 -0.397338999364159 -0.000160701657324725 0.485985066471323 25 5.5 5.49399960026595 -0.0153873066090311 0.00600039973404482 1.58202586966257 26 5.6 5.59298140995175 0.0963144004655587 0.00701859004825286 0.463081881057796 27 5.8 5.80749816570284 0.210931531069805 -0.00749816570284082 0.476226005450853 28 5.9 5.89843543212545 0.0947024869909643 0.00156456787455183 -0.481200501660963 29 6.1 6.09747947505157 0.195774205083794 0.00252052494842619 0.41859107594146 30 6.1 6.10474415012635 0.0131619052041264 -0.00474415012635025 -0.756273520089822 31 6 6.00004468809009 -0.101011726964120 -4.46880900908772e-05 -0.472840848662802 32 6 6.00321778512485 -8.70050724529753e-05 -0.00321778512485429 0.417971520913078 33 5.9 5.89378461292126 -0.106011607387369 0.00621538707874165 -0.438678120515491 34 5.5 5.51396360252218 -0.37125323279174 -0.0139636025221789 -1.09847660896160 35 5.6 5.58173306876045 0.0540330601232895 0.0182669312395535 1.76128872590351 36 5.4 5.41421378592133 -0.160585822070662 -0.0142137859213330 -0.888827211245181 37 5.2 5.19562301857758 -0.216770702132943 0.0043769814224184 -0.232720492953543 38 5.2 5.19360557190027 -0.0086987165242462 0.00639442809972834 0.862275194198476 39 5.2 5.20190747552098 0.0076847069001057 -0.0019074755209796 0.068010706536208 40 5.5 5.49850417747576 0.286015370002777 0.00149582252424102 1.15232777236473 41 5.8 5.79469937014512 0.295821345738657 0.00530062985488497 0.0406118825422641 42 5.8 5.80582243223237 0.0215580799705882 -0.00582243223236669 -1.13583787026343 43 5.5 5.51191357179922 -0.282345598274516 -0.0119135717992181 -1.25859262625289 44 5.3 5.30200515969737 -0.212563904753882 -0.00200515969737416 0.288995201556250 45 5.1 5.07691512668202 -0.224630833187949 0.0230848733179795 -0.0499742023660053 46 5.2 5.22309337936363 0.132584926646026 -0.023093379363633 1.47938000429862 47 5.8 5.76785510696308 0.52965338684852 0.0321448930369196 1.64442727565032 48 5.8 5.82250193702928 0.072064157359714 -0.0225019370292789 -1.89507026558255 49 5.5 5.51027369316912 -0.298106915018495 -0.010273693169116 -1.53330788173242 50 5 4.99125394428652 -0.510949537531044 0.00874605571347878 -0.881785297819474 51 4.9 4.89885467575368 -0.109261599430379 0.00114532424631634 1.66634087652492 52 5.3 5.29238487599785 0.373323917032699 0.00761512400215245 1.99808449014423 53 6.1 6.08227568793519 0.773063685238924 0.0177243120648116 1.65552840689468 54 6.5 6.50481287239076 0.436667506505551 -0.00481287239075659 -1.39315722914169 55 6.8 6.81867230351617 0.318809639292635 -0.0186723035161743 -0.488098869759394 56 6.6 6.60604110816872 -0.191206426526746 -0.00604110816871922 -2.11219003005265 57 6.4 6.37966157589264 -0.224961508823594 0.0203384241073565 -0.139793928781406 58 6.4 6.43870483881188 0.047593964335382 -0.0387048388118812 1.12876631249156 59 6.6 6.55781274595347 0.116225189273000 0.0421872540465295 0.284230857820430

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259947466269v1fcs9fqls3e/1p9mh1259947365.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259947466269v1fcs9fqls3e/1p9mh1259947365.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259947466269v1fcs9fqls3e/2ypll1259947365.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259947466269v1fcs9fqls3e/2ypll1259947365.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259947466269v1fcs9fqls3e/383ic1259947365.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259947466269v1fcs9fqls3e/383ic1259947365.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259947466269v1fcs9fqls3e/4lik11259947365.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259947466269v1fcs9fqls3e/4lik11259947365.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259947466269v1fcs9fqls3e/5ohd91259947365.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259947466269v1fcs9fqls3e/5ohd91259947365.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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