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Data:
3567.2 3968.25 4285.35 4130.95 4219.4 4626.2 3860.75 4174.15 4668.65 4630.05 4553.7 4603.85 4310.7 4831.3 5145.3 4886.65 4934.05 5304.7 4419.45 4804.85 5105 5132.6 4982.5 4906.7 4506.4 5010.85 5392.25 5049.7 5143.9 5449.9 4520.4 4936.95 5358.55 5289.5 5123.55 4985.65 4682.65 5175.55 5374.7 5289 5176.15 5604.25 4608.8 4898.15 5448.65 5373.05 5078.6 5233.4 4629.2 5387.8 5736.65 5357.9 5337.95 5795.5 4804.05 5120.5 5850.45 5734.75 5539 5582.85 4983.1 5672 6185.8 5835.6 5930.4 6444.65 5171.05 5739.1 6413.9 6230.2 6015.45 6174.25 5579.25 6133.45 6478.7 6184.4 6185.65 6556 5123.25 6028.9 6499.95 6190.05 6027.95 6034 5128.75 6087.7 6628.15 6075.3 6352.1 6824 5412.35 6171.25 6521.35 6457.6 5930.95 5842.7 5120.1 5719.95 5946.7 5921.1 6072 6489.4 5291.15 5986.45 6538.15 6442.8 6169.55 5793 5254.85 6050.75 6606.15 6221.15 6293.4 6908.4 5498.95 6145.35
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Testing Period
(?)
Default
0
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Box-Cox lambda transformation parameter (lambda)
1
1
-2.0
-1.9
-1.8
-1.7
-1.6
-1.5
-1.4
-1.3
-1.2
-1.1
-1.0
-0.9
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0.0
0.1
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0.9
1.0
1.1
1.2
1.3
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1.5
1.6
1.7
1.8
1.9
2.0
Degree of non-seasonal differencing (d)
0
0
1
2
Degree of seasonal differencing (D)
0
0
1
Seasonal period (s)
12
1
2
3
4
6
12
AR(p) order
White Noise
0
1
2
3
MA(q) order
0.95
0
1
2
SAR(P) order
0
1
2
SMA(Q) order
0
1
Include mean?
FALSE
TRUE
Chart options
R Code
par1 <- as.numeric(par1) #cut off periods par2 <- as.numeric(par2) #lambda par3 <- as.numeric(par3) #degree of non-seasonal differencing par4 <- as.numeric(par4) #degree of seasonal differencing par5 <- as.numeric(par5) #seasonal period par6 <- as.numeric(par6) #p par7 <- as.numeric(par7) #q par8 <- as.numeric(par8) #P par9 <- as.numeric(par9) #Q if (par10 == 'TRUE') par10 <- TRUE if (par10 == 'FALSE') par10 <- FALSE if (par2 == 0) x <- log(x) if (par2 != 0) x <- x^par2 lx <- length(x) first <- lx - 2*par1 nx <- lx - par1 nx1 <- nx + 1 fx <- lx - nx if (fx < 1) { fx <- par5*2 nx1 <- lx + fx - 1 first <- lx - 2*fx } first <- 1 if (fx < 3) fx <- round(lx/10,0) (arima.out <- arima(x[1:nx], order=c(par6,par3,par7), seasonal=list(order=c(par8,par4,par9), period=par5), include.mean=par10, method='ML')) (forecast <- predict(arima.out,fx)) (lb <- forecast$pred - 1.96 * forecast$se) (ub <- forecast$pred + 1.96 * forecast$se) if (par2 == 0) { x <- exp(x) forecast$pred <- exp(forecast$pred) lb <- exp(lb) ub <- exp(ub) } if (par2 != 0) { x <- x^(1/par2) forecast$pred <- forecast$pred^(1/par2) lb <- lb^(1/par2) ub <- ub^(1/par2) } if (par2 < 0) { olb <- lb lb <- ub ub <- olb } (actandfor <- c(x[1:nx], forecast$pred)) (perc.se <- (ub-forecast$pred)/1.96/forecast$pred) bitmap(file='test1.png') opar <- par(mar=c(4,4,2,2),las=1) ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub)) plot(x,ylim=ylim,type='n',xlim=c(first,lx)) usr <- par('usr') rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon') rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender') abline(h= (-3:3)*2 , col ='gray', lty =3) polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA) lines(nx1:lx, lb , lty=2) lines(nx1:lx, ub , lty=2) lines(x, lwd=2) lines(nx1:lx, forecast$pred , lwd=2 , col ='white') box() par(opar) dev.off() prob.dec <- array(NA, dim=fx) prob.sdec <- array(NA, dim=fx) prob.ldec <- array(NA, dim=fx) prob.pval <- array(NA, dim=fx) perf.pe <- array(0, dim=fx) perf.spe <- array(0, dim=fx) perf.scalederr <- array(0, dim=fx) perf.mase <- array(0, dim=fx) perf.mase1 <- array(0, dim=fx) perf.mape <- array(0, dim=fx) perf.smape <- array(0, dim=fx) perf.mape1 <- array(0, dim=fx) perf.smape1 <- array(0,dim=fx) perf.se <- array(0, dim=fx) perf.mse <- array(0, dim=fx) perf.mse1 <- array(0, dim=fx) perf.rmse <- array(0, dim=fx) perf.scaleddenom <- 0 for (i in 2:fx) { perf.scaleddenom = perf.scaleddenom + abs(x[nx+i] - x[nx+i-1]) } perf.scaleddenom = perf.scaleddenom / (fx-1) for (i in 1:fx) { locSD <- (ub[i] - forecast$pred[i]) / 1.96 perf.scalederr[i] = (x[nx+i] - forecast$pred[i]) / perf.scaleddenom perf.pe[i] = (x[nx+i] - forecast$pred[i]) / x[nx+i] perf.spe[i] = 2*(x[nx+i] - forecast$pred[i]) / (x[nx+i] + forecast$pred[i]) perf.se[i] = (x[nx+i] - forecast$pred[i])^2 prob.dec[i] = pnorm((x[nx+i-1] - forecast$pred[i]) / locSD) prob.sdec[i] = pnorm((x[nx+i-par5] - forecast$pred[i]) / locSD) prob.ldec[i] = pnorm((x[nx] - forecast$pred[i]) / locSD) prob.pval[i] = pnorm(abs(x[nx+i] - forecast$pred[i]) / locSD) } perf.mape[1] = abs(perf.pe[1]) perf.smape[1] = abs(perf.spe[1]) perf.mape1[1] = perf.mape[1] perf.smape1[1] = perf.smape[1] perf.mse[1] = perf.se[1] perf.mase[1] = abs(perf.scalederr[1]) perf.mase1[1] = perf.mase[1] for (i in 2:fx) { perf.mape[i] = perf.mape[i-1] + abs(perf.pe[i]) perf.mape1[i] = perf.mape[i] / i perf.smape[i] = perf.smape[i-1] + abs(perf.spe[i]) perf.smape1[i] = perf.smape[i] / i perf.mse[i] = perf.mse[i-1] + perf.se[i] perf.mse1[i] = perf.mse[i] / i perf.mase[i] = perf.mase[i-1] + abs(perf.scalederr[i]) perf.mase1[i] = perf.mase[i] / i } perf.rmse = sqrt(perf.mse1) bitmap(file='test2.png') plot(forecast$pred, pch=19, type='b',main='ARIMA Extrapolation Forecast', ylab='Forecast and 95% CI', xlab='time',ylim=c(min(lb),max(ub))) dum <- forecast$pred dum[1:par1] <- x[(nx+1):lx] lines(dum, lty=1) lines(ub,lty=3) lines(lb,lty=3) dev.off() load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Univariate ARIMA Extrapolation Forecast',9,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'time',1,header=TRUE) a<-table.element(a,'Y[t]',1,header=TRUE) a<-table.element(a,'F[t]',1,header=TRUE) a<-table.element(a,'95% LB',1,header=TRUE) a<-table.element(a,'95% UB',1,header=TRUE) a<-table.element(a,'p-value<br />(H0: Y[t] = F[t])',1,header=TRUE) a<-table.element(a,'P(F[t]>Y[t-1])',1,header=TRUE) a<-table.element(a,'P(F[t]>Y[t-s])',1,header=TRUE) mylab <- paste('P(F[t]>Y[',nx,sep='') mylab <- paste(mylab,'])',sep='') a<-table.element(a,mylab,1,header=TRUE) a<-table.row.end(a) for (i in (nx-par5):nx) { a<-table.row.start(a) a<-table.element(a,i,header=TRUE) a<-table.element(a,x[i]) a<-table.element(a,'-') a<-table.element(a,'-') a<-table.element(a,'-') a<-table.element(a,'-') a<-table.element(a,'-') a<-table.element(a,'-') a<-table.element(a,'-') a<-table.row.end(a) } for (i in 1:fx) { a<-table.row.start(a) a<-table.element(a,nx+i,header=TRUE) a<-table.element(a,round(x[nx+i],4)) a<-table.element(a,round(forecast$pred[i],4)) a<-table.element(a,round(lb[i],4)) a<-table.element(a,round(ub[i],4)) a<-table.element(a,round((1-prob.pval[i]),4)) a<-table.element(a,round((1-prob.dec[i]),4)) a<-table.element(a,round((1-prob.sdec[i]),4)) a<-table.element(a,round((1-prob.ldec[i]),4)) 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,'Univariate ARIMA Extrapolation Forecast Performance',10,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'time',1,header=TRUE) a<-table.element(a,'% S.E.',1,header=TRUE) a<-table.element(a,'PE',1,header=TRUE) a<-table.element(a,'MAPE',1,header=TRUE) a<-table.element(a,'sMAPE',1,header=TRUE) a<-table.element(a,'Sq.E',1,header=TRUE) a<-table.element(a,'MSE',1,header=TRUE) a<-table.element(a,'RMSE',1,header=TRUE) a<-table.element(a,'ScaledE',1,header=TRUE) a<-table.element(a,'MASE',1,header=TRUE) a<-table.row.end(a) for (i in 1:fx) { a<-table.row.start(a) a<-table.element(a,nx+i,header=TRUE) a<-table.element(a,round(perc.se[i],4)) a<-table.element(a,round(perf.pe[i],4)) a<-table.element(a,round(perf.mape1[i],4)) a<-table.element(a,round(perf.smape1[i],4)) a<-table.element(a,round(perf.se[i],4)) a<-table.element(a,round(perf.mse1[i],4)) a<-table.element(a,round(perf.rmse[i],4)) a<-table.element(a,round(perf.scalederr[i],4)) a<-table.element(a,round(perf.mase1[i],4)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable1.tab')
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