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 | :: Exponential Smoothing - Free Statistics Software (Calculator) :: | |
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All rights reserved. The non-commercial (academic) use of this software is free of charge. The only thing that is asked in return is to cite this software when results are used in publications.
This free online software (calculator) computes the following forecasting models: single (Brown model), double (Brown model), and triple exponential smoothing (Holt-Winters model).
Click here to edit the underlying code of this R Module.Enter (or paste) your data delimited by hard returns. Click here to edit the underlying code of this R Module.
| Cite this software as: | | Wessa P., (2008), Exponential Smoothing (v1.0.3) in Free Statistics Software (v1.1.22-r6), Office for Research Development and Education, URL http://www.wessa.net/rwasp_exponentialsmoothing.wasp/ | | | The R code is based on : | | | C. C. Holt (1957), Forecasting seasonals and trends by exponentially weighted moving averages, ONR Research Memorandum, Carnegie Institute 52. | | | P. R. Winters (1960), Forecasting sales by exponentially weighted moving averages, Management Science 6, 324–342. | | | | | | | | | | | |
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| Source code of R module | | 1 | par1 <- as.numeric(par1) | | 2 | if (par2 == "Single") K <- 1 | | 3 | if (par2 == "Double") K <- 2 | | 4 | if (par2 == "Triple") K <- par1 | | 5 | nx <- length(x) | | 6 | nxmK <- nx - K | | 7 | x <- ts(x, frequency = par1) | | 8 | if (par2 == "Single") fit <- HoltWinters(x, gamma=0, beta=0) | | 9 | if (par2 == "Double") fit <- HoltWinters(x, gamma=0) | | 10 | if (par2 == "Triple") fit <- HoltWinters(x, seasonal=par3) | | 11 | fit | | 12 | myresid <- x - fit$fitted[,"xhat"] | | 13 | bitmap(file="test1.png") | | 14 | op <- par(mfrow=c(2,1)) | | 15 | plot(fit,ylab="Observed (black) / Fitted (red)",main="Interpolation Fit of Exponential Smoothing") | | 16 | plot(myresid,ylab="Residuals",main="Interpolation Prediction Errors") | | 17 | par(op) | | 18 | dev.off() | | 19 | bitmap(file="test2.png") | | 20 | p <- predict(fit, par1, prediction.interval=TRUE) | | 21 | np <- length(p[,1]) | | 22 | plot(fit,p,ylab="Observed (black) / Fitted (red)",main="Extrapolation Fit of Exponential Smoothing") | | 23 | dev.off() | | 24 | bitmap(file="test3.png") | | 25 | op <- par(mfrow = c(2,2)) | | 26 | acf(as.numeric(myresid),lag.max = nx/2,main="Residual ACF") | | 27 | spectrum(myresid,main="Residals Periodogram") | | 28 | cpgram(myresid,main="Residal Cumulative Periodogram") | | 29 | qqnorm(myresid,main="Residual Normal QQ Plot") | | 30 | qqline(myresid) | | 31 | par(op) | | 32 | dev.off() | | 33 | load(file="createtable") | | 34 | a<-table.start() | | 35 | a<-table.row.start(a) | | 36 | a<-table.element(a,"Estimated Parameters of Exponential Smoothing",2,TRUE) | | 37 | a<-table.row.end(a) | | 38 | a<-table.row.start(a) | | 39 | a<-table.element(a,"Parameter",header=TRUE) | | 40 | a<-table.element(a,"Value",header=TRUE) | | 41 | a<-table.row.end(a) | | 42 | a<-table.row.start(a) | | 43 | a<-table.element(a,"alpha",header=TRUE) | | 44 | a<-table.element(a,fit$alpha) | | 45 | a<-table.row.end(a) | | 46 | a<-table.row.start(a) | | 47 | a<-table.element(a,"beta",header=TRUE) | | 48 | a<-table.element(a,fit$beta) | | 49 | a<-table.row.end(a) | | 50 | a<-table.row.start(a) | | 51 | a<-table.element(a,"gamma",header=TRUE) | | 52 | a<-table.element(a,fit$gamma) | | 53 | a<-table.row.end(a) | | 54 | a<-table.end(a) | | 55 | table.save(a,file="mytable.tab") | | 56 | a<-table.start() | | 57 | a<-table.row.start(a) | | 58 | a<-table.element(a,"Interpolation Forecasts of Exponential Smoothing",4,TRUE) | | 59 | a<-table.row.end(a) | | 60 | a<-table.row.start(a) | | 61 | a<-table.element(a,"t",header=TRUE) | | 62 | a<-table.element(a,"Observed",header=TRUE) | | 63 | a<-table.element(a,"Fitted",header=TRUE) | | 64 | a<-table.element(a,"Residuals",header=TRUE) | | 65 | a<-table.row.end(a) | | 66 | for (i in 1:nxmK) { | | 67 | a<-table.row.start(a) | | 68 | a<-table.element(a,i+K,header=TRUE) | | 69 | a<-table.element(a,x[i+K]) | | 70 | a<-table.element(a,fit$fitted[i,"xhat"]) | | 71 | a<-table.element(a,myresid[i]) | | 72 | a<-table.row.end(a) | | 73 | } | | 74 | a<-table.end(a) | | 75 | table.save(a,file="mytable1.tab") | | 76 | a<-table.start() | | 77 | a<-table.row.start(a) | | 78 | a<-table.element(a,"Extrapolation Forecasts of Exponential Smoothing",4,TRUE) | | 79 | a<-table.row.end(a) | | 80 | a<-table.row.start(a) | | 81 | a<-table.element(a,"t",header=TRUE) | | 82 | a<-table.element(a,"Forecast",header=TRUE) | | 83 | a<-table.element(a,"95% Lower Bound",header=TRUE) | | 84 | a<-table.element(a,"95% Upper Bound",header=TRUE) | | 85 | a<-table.row.end(a) | | 86 | for (i in 1:np) { | | 87 | a<-table.row.start(a) | | 88 | a<-table.element(a,nx+i,header=TRUE) | | 89 | a<-table.element(a,p[i,"fit"]) | | 90 | a<-table.element(a,p[i,"lwr"]) | | 91 | a<-table.element(a,p[i,"upr"]) | | 92 | a<-table.row.end(a) | | 93 | } | | 94 | a<-table.end(a) | | 95 | table.save(a,file="mytable2.tab") |
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To cite Wessa.net in publications use:
Wessa, P. (2008), Free Statistics Software, Office for Research Development and Education,
version 1.1.22-r6, URL http://www.wessa.net/
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