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Data:
3469648.00 3456726.00 3443622.00 3416504.00 3684772.00 3670576.00 3469648.00 3336060.00 3348982.00 3348982.00 3363360.00 3389204.00 3429426.00 3429426.00 3403582.00 3336060.00 3684772.00 3737916.00 3657654.00 3469648.00 3550092.00 3429426.00 3483844.00 3509870.00 3536988.00 3469648.00 3483844.00 3389204.00 3684772.00 3778138.00 3697876.00 3550092.00 3710798.00 3536988.00 3697876.00 3684772.00 3724994.00 3577210.00 3737916.00 3724994.00 3966144.00 3911726.00 3697876.00 3590132.00 3737916.00 3536988.00 3684772.00 3710798.00 3765216.00 3644732.00 3710798.00 3751020.00 3898804.00 3778138.00 3617432.00 3443622.00 3604510.00 3162250.00 3376282.00 3496766.00 3617432.00 3443622.00 3443622.00 3443622.00 3536988.00 3403582.00 3228498.00 3081988.00 3188276.00 2773316.00 3027570.00 3175354.00 3202472.00 3054688.00 3067610.00 3027570.00 3162250.00 3067610.00 2881060.00 2746198.00 2974244.00 2479022.00 2800616.00 2947126.00 2947126.00 2773316.00 2612610.00 2599688.00 2746198.00 2612610.00 2358538.00 2183454.00 2371460.00 1929382.00 2331238.00 2545088.00 2612610.00 2464826.00 2278094.00 2411682.00 2464826.00 2424604.00 2022566.00 1836016.00 1969422.00 1567566.00 1982526.00 2130310.00 2250794.00 2049866.00 1861860.00 1969422.00 2022566.00 1916278.00 1514422.00 1339338.00 1500044.00 1057966.00 1540266.00 1836016.00
Seasonal period
12
12
1
2
3
4
5
6
7
8
9
10
11
12
Type of Exponential Smoothing
(?)
Triple
Single
Double
Triple
Type of seasonality
(?)
additive
additive
multiplicative
Number of Forecasts
12
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Chart options
R Code
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=F, beta=F) if (par2 == 'Double') fit <- HoltWinters(x, gamma=F) 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')
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Computing time
0 seconds
R Server
Big Analytics Cloud Computing Center
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