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Data:
62.4 67.4 76.1 67.4 74.5 72.6 60.5 66.1 76.5 76.8 77 71 74.8 73.7 80.5 71.8 76.9 79.9 65.9 69.5 75.1 79.6 75.2 68 72.8 71.5 78.5 76.8 75.3 76.7 69.7 67.8 77.5 82.5 75.3 70.9 76 73.7 79.7 77.8 73.3 78.3 71.9 67 82 83.7 74.8 80 74.3 76.8 89 81.9 76.8 88.9 75.8 75.5 89.1 88 85.9 89.3 82.9 81.2 90.5 86.4 81.8 91.3 73.4 76.6 91 87 89.7 90.7 86.5 86.6 98.8 84.4 91.4 95.7 78.5 81.7 94.3 98.5 95.4 91.7 92.8 90.5 102.2 91.8 95 102 88.9 89.6 97.9 108.6 100.8 95.1 101 100.9 102.5 105.4 98.4 105.3 96.5 88.1 107.9 107 92.5 95.7 85.2 85.5 94.7 86.2 88.8 93.4 83.4 82.9 96.7 96.2 92.8 92.8 90 95.4 108.3 96.3 95 109 92 92.3 107 105.5 105.4 103.9 99.2 102.2 121.5 102.3 110 105.9 91.9 100 111.7 104.9 103.3 101.8 100.8 104.2 116.5 97.9 100.7 107 96.3 96 104.5 107.4 102.4 94.9 98.8 96.8 108.2 103.8 102.3 107.2 102 92.6 105.2 113 105.6 101.6 101.7 102.7 109 105.5 103.3 108.6 98.2 90 112.4 111.9 102.1 102.4 101.7 98.7 114 105.1 98.3 110 96.5 92.2 112 111.4 107.5 103.4 103.5 107.4 117.6 110.2 104.3 115.9 98.9 101.9 113.5 109.5 110 114.2 106.9 109.2 124.2 104.7 111.9 119 102.9 106.3
Seasonal period
12
1
2
3
4
5
6
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9
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11
12
Type of Exponential Smoothing
(?)
Single
Double
Triple
Type of seasonality
(?)
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) par4 <- as.numeric(par4) 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$fitted[,'xhat'] bitmap(file='test1.png') op <- par(mfrow=c(2,1)) plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing') plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors') par(op) dev.off() bitmap(file='test2.png') p <- predict(fit, par4, prediction.interval=TRUE) np <- length(p[,1]) plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing') dev.off() bitmap(file='test3.png') op <- par(mfrow = c(2,2)) acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF') spectrum(myresid,main='Residals Periodogram') cpgram(myresid,main='Residal Cumulative Periodogram') qqnorm(myresid,main='Residual Normal QQ Plot') qqline(myresid) par(op) dev.off() load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'Value',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'alpha',header=TRUE) a<-table.element(a,fit$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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Big Analytics Cloud Computing Center
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