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Data:
2443.6 2460.2 2448.2 2470.4 2484.7 2466.8 2487.9 2508.4 2510.5 2497.4 2532.5 2556.8 2561 2547.3 2541.5 2558.5 2587.9 2580.5 2579.6 2589.3 2595 2595.6 2588.8 2591.7 2601.7 2585.4 2573.3 2597.4 2600.6 2570.6 2569.4 2584.9 2608.8 2617.2 2621 2540.5 2554.5 2601.9 2623 2640.7 2640.7 2619.8 2624.2 2638.2 2645.7 2679.6 2669 2664.6 2663.3 2667.4 2653.2 2630.8 2626.6 2641.9 2625.8 2606 2594.4 2583.6 2588.7 2600.3 2579.5 2576.6 2597.8 2595.6 2599 2621.7 2645.6 2644.2 2625.6 2624.6 2596.2 2599.5 2584.1 2570.8 2555 2574.5 2576.7 2579 2588.7 2601.1 2575.7 2559.5 2561.1 2528.3 2514.7 2558.5 2553.3 2577.1 2566 2549.5 2527.8 2540.9 2534.2 2538 2559 2554.9 2575.5 2546.5 2561.6 2546.6 2502.9 2463.1 2472.6 2463.5 2446.3 2456.2 2471.5 2447.5 2428.6 2420.2 2414.9 2420.2 2423.8 2407 2388.7 2409.6 2392 2380.2 2423.3 2451.6 2440.8 2432.9 2413.6 2391.6 2358.1 2345.4 2384.4 2384.4 2384.4 2418.7 2420 2493.1 2493.1 2492.8
Seasonal period
12
12
1
2
3
4
5
6
7
8
9
10
11
12
Type of Exponential Smoothing
(?)
Double
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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