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Data:
3221816.00 3209817.00 3197649.00 3172468.00 3421574.00 3408392.00 3221816.00 3097770.00 3109769.00 3109769.00 3123120.00 3147118.00 3184467.00 3184467.00 3160469.00 3097770.00 3421574.00 3470922.00 3396393.00 3221816.00 3296514.00 3184467.00 3234998.00 3259165.00 3284346.00 3221816.00 3234998.00 3147118.00 3421574.00 3508271.00 3433742.00 3296514.00 3445741.00 3284346.00 3433742.00 3421574.00 3458923.00 3321695.00 3470922.00 3458923.00 3682848.00 3632317.00 3433742.00 3333694.00 3470922.00 3284346.00 3421574.00 3445741.00 3496272.00 3384394.00 3445741.00 3483090.00 3620318.00 3508271.00 3359044.00 3197649.00 3347045.00 2936375.00 3135119.00 3246997.00 3359044.00 3197649.00 3197649.00 3197649.00 3284346.00 3160469.00 2997891.00 2861846.00 2960542.00 2575222.00 2811315.00 2948543.00 2973724.00 2836496.00 2848495.00 2811315.00 2936375.00 2848495.00 2675270.00 2550041.00 2761798.00 2301949.00 2600572.00 2736617.00 2736617.00 2575222.00 2425995.00 2413996.00 2550041.00 2425995.00 2190071.00 2027493.00 2202070.00 1791569.00 2164721.00 2363296.00 2425995.00 2288767.00 2115373.00 2239419.00 2288767.00 2251418.00 1878097.00 1704872.00 1828749.00 1455597.00 1840917.00 1978145.00 2090023.00 1903447.00 1728870.00 1828749.00 1878097.00 1779401.00 1406249.00 1243671.00 1392898.00 982397.00 1430247.00 1704872.00
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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Raw Output
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Computing time
1 seconds
R Server
Big Analytics Cloud Computing Center
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