R version 2.9.0 (2009-04-17)
Copyright (C) 2009 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> x <- c(11.40,11.00,9.20,7.10,9.30,9.30,11.50,13.00,13.20,13.10,13.90,11.00,11.30,10.80,11.20,12.90,13.90,14.50,14.50,13.30,12.00,11.50,11.00,12.10,13.00,14.00,15.10,14.50,14.20,13.30,12.70,11.80,11.40,10.50,9.60,10.80,10.70,11.90,12.00,11.10,10.90,10.40,10.70,12.10,12.80,13.90,13.50,12.00,12.00,11.50,12.50,13.10,12.70,12.80,12.50,13.00,13.20,12.80,12.40,12.00,11.80,11.10,8.50,6.30)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '1'
> par6 = '3'
> par5 = '12'
> par4 = '0'
> par3 = '1'
> par2 = '1'
> par1 = '24'
> par1 <- as.numeric(par1) #cut off periods
> par1 <- 28
> 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
> par6 <- 3
> par7 <- as.numeric(par7) #q
> par7 <- 3
> 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
+ 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'))

Call:
arima(x = x[1:nx], order = c(par6, par3, par7), seasonal = list(order = c(par8, 
    par4, par9), period = par5), include.mean = par10, method = "ML")

Coefficients:
         ar1      ar2      ar3      ma1     ma2      ma3
      1.2705  -0.5531  -0.2026  -1.5031  1.2576  -0.5336
s.e.  0.3982   0.6025   0.3732   0.4144  0.6049   0.3414

sigma^2 estimated as 0.6814:  log likelihood = -44.57,  aic = 103.14
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 37 
End = 64 
Frequency = 1 
 [1] 10.65284 11.75353 12.58627 13.06532 12.99034 12.46140 11.73377 11.11705
 [9] 10.84314 10.98367 11.43867 11.99453 12.42062 12.56233 12.39409 12.01561
[17] 11.59909 11.31333 11.25732 11.42862 11.73513 12.04116 12.22574 12.22888
[25] 12.06876 11.82620 11.60595 11.49272

$se
Time Series:
Start = 37 
End = 64 
Frequency = 1 
 [1] 0.8254623 1.0404816 1.4231447 1.6828978 1.8069850 1.8359387 1.8365894
 [8] 1.8378711 1.8378724 1.8501829 1.9078774 2.0173551 2.1401072 2.2317407
[15] 2.2783397 2.2942658 2.2987357 2.3019777 2.3109524 2.3364391 2.3856808
[22] 2.4512816 2.5147627 2.5613551 2.5887222 2.6034428 2.6133462 2.6245304

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 37 
End = 64 
Frequency = 1 
 [1] 9.034936 9.714188 9.796905 9.766839 9.448654 8.862957 8.134052 7.514827
 [9] 7.240912 7.357310 7.699229 8.040511 8.226008 8.188123 7.928543 7.518851
[17] 7.093572 6.801452 6.727856 6.849199 7.059197 7.236651 7.296805 7.208620
[25] 6.994867 6.723455 6.483793 6.348641
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 37 
End = 64 
Frequency = 1 
 [1] 12.27075 13.79288 15.37563 16.36380 16.53203 16.05984 15.33348 14.71928
 [9] 14.44537 14.61003 15.17811 15.94854 16.61523 16.93655 16.85963 16.51237
[17] 16.10462 15.82521 15.78679 16.00804 16.41107 16.84568 17.15468 17.24913
[25] 17.14266 16.92895 16.72811 16.63680
> 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$pred))
 [1] 11.40000 11.00000  9.20000  7.10000  9.30000  9.30000 11.50000 13.00000
 [9] 13.20000 13.10000 13.90000 11.00000 11.30000 10.80000 11.20000 12.90000
[17] 13.90000 14.50000 14.50000 13.30000 12.00000 11.50000 11.00000 12.10000
[25] 13.00000 14.00000 15.10000 14.50000 14.20000 13.30000 12.70000 11.80000
[33] 11.40000 10.50000  9.60000 10.80000 10.65284 11.75353 12.58627 13.06532
[41] 12.99034 12.46140 11.73377 11.11705 10.84314 10.98367 11.43867 11.99453
[49] 12.42062 12.56233 12.39409 12.01561 11.59909 11.31333 11.25732 11.42862
[57] 11.73513 12.04116 12.22574 12.22888 12.06876 11.82620 11.60595 11.49272
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 37 
End = 64 
Frequency = 1 
 [1] 0.07748752 0.08852501 0.11307122 0.12880649 0.13910216 0.14733009
 [7] 0.15652172 0.16531997 0.16949630 0.16844854 0.16679191 0.16818964
[13] 0.17230280 0.17765334 0.18382471 0.19094041 0.19818235 0.20347484
[19] 0.20528436 0.20443757 0.20329391 0.20357516 0.20569411 0.20945139
[25] 0.21449773 0.22014190 0.22517294 0.22836459
> postscript(file="/var/www/html/rcomp/tmp/1z9un1260564135.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$pred , lwd=2 , col ='white')
> box()
> par(opar)
> dev.off()
null device 
          1 
> 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.mape <- array(0, dim=fx)
> perf.mape1 <- 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)
> for (i in 1:fx) {
+ locSD <- (ub[i] - forecast$pred[i]) / 1.96
+ perf.pe[i] = (x[nx+i] - forecast$pred[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.mse[1] = abs(perf.se[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.mse[i] = perf.mse[i-1] + perf.se[i]
+ perf.mse1[i] = perf.mse[i] / i
+ }
> perf.rmse = sqrt(perf.mse1)
> postscript(file="/var/www/html/rcomp/tmp/2k38w1260564135.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> 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()
null device 
          1 
> 
> #Note: the /var/www/html/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/html/rcomp/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="/var/www/html/rcomp/tmp/3wj091260564135.tab") 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Univariate ARIMA Extrapolation Forecast Performance',7,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,'Sq.E',1,header=TRUE)
> a<-table.element(a,'MSE',1,header=TRUE)
> a<-table.element(a,'RMSE',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.se[i],4))
+ a<-table.element(a,round(perf.mse1[i],4))
+ a<-table.element(a,round(perf.rmse[i],4))
+ a<-table.row.end(a)
+ }
> a<-table.end(a)
> table.save(a,file="/var/www/html/rcomp/tmp/45nxg1260564135.tab") 
> 
> system("convert tmp/1z9un1260564135.ps tmp/1z9un1260564135.png")
> system("convert tmp/2k38w1260564135.ps tmp/2k38w1260564135.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.760   0.329   0.889