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Data:
97.7 88.9 96.5 89.5 85.4 84.3 83.7 86.2 90.7 95.7 95.6 97 97.2 86.6 88.4 81.4 86.9 84.9 83.7 86.8 88.3 92.5 94.7 94.5 98.7 88.6 95.2 91.3 91.7 89.3 88.7 91.2 88.6 94.6 96 94.3 102 93.4 96.7 93.7 91.6 89.6 92.9 94.1 92 97.5 92.7 100.7 105.9 95.3 99.8 91.3 90.8 87.1 91.4 86.1 87.1 92.6 96.6 105.3 102.4 98.2 98.6 92.6 87.9 84.1 86.7 84.4 86 90.4 92.9 105.8 106 99.1 99.9 88.1 87.8 87.1 85.9 86.5 84.1 92.1 93.3 98.9 103 98.4 100.7 92.3 89 88.9 85.5 90.1 87 97.1 101.5 103 106.1 96.1 94.2 89.1 85.2 86.5 88 88.4 87.9 95.7 94.8 105.2 108.7 96.1 98.3 88.6 90.8 88.1 91.9 98.5 98.6 100.3 98.7 110.7 115.4 105.4 108 94.5 96.5 91 94.1 96.4 93.1 97.5 102.5 105.7 109.1 97.2 100.3 91.3 94.3 89.5 89.3 93.4 91.9 92.9 93.7 100.1 105.5 110.5 89.5 90.4 89.9 84.6 86.2 83.4 82.9 81.8 87.6 94.6 99.6 96.7 99.8 83.8 82.4 86.8 91 85.3 83.6 94 100.3 107.1 100.7 95.5 92.9 79.2 82 79.3 81.5 76 73.1 80.4 82.1 90.5 98.1 89.5 86.5 77 74.7 73.4 72.5 69.3 75.2 83.5 90.5 92.2 110.5 101.8 107.4 95.5 84.5 81.1 86.2 91.5 84.7 92.2 99.2 104.5 113 100.4 101 84.8 86.5 91.7 94.8 95
Seasonal period
112001150013313112additive1212
12
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9
10
11
12
Type of Exponential Smoothing
(?)
Do not include Seasonal DummiesDo not include Seasonal Dummies5Do not include Seasonal DummiesDo not include Seasonal Dummies12Do not include Seasonal Dummies11Do not include Seasonal Dummies1Do not include Seasonal DummiesSingle12TripleTriple
Single
Double
Triple
Type of seasonality
(?)
No Linear TrendNo Linear Trend0No Linear TrendNo Linear Trend5No Linear Trend22No Linear Trend2No Linear Trendadditiveadditivemultiplicative
additive
multiplicative
Number of Forecasts
00P1 P5 Q1 Q3 P95 P9900P1 P5 Q1 Q3 P95 P99P1 P5 Q1 Q3 P95 P990TRUE0TRUE121212
12
1
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18
Chart options
R Code
par4 <- '12' par3 <- 'additive' par2 <- 'Triple' par1 <- '12' 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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R Server
Big Analytics Cloud Computing Center
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