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Data:
38327240.00 38147255.00 37964735.00 37587020.00 41323610.00 41125880.00 38327240.00 36466550.00 36646535.00 36646535.00 36846800.00 37206770.00 37767005.00 37767005.00 37407035.00 36466550.00 41323610.00 42063830.00 40945895.00 38327240.00 39447710.00 37767005.00 38524970.00 38887475.00 39265190.00 38327240.00 38524970.00 37206770.00 41323610.00 42624065.00 41506130.00 39447710.00 41686115.00 39265190.00 41506130.00 41323610.00 41883845.00 39825425.00 42063830.00 41883845.00 45242720.00 44484755.00 41506130.00 40005410.00 42063830.00 39265190.00 41323610.00 41686115.00 42444080.00 40765910.00 41686115.00 42246350.00 44304770.00 42624065.00 40385660.00 37964735.00 40205675.00 34045625.00 37026785.00 38704955.00 40385660.00 37964735.00 37964735.00 37964735.00 39265190.00 37407035.00 34968365.00 32927690.00 34408130.00 28628330.00 32169725.00 34228145.00 34605860.00 32547440.00 32727425.00 32169725.00 34045625.00 32727425.00 30129050.00 28250615.00 31426970.00 24529235.00 29008580.00 31049255.00 31049255.00 28628330.00 26389925.00 26209940.00 28250615.00 26389925.00 22851065.00 20412395.00 23031050.00 16873535.00 22470815.00 25449440.00 26389925.00 24331505.00 21730595.00 23591285.00 24331505.00 23771270.00 18171455.00 15573080.00 17431235.00 11833955.00 17613755.00 19672175.00 21350345.00 18551705.00 15933050.00 17431235.00 18171455.00 16691015.00 11093735.00 8655065.00 10893470.00 4735955.00 11453705.00 15573080.00
Seasonal period
48481212additiveadditive12
12
1
2
3
4
5
6
7
8
9
10
11
12
Type of Exponential Smoothing
(?)
111212Triple
Single
Double
Triple
Type of seasonality
(?)
01additive
additive
multiplicative
Number of Forecasts
0112
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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R Server
Big Analytics Cloud Computing Center
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