WS 9: 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: Fri, 04 Dec 2009 10:20:25 -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/t1259947284gsa2gz0yu1ojto8.htm/, Retrieved Fri, 04 Dec 2009 18:21:30 +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/t1259947284gsa2gz0yu1ojto8.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 «

114 116 153 162 161 149 139 135 130 127 122 117 112 113 149 157 157 147 137 132 125 123 117 114 111 112 144 150 149 134 123 116 117 111 105 102 95 93 124 130 124 115 106 105 105 101 95 93 84 87 116 120 117 109 105 107 109 109 108 107

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 1 114 114 0 0 0 2 116 115.702643740845 1.66896046888063 0.297356259155059 0.294876726859141 3 153 146.494977853246 23.6504664783382 6.50502214675349 3.77191065445581 4 162 164.657147603009 19.3405364523551 -2.6571476030092 -0.69617385229692 5 161 164.271417160031 4.13027010648658 -3.27141716003076 -2.4403014219544 6 149 151.006279203135 -9.3017669835315 -2.00627920313463 -2.16432047714572 7 139 138.323670309618 -11.9161278671201 0.676329690382264 -0.420844255351675 8 135 133.119291410535 -6.72588941002604 1.88070858946505 0.835509735540786 9 130 129.442698120416 -4.36822244709808 0.557301879584154 0.379530882275775 10 127 126.544976299828 -3.23133584288738 0.455023700171893 0.183011992933156 11 122 122.008616712248 -4.24029804266581 -0.0086167122483617 -0.162419293972219 12 117 116.782540539251 -5.00245215283087 0.217459460748732 -0.122688952034130 13 112 112.417809433571 -4.51082158791396 -0.417809433571176 0.0797002276452974 14 113 118.483516781324 3.61573463897883 -5.48351678132422 1.32125872853874 15 149 139.917740853605 16.7862873934667 9.08225914639485 2.12504634107215 16 157 157.03439705099 17.0329433309658 -0.0343970509900763 0.0401053876743118 17 157 159.556040949644 6.22144182377092 -2.55604094964360 -1.73463267004782 18 147 150.467136773757 -5.139067873983 -3.46713677375708 -1.82834303326795 19 137 138.280202614551 -10.3766718097926 -1.28020261455135 -0.843443575154147 20 132 129.811872949628 -8.95761686001301 2.18812705037248 0.228425326005112 21 125 124.153732206407 -6.50408593852914 0.846267793592729 0.394959976351661 22 123 121.586522854044 -3.57671561258589 1.41347714595607 0.471252261252070 23 117 116.666836395995 -4.57508436362275 0.333163604005065 -0.160713623635738 24 114 112.455631237544 -4.30482307310549 1.54436876245557 0.0435266137913398 25 111 112.398667599700 -1.14896725404076 -1.39866759970020 0.509762418788215 26 112 120.975831256661 6.07006972133675 -8.9758312566607 1.16243049710649 27 144 135.128615923444 11.9974007739406 8.87138407655556 0.954012623437767 28 150 147.558492496076 12.315338916866 2.44150750392430 0.0514565998105306 29 149 150.041880899574 5.07198310554524 -1.04188089957386 -1.16503410900246 30 134 138.676504476299 -6.99633976396462 -4.67650447629897 -1.94055268562018 31 123 125.333643000286 -11.6566246577464 -2.33364300028565 -0.750425480833146 32 116 114.236926366921 -11.2451011132596 1.76307363307930 0.0662493528025322 33 117 114.576090563726 -2.72901846128121 2.4239094362744 1.37086005291596 34 111 109.638847384399 -4.35222547896544 1.36115261560106 -0.261311896628606 35 105 104.071272001815 -5.24513825011138 0.928727998185038 -0.143739878147149 36 102 100.340981746844 -4.13290623937157 1.65901825315618 0.179184125883452 37 95 98.3374693017223 -2.56826323028658 -3.33746930172227 0.252346669507806 38 93 103.360733953500 3.00199029217631 -10.3607339535002 0.896112984635853 39 124 114.989223032686 9.29529211996098 9.01077696731369 1.01286248787740 40 130 125.747309184084 10.3634582639752 4.25269081591565 0.172462513077168 41 124 123.471544186286 1.11387671322238 0.528455813714395 -1.48917829627881 42 115 118.488865605073 -3.33897121051313 -3.48886560507335 -0.716038457862916 43 106 109.459149885785 -7.49292439364667 -3.45914988578483 -0.668697041568339 44 105 105.487422199554 -4.92067445616287 -0.487422199554088 0.414114902367592 45 105 101.738001347294 -4.06476174723596 3.26199865270597 0.137779693616591 46 101 98.6953085037839 -3.31794982324852 2.30469149621614 0.120221876332748 47 95 94.026392137282 -4.30458588813939 0.973607862717959 -0.158838137405740 48 93 90.8887679874983 -3.45253923105605 2.11123201250169 0.137265939991958 49 84 89.0008258798454 -2.30945510230920 -5.00082587984536 0.184197483755488 50 87 98.0495670253244 5.97745504760098 -11.0495670253244 1.33313803269666 51 116 107.665841184860 8.62345687361788 8.33415881513967 0.425883314652667 52 120 113.447640074266 6.55611048482496 6.55235992573387 -0.333400597719954 53 117 115.688111400241 3.41104437742443 1.31188859975868 -0.50649753193152 54 109 112.283608379213 -1.55095811849093 -3.28360837921311 -0.798135745454033 55 105 109.550869706606 -2.41067338075168 -4.55086970660589 -0.138366145542324 56 107 107.751506809735 -1.96576160857763 -0.751506809735046 0.0716254325462566 57 109 105.873779996985 -1.90166524972071 3.12622000301535 0.0103180083492711 58 109 105.538888642367 -0.76101914592312 3.46111135763341 0.183618737321425 59 108 106.273776002188 0.327642145007529 1.72622399781244 0.17527493814258 60 107 105.196236799355 -0.695010965770706 1.80376320064542 -0.164730001410012

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259947284gsa2gz0yu1ojto8/1cyb31259947223.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259947284gsa2gz0yu1ojto8/1cyb31259947223.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259947284gsa2gz0yu1ojto8/2t70a1259947223.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259947284gsa2gz0yu1ojto8/2t70a1259947223.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259947284gsa2gz0yu1ojto8/3yfwy1259947223.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259947284gsa2gz0yu1ojto8/3yfwy1259947223.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259947284gsa2gz0yu1ojto8/4n9xd1259947223.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259947284gsa2gz0yu1ojto8/4n9xd1259947223.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259947284gsa2gz0yu1ojto8/5yuef1259947223.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259947284gsa2gz0yu1ojto8/5yuef1259947223.ps (open in new window)

Parameters (Session):

par1 = FALSE ; par2 = 0.5 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;

Parameters (R input):

par1 = 12 ; par2 = 0.5 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;

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')

Copyright

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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