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Data:
17/10/19 0.57% 18/10/19 -1.68% 21/10/19 1.60% 22/10/19 -1.12% 23/10/19 -0.20% 24/10/19 1.06% 25/10/19 -1.09% 28/10/19 0.89% 29/10/19 -0.81% 30/10/19 0.98% 31/10/19 -0.19% 1/11/19 0.83% 4/11/19 0.74% 5/11/19 -0.16% 6/11/19 -0.33% 7/11/19 -0.42% 8/11/19 -0.13% 11/11/19 -0.80% 12/11/19 0.36% 13/11/19 -1.40% 14/11/19 0.08% 15/11/19 -0.86% 18/11/19 0.75% 19/11/19 0.01% 20/11/19 -0.41% 21/11/19 -0.62% 22/11/19 0.63% 25/11/19 1.61% 26/11/19 1.30% 27/11/19 1.20% 29/11/19 -0.97% 2/12/19 -1.07% 3/12/19 -0.65% 4/12/19 -0.52% 5/12/19 -1.15% 6/12/19 0.64% 9/12/19 -0.12% 10/12/19 -0.59% 11/12/19 0.55% 12/12/19 0.66% 13/12/19 0.03% 16/12/19 0.47% 17/12/19 1.21% 18/12/19 -0.37% 19/12/19 0.46% 20/12/19 -0.32% 23/12/19 0.36% 24/12/19 -0.21% 26/12/19 4.45% 27/12/19 0.06% 30/12/19 -1.23% 31/12/19 0.05% 2/1/20 2.72% 3/1/20 -1.21% 6/1/20 1.49% 7/1/20 0.21% 8/1/20 -0.78% 9/1/20 0.48% 10/1/20 -0.94% 13/1/20 0.43% 14/1/20 -1.16% 15/1/20 -0.40% 16/1/20 0.85% 17/1/20 -0.70% 21/1/20 1.46% 22/1/20 -0.24% 23/1/20 -0.15% 24/1/20 -1.22% 27/1/20 -1.79% 28/1/20 1.36% 29/1/20 0.26% 30/1/20 0.68% 31/1/20 7.38% 3/2/20 -0.23% 4/2/20 2.27% 5/2/20 -0.48% 6/2/20 0.51% 7/2/20 1.42% 10/2/20 2.63% 11/2/20 0.79% 12/2/20 0.43% 13/2/20 -0.47% 14/2/20 -0.70% 18/2/20 0.97% 19/2/20 0.67% 20/2/20 -0.79% 21/2/20 -2.65% 24/2/20 -4.14% 25/2/20 -1.82% 26/2/20 0.35% 27/2/20 -4.81% 28/2/20 -0.03% 2/3/20 3.73% 3/3/20 -2.30% 4/3/20 3.50% 5/3/20 -2.62% 6/3/20 -1.19% 9/3/20 -5.29% 10/3/20 5.07% 11/3/20 -3.75% 12/3/20 -7.92% 13/3/20 6.46% 16/3/20 -5.37% 17/3/20 7.03% 18/3/20 1.23% 19/3/20 2.78% 20/3/20 -1.85% 23/3/20 3.07% 24/3/20 1.96% 25/3/20 -2.80% 26/3/20 3.69% 27/3/20 -2.83% 30/3/20 3.36% 31/3/20 -0.72% 1/4/20 -2.16% 2/4/20 0.58% 3/4/20 -0.64% 6/4/20 4.77% 7/4/20 0.70% 8/4/20 1.56% 9/4/20 -0.01% 13/4/20 6.17% 14/4/20 5.28% 15/4/20 1.07% 16/4/20 4.36% 17/4/20 -1.38% 20/4/20 0.78% 21/4/20 -2.74% 22/4/20 1.52% 23/4/20 1.52% 24/4/20 0.45% 27/4/20 -1.42% 28/4/20 -2.61% 29/4/20 2.53% 30/4/20 4.27% 1/5/20 -7.60% 4/5/20 1.31% 5/5/20 0.08% 6/5/20 1.44% 7/5/20 0.70% 8/5/20 0.51% 11/5/20 1.24% 12/5/20 -2.16% 13/5/20 0.47% 14/5/20 0.88% 15/5/20 0.88% 18/5/20 0.68% 19/5/20 0.95% 20/5/20 1.98% 21/5/20 -2.05% 22/5/20 -0.40% 26/5/20 -0.62% 27/5/20 -0.47% 28/5/20 -0.39% 29/5/20 1.72% 1/6/20 1.17% 2/6/20 0.06% 3/6/20 0.24% 4/6/20 -0.72% 5/6/20 0.91% 8/6/20 1.65% 9/6/20 3.04% 10/6/20 1.79% 11/6/20 -3.38% 12/6/20 -0.51% 15/6/20 1.09% 16/6/20 1.66% 17/6/20 0.98% 18/6/20 0.49% 19/6/20 0.79% 22/6/20 1.45% 23/6/20 1.86% 24/6/20 -1.09% 25/6/20 0.74% 26/6/20 -2.24% 29/6/20 -0.46% 30/6/20 2.93% 1/7/20 4.35% 2/7/20 0.40% 6/7/20 5.77% 7/7/20 -1.86% 8/7/20 2.70% 9/7/20 3.29% 10/7/20 0.55% 13/7/20 -3.00% 14/7/20 -0.64% 15/7/20 -2.44% 16/7/20 -0.30% 17/7/20 -1.26% 20/7/20 7.93% 21/7/20 -1.83% 22/7/20 -1.22% 23/7/20 -3.66% 24/7/20 0.75% 27/7/20 1.54% 28/7/20 -1.80% 29/7/20 1.11% 30/7/20 0.60% 31/7/20 3.70% 3/8/20 -1.67% 4/8/20 0.87% 5/8/20 2.11% 6/8/20 0.62% 7/8/20 -1.78% 10/8/20 -0.61% 11/8/20 -2.14% 12/8/20 2.65% 13/8/20 -0.04% 14/8/20 -0.41% 17/8/20 1.09% 18/8/20 4.09% 19/8/20 -1.57% 20/8/20 1.13% 21/8/20 -0.38% 24/8/20 0.69% 25/8/20 1.18% 26/8/20 2.85% 27/8/20 -1.22% 28/8/20 0.05% 31/8/20 1.45% 1/9/20 1.40% 2/9/20 0.92% 3/9/20 -4.63% 4/9/20 -2.18% 8/9/20 -4.39% 9/9/20 3.77% 10/9/20 -2.86% 11/9/20 -1.85% 14/9/20 -0.43% 15/9/20 1.71% 16/9/20 -2.47% 17/9/20 -2.25% 18/9/20 -1.79% 21/9/20 0.19% 22/9/20 5.69% 23/9/20 -4.13% 24/9/20 0.66% 25/9/20 2.49% 28/9/20 2.55% 29/9/20 -0.92% 30/9/20 0.12% 1/10/20 2.30% 2/10/20 -2.99% 5/10/20 2.37% 6/10/20 -3.10% 7/10/20 3.09% 8/10/20 -0.16% 9/10/20 3.01% 12/10/20 4.75% 13/10/20 0.02% 14/10/20 -2.32% 15/10/20 -0.75%
Seasonal period
12
12
1
2
3
4
5
6
7
8
9
10
11
12
Type of Exponential Smoothing
(?)
Single
Single
Double
Triple
Type of seasonality
(?)
additive
additive
multiplicative
Number of Forecasts
12
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')
Compute
Summary of computational transaction
Raw Input
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Raw Output
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Computing time
1 seconds
R Server
Big Analytics Cloud Computing Center
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