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Data:
62.4 67.4 76.1 67.4 74.5 72.6 60.5 66.1 76.5 76.8 77 71 74.8 73.7 80.5 71.8 76.9 79.9 65.9 69.5 75.1 79.6 75.2 68 72.8 71.5 78.5 76.8 75.3 76.7 69.7 67.8 77.5 82.5 75.3 70.9 76 73.7 79.7 77.8 73.3 78.3 71.9 67 82 83.7 74.8 80 74.3 76.8 89 81.9 76.8 88.9 75.8 75.5 89.1 88 85.9 89.3 82.9 81.2 90.5 86.4 81.8 91.3 73.4 76.6 91 87 89.7 90.7 86.5 86.6 98.8 84.4 91.4 95.7 78.5 81.7 94.3 98.5 95.4 91.7 92.8 90.5 102.2 91.8 95 102 88.9 89.6 97.9 108.6 100.8 95.1 101 100.9 102.5 105.4 98.4 105.3 96.5 88.1 107.9 107 92.5 95.7 85.2 85.5 94.7 86.2 88.8 93.4 83.4 82.9 96.7 96.2 92.8 92.8 90 95.4 108.3 96.3 95 109 92 92.3 107 105.5 105.4 103.9 99.2 102.2 121.5 102.3 110 105.9 91.9 100 111.7 104.9 103.3 101.8 100.8 104.2 116.5 97.9 100.7 107 96.3 96 104.5 107.4 102.4 94.9 98.8 96.8 108.2 103.8 102.3 107.2 102 92.6 105.2 113 105.6 101.6 101.7 102.7 109 105.5 103.3 108.6 98.2 90 112.4 111.9 102.1 102.4 101.7 98.7 114 105.1 98.3 110 96.5 92.2 112 111.4 107.5 103.4 103.5 107.4 117.6 110.2 104.3 115.9 98.9 101.9 113.5 109.5 110 114.2 106.9 109.2 124.2 104.7 111.9 119 102.9 106.3


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Testing Period (?)


Box-Cox lambda transformation parameter (lambda)


Degree of non-seasonal differencing (d)


Degree of seasonal differencing (D)


Seasonal period (s)


AR(p) order


MA(q) order


SAR(P) order


SMA(Q) order


Include mean?


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 - 2par1 nx <- lx - par1 nx1 <- nx + 1 fx <- lx - nx if (fx < 1) { fx <- par52 nx1 <- lx + fx - 1 first <- lx - 2fx } 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')

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	Big Analytics Cloud Computing Center