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(8.2,8,7.5,6.8,6.5,6.6,7.6,8,8.1,7.7,7.5,7.6,7.8,7.8,7.8,7.5,7.5,7.1,7.5,7.5,7.6,7.7,7.7,7.9,8.1,8.2,8.2,8.2,7.9,7.3,6.9,6.6,6.7,6.9,7,7.1,7.2,7.1,6.9,7,6.8,6.4,6.7,6.6,6.4,6.3,6.2,6.5,6.8,6.8,6.4,6.1,5.8,6.1,7.2,7.3,6.9,6.1,5.8,6.2,7.1,7.7,7.9,7.7,7.4,7.5,8,8.1)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '1'
> par6 = '3'
> par5 = '12'
> par4 = '0'
> par3 = '2'
> par2 = '1'
> par1 = '12'
> 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
      0.4214  -0.1293  -0.4188  -0.9433  0.2676  -0.3244
s.e.  0.2884   0.2832   0.2340   0.3660  0.3535   0.3916

sigma^2 estimated as 0.05051:  log likelihood = 0.48,  aic = 13.04
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 41 
End = 68 
Frequency = 1 
 [1] 7.062763 7.232782 7.236432 7.171699 7.054751 6.994315 6.993084 7.031358
 [9] 7.054957 7.042468 7.000126 6.956018 6.930139 6.924672 6.926188 6.920373
[17] 6.902018 6.876402 6.852418 6.835313 6.823936 6.813400 6.799596 6.781908
[25] 6.762654 6.744610 6.728906 6.714687

$se
Time Series:
Start = 41 
End = 68 
Frequency = 1 
 [1] 0.2276653 0.4110889 0.6028757 0.7125954 0.7733823 0.8099073 0.8502155
 [8] 0.9066478 0.9786029 1.0507907 1.1123649 1.1630019 1.2092642 1.2575622
[15] 1.3106371 1.3666144 1.4216677 1.4734695 1.5224393 1.5705329 1.6194598
[22] 1.6696173 1.7202087 1.7701739 1.8190448 1.8671080 1.9149833 1.9631030

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 41 
End = 68 
Frequency = 1 
 [1] 6.616539 6.427048 6.054796 5.775012 5.538921 5.406897 5.326661 5.254328
 [9] 5.136895 4.982918 4.819891 4.676534 4.559981 4.459850 4.357340 4.241809
[17] 4.115549 3.988402 3.868437 3.757069 3.649795 3.540950 3.427987 3.312367
[25] 3.197326 3.085078 2.975538 2.867005
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 41 
End = 68 
Frequency = 1 
 [1]  7.508987  8.038516  8.418069  8.568386  8.570580  8.581733  8.659506
 [8]  8.808388  8.973018  9.102017  9.180361  9.235502  9.300297  9.389494
[15]  9.495037  9.598938  9.688487  9.764402  9.836399  9.913558  9.998077
[22] 10.085850 10.171205 10.251449 10.327981 10.404142 10.482273 10.562368
> 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$pred))
 [1] 8.200000 8.000000 7.500000 6.800000 6.500000 6.600000 7.600000 8.000000
 [9] 8.100000 7.700000 7.500000 7.600000 7.800000 7.800000 7.800000 7.500000
[17] 7.500000 7.100000 7.500000 7.500000 7.600000 7.700000 7.700000 7.900000
[25] 8.100000 8.200000 8.200000 8.200000 7.900000 7.300000 6.900000 6.600000
[33] 6.700000 6.900000 7.000000 7.100000 7.200000 7.100000 6.900000 7.000000
[41] 7.062763 7.232782 7.236432 7.171699 7.054751 6.994315 6.993084 7.031358
[49] 7.054957 7.042468 7.000126 6.956018 6.930139 6.924672 6.926188 6.920373
[57] 6.902018 6.876402 6.852418 6.835313 6.823936 6.813400 6.799596 6.781908
[65] 6.762654 6.744610 6.728906 6.714687
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 41 
End = 68 
Frequency = 1 
 [1] 0.03223459 0.05683690 0.08331118 0.09936215 0.10962574 0.11579508
 [7] 0.12157948 0.12894348 0.13871140 0.14920775 0.15890641 0.16719363
[13] 0.17449349 0.18160603 0.18922920 0.19747698 0.20597856 0.21427914
[19] 0.22217548 0.22976751 0.23732048 0.24504908 0.25298690 0.26101414
[25] 0.26898388 0.27682964 0.28459060 0.29235959
> postscript(file="/var/www/html/rcomp/tmp/1y2f51260543921.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/224r31260543921.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/3md4e1260543921.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/4y7qo1260543921.tab") 
> 
> system("convert tmp/1y2f51260543921.ps tmp/1y2f51260543921.png")
> system("convert tmp/224r31260543921.ps tmp/224r31260543921.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.735   0.317   1.078