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

Title produced by software: Exponential Smoothing

Date of computation: Sat, 24 May 2008 09:01:48 -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/24/t121164134878qleado65ys5xx.htm/, Retrieved Sat, 24 May 2008 17:02:28 +0200

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Dataseries X:

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164 148 152 144 155 125 153 146 138 190 192 192 147 133 163 150 129 131 145 137 138 168 176 188 139 143 150 154 137 129 128 140 143 151 177 184 151 134 164 126 131 125 127 143 143 160 190 182 138 136 152 127 151 130 119 153

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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 5 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.097686644783782 beta 0 gamma 0.704993778027152 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 147 150.222388484918 -3.22238848491787 14 133 136.253352653925 -3.25335265392508 15 163 167.003592078021 -4.00359207802069 16 150 154.242991663531 -4.24299166353097 17 129 133.675872901086 -4.67587290108574 18 131 136.033184156634 -5.03318415663361 19 145 150.526673285804 -5.52667328580421 20 137 141.633016493222 -4.63301649322182 21 138 142.329422975999 -4.32942297599899 22 168 173.188585697595 -5.18858569759473 23 176 180.302323409496 -4.30232340949649 24 188 191.827371236434 -3.82737123643423 25 139 143.287232271632 -4.28723227163181 26 143 129.651218906877 13.348781093123 27 150 160.875003115433 -10.8750031154329 28 154 147.608385764293 6.3916142357073 29 137 128.186296320586 8.81370367941375 30 129 131.598775622260 -2.59877562226032 31 128 145.893302455164 -17.8933024551636 32 140 136.474391316879 3.52560868312051 33 143 138.139053015829 4.86094698417139 34 151 169.220855999203 -18.2208559992025 35 177 175.525217874764 1.47478212523592 36 184 187.809982206161 -3.80998220616084 37 151 139.376406917433 11.6235930825669 38 134 138.423318646518 -4.42331864651754 39 164 152.304683464929 11.6953165350708 40 126 152.205019790921 -26.2050197909209 41 131 131.425096094505 -0.425096094504681 42 125 126.786532893885 -1.78653289388504 43 127 131.181982964732 -4.18198296473159 44 143 136.632809127610 6.3671908723897 45 143 139.385853366925 3.61414663307528 46 160 155.320382149968 4.67961785003163 47 190 176.380329524449 13.6196704755514 48 182 186.539718958705 -4.53971895870535 49 138 147.568772514982 -9.56877251498156 50 136 134.434633515081 1.56536648491925 51 152 158.992129888929 -6.99212988892876 52 127 133.083186866181 -6.08318686618082 53 151 130.674735849844 20.3252641501555 54 130 127.131114001920 2.86888599808049 55 119 130.496086918391 -11.4960869183913 56 153 142.048098239586 10.9519017604144 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 57 143.496715447539 130.650414368644 156.343016526434 58 159.914123947998 146.914200353622 172.914047542375 59 186.330652511677 173.22637608088 199.434928942474 60 183.601696959642 170.534149159407 196.669244759877 61 141.746655871753 128.591189617804 154.902122125702 62 136.585153937784 123.196050203477 149.974257672091 63 155.666866327906 142.357833752865 168.975898902946 64 130.712348374896 117.158383238447 144.266313511345 65 145.744420893647 132.254487981846 159.234353805448 66 129.089148263673 115.558960955790 142.619335571556 67 122.979433377715 108.970522378058 136.988344377372 68 150.084734583256 NA NA

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/24/t121164134878qleado65ys5xx/16ibu1211641299.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/24/t121164134878qleado65ys5xx/16ibu1211641299.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/24/t121164134878qleado65ys5xx/2ra9f1211641299.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/24/t121164134878qleado65ys5xx/2ra9f1211641299.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/24/t121164134878qleado65ys5xx/37yku1211641299.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/24/t121164134878qleado65ys5xx/37yku1211641299.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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