ExponentialSmoothingOpg10.2Single-GrietjeCordeel

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 28 May 2008 12:56:30 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/May/28/t1212001262pg4q77yc5yelgsm.htm/, Retrieved Wed, 28 May 2008 21:01:02 +0200

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Dataseries X:

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1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.44 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.57 1.58 1.58 1.58 1.58 1.59 1.6 1.6 1.61 1.61 1.61 1.62 1.63 1.63 1.64 1.64 1.64 1.64 1.64 1.65 1.65 1.65 1.65

Text written by user:

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 2 1.43 1.43 0 3 1.43 1.43 0 4 1.43 1.43 0 5 1.43 1.43 0 6 1.43 1.43 0 7 1.43 1.43 0 8 1.43 1.43 0 9 1.43 1.43 0 10 1.43 1.43 0 11 1.43 1.43 0 12 1.43 1.43 0 13 1.43 1.43 0 14 1.43 1.43 0 15 1.43 1.43 0 16 1.43 1.43 0 17 1.43 1.43 0 18 1.43 1.43 0 19 1.43 1.43 0 20 1.44 1.43 0.01 21 1.48 1.44 0.04 22 1.48 1.48 0 23 1.48 1.48 0 24 1.48 1.48 0 25 1.48 1.48 0 26 1.48 1.48 0 27 1.48 1.48 0 28 1.48 1.48 0 29 1.48 1.48 0 30 1.48 1.48 0 31 1.48 1.48 0 32 1.48 1.48 0 33 1.48 1.48 0 34 1.48 1.48 0 35 1.48 1.48 0 36 1.48 1.48 0 37 1.48 1.48 0 38 1.48 1.48 0 39 1.48 1.48 0 40 1.48 1.48 0 41 1.48 1.48 0 42 1.48 1.48 0 43 1.48 1.48 0 44 1.48 1.48 0 45 1.48 1.48 0 46 1.48 1.48 0 47 1.48 1.48 0 48 1.48 1.48 0 49 1.48 1.48 0 50 1.48 1.48 0 51 1.57 1.48 0.09 52 1.58 1.57 0.01 53 1.58 1.58 0 54 1.58 1.58 0 55 1.58 1.58 0 56 1.59 1.58 0.01 57 1.6 1.59 0.01 58 1.6 1.6 0 59 1.61 1.6 0.01 60 1.61 1.61 0 61 1.61 1.61 0 62 1.62 1.61 0.01 63 1.63 1.62 0.00999999999999979 64 1.63 1.63 0 65 1.64 1.63 0.01 66 1.64 1.64 0 67 1.64 1.64 0 68 1.64 1.64 0 69 1.64 1.64 0 70 1.65 1.64 0.01 71 1.65 1.65 0 72 1.65 1.65 0 73 1.65 1.65 0 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 74 1.65 1.62682365535926 1.67317634464074 75 1.65 1.61722369908284 1.68277630091716 76 1.65 1.60985739354852 1.69014260645148 77 1.65 1.60364731071853 1.69635268928147 78 1.65 1.59817611791335 1.70182388208665 79 1.65 1.59322978152731 1.70677021847269 80 1.65 1.58868115578109 1.71131884421891 81 1.65 1.58444739816568 1.71555260183432 82 1.65 1.58047096607779 1.71952903392221 83 1.65 1.57670996309824 1.72329003690176 84 1.65 1.57313276081472 1.72686723918528 85 1.65 1.56971478709704 1.73028521290296

Charts produced by software:

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Parameters (Session):

par1 = 12 ; par2 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; par3 = additive ;

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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