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Data:
5947968.00 5925816.00 5903352.00 5856864.00 6316752.00 6292416.00 5947968.00 5718960.00 5741112.00 5741112.00 5765760.00 5810064.00 5879016.00 5879016.00 5834712.00 5718960.00 6316752.00 6407856.00 6270264.00 5947968.00 6085872.00 5879016.00 5972304.00 6016920.00 6063408.00 5947968.00 5972304.00 5810064.00 6316752.00 6476808.00 6339216.00 6085872.00 6361368.00 6063408.00 6339216.00 6316752.00 6385704.00 6132360.00 6407856.00 6385704.00 6799104.00 6705816.00 6339216.00 6154512.00 6407856.00 6063408.00 6316752.00 6361368.00 6454656.00 6248112.00 6361368.00 6430320.00 6683664.00 6476808.00 6201312.00 5903352.00 6179160.00 5421000.00 5787912.00 5994456.00 6201312.00 5903352.00 5903352.00 5903352.00 6063408.00 5834712.00 5534568.00 5283408.00 5465616.00 4754256.00 5190120.00 5443464.00 5489952.00 5236608.00 5258760.00 5190120.00 5421000.00 5258760.00 4938960.00 4707768.00 5098704.00 4249752.00 4801056.00 5052216.00 5052216.00 4754256.00 4478760.00 4456608.00 4707768.00 4478760.00 4043208.00 3743064.00 4065360.00 3307512.00 3996408.00 4363008.00 4478760.00 4225416.00 3905304.00 4134312.00 4225416.00 4156464.00 3467256.00 3147456.00 3376152.00 2687256.00 3398616.00 3651960.00 3858504.00 3514056.00 3191760.00 3376152.00 3467256.00 3285048.00 2596152.00 2296008.00 2571504.00 1813656.00 2640456.00 3147456.00
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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