shwws9vr1

*The author of this computation has been verified*

R Software Module: /rwasp_exponentialsmoothing.wasp (opens new window with default values)

Title produced by software: Exponential Smoothing

Date of computation: Fri, 11 Dec 2009 09:29:38 -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/11/t12605490327v8f0b5gnvb95s0.htm/, Retrieved Fri, 11 Dec 2009 17:30:35 +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/11/t12605490327v8f0b5gnvb95s0.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:

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102.1 102.86 102.99 103.73 105.02 104.43 104.63 104.93 105.87 105.66 106.76 106 107.22 107.33 107.11 108.86 107.72 107.88 108.38 107.72 108.41 109.9 111.45 112.18 113.34 113.46 114.06 115.54 116.39 115.94 116.97 115.94 115.91 116.43 116.26 116.35 117.9 117.7 117.53 117.86 117.65 116.51 115.93 115.31 115

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 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.781527354716212 beta 0.167068730875885 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 107.22 105.267261496837 1.95273850316312 14 107.33 107.196788614964 0.133211385035580 15 107.11 107.440213638756 -0.33021363875568 16 108.86 109.192405401537 -0.332405401537116 17 107.72 107.915115055254 -0.195115055254206 18 107.88 107.939844697002 -0.0598446970022053 19 108.38 108.726662894449 -0.346662894449253 20 107.72 108.769652750896 -1.04965275089566 21 108.41 108.82763777212 -0.417637772119988 22 109.9 108.116856499068 1.78314350093233 23 111.45 110.771761050778 0.678238949221722 24 112.18 110.787937396092 1.39206260390803 25 113.34 114.031755868548 -0.691755868548086 26 113.46 113.539795156877 -0.0797951568771111 27 114.06 113.531760608104 0.528239391896165 28 115.54 116.209424535710 -0.669424535709823 29 116.39 114.721851713204 1.66814828679625 30 115.94 116.5706971202 -0.630697120199969 31 116.97 117.156822878021 -0.186822878021488 32 115.94 117.45387530098 -1.51387530098005 33 115.91 117.59093443875 -1.68093443874993 34 116.43 116.439547916341 -0.0095479163409209 35 116.26 117.329358455594 -1.06935845559369 36 116.35 115.711416965734 0.638583034266318 37 117.9 117.461801712373 0.438198287627401 38 117.7 117.634026034562 0.065973965438431 39 117.53 117.541630755777 -0.0116307557772899 40 117.86 119.185354590308 -1.32535459030792 41 117.65 117.197042238727 0.452957761272913 42 116.51 116.959900913531 -0.449900913531437 43 115.93 117.182351202069 -1.25235120206877 44 115.31 115.617201985121 -0.307201985120514 45 115 116.066295343314 -1.06629534331367 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 46 115.251016111138 113.455650371297 117.046381850979 47 115.403023555089 112.969626583469 117.836420526709 48 114.630344496376 111.569387770653 117.691301222099 49 115.369038253103 111.631510919358 119.106565586847 50 114.620191651546 110.223876054895 119.016507248197 51 113.955922364756 108.878998151014 119.032846578499 52 114.768465675007 108.922918655949 120.614012694064 53 113.878539692984 107.319242628010 120.437836757959 54 112.721572721518 105.447905409429 119.995240033607 55 112.767700492496 104.684804747219 120.850596237773 56 112.219088527184 103.344746399564 121.093430654804 57 112.586148749719 99.5228850780697 125.649412421368

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/11/t12605490327v8f0b5gnvb95s0/1b4r81260548975.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t12605490327v8f0b5gnvb95s0/1b4r81260548975.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t12605490327v8f0b5gnvb95s0/2vurg1260548975.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t12605490327v8f0b5gnvb95s0/2vurg1260548975.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t12605490327v8f0b5gnvb95s0/3eq941260548975.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t12605490327v8f0b5gnvb95s0/3eq941260548975.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

R code (references can be found in the software module):

par1 <- as.numeric(par1) if (par2 == 'Single') K <- 1 if (par2 == 'Double') K <- 2 if (par2 == 'Triple') K <- par1 nx <- length(x) nxmK <- nx - K x <- ts(x, frequency = par1) if (par2 == 'Single') fit <- HoltWinters(x, gamma=0, beta=0) if (par2 == 'Double') fit <- HoltWinters(x, gamma=0) if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3) fit myresid <- x - fit$fitted[,'xhat'] bitmap(file='test1.png') op <- par(mfrow=c(2,1)) plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing') plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors') par(op) dev.off() bitmap(file='test2.png') p <- predict(fit, par1, prediction.interval=TRUE) np <- length(p[,1]) plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing') dev.off() bitmap(file='test3.png') op <- par(mfrow = c(2,2)) acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF') spectrum(myresid,main='Residals Periodogram') cpgram(myresid,main='Residal Cumulative Periodogram') qqnorm(myresid,main='Residual Normal QQ Plot') qqline(myresid) par(op) dev.off() load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'Value',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'alpha',header=TRUE) a<-table.element(a,fit$alpha) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'beta',header=TRUE) a<-table.element(a,fit$beta) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'gamma',header=TRUE) a<-table.element(a,fit$gamma) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,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,'Fitted',header=TRUE) a<-table.element(a,'Residuals',header=TRUE) a<-table.row.end(a) for (i in 1:nxmK) { a<-table.row.start(a) a<-table.element(a,i+K,header=TRUE) a<-table.element(a,x[i+K]) a<-table.element(a,fit$fitted[i,'xhat']) a<-table.element(a,myresid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'t',header=TRUE) a<-table.element(a,'Forecast',header=TRUE) a<-table.element(a,'95% Lower Bound',header=TRUE) a<-table.element(a,'95% Upper Bound',header=TRUE) a<-table.row.end(a) for (i in 1:np) { a<-table.row.start(a) a<-table.element(a,nx+i,header=TRUE) a<-table.element(a,p[i,'fit']) a<-table.element(a,p[i,'lwr']) a<-table.element(a,p[i,'upr']) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.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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