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(8.6,8.5,8.3,7.8,7.8,8,8.6,8.9,8.9,8.6,8.3,8.3,8.3,8.4,8.5,8.4,8.6,8.5,8.5,8.4,8.5,8.5,8.5,8.5,8.5,8.5,8.5,8.5,8.6,8.4,8.1,8,8,8,8,7.9,7.8,7.8,7.9,8.1,8,7.6,7.3,7,6.8,7,7.1,7.2,7.1,6.9,6.7,6.7,6.6,6.9,7.3,7.5,7.3,7.1,6.9,7.1)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '0'
> par6 = '0'
> par5 = '12'
> par4 = '0'
> par3 = '1'
> 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
      0.6536  -0.3348  -0.2413  -0.4973  0.2107  -0.7134
s.e.  0.2139   0.2703   0.2318   0.2275  0.2314   0.2638

sigma^2 estimated as 0.01293:  log likelihood = 20.68,  aic = -27.36
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1] 8.139230 8.490396 8.655533 8.612319 8.444067 8.308722 8.287011 8.358723
 [9] 8.445516 8.483476 8.461930 8.414199 8.381057 8.380572 8.402866 8.425595
[17] 8.433105 8.425026 8.411747 8.403961 8.405267 8.411930 8.417727 8.418970
[25] 8.416234 8.412632 8.410893 8.411622

$se
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1] 0.1154681 0.1791452 0.2263155 0.2273471 0.2337595 0.2439005 0.2451192
 [8] 0.2466330 0.2518601 0.2545976 0.2545740 0.2546788 0.2548203 0.2546998
[15] 0.2550650 0.2557495 0.2560715 0.2560252 0.2558911 0.2557722 0.2557425
[22] 0.2558407 0.2559699 0.2560245 0.2560008 0.2559478 0.2559088 0.2559068

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1] 7.912913 8.139271 8.211955 8.166719 7.985898 7.830677 7.806578 7.875322
 [9] 7.951871 7.984465 7.962965 7.915029 7.881609 7.881360 7.902938 7.924326
[17] 7.931205 7.923217 7.910201 7.902648 7.904011 7.910482 7.916026 7.917162
[25] 7.914473 7.910974 7.909311 7.910045
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1] 8.365548 8.841520 9.099112 9.057919 8.902236 8.786767 8.767445 8.842124
 [9] 8.939162 8.982487 8.960895 8.913369 8.880505 8.879784 8.902793 8.926864
[17] 8.935005 8.926835 8.913294 8.905275 8.906522 8.913378 8.919428 8.920778
[25] 8.917996 8.914289 8.912474 8.913199
> 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$pred))
 [1] 8.600000 8.500000 8.300000 7.800000 7.800000 8.000000 8.600000 8.900000
 [9] 8.900000 8.600000 8.300000 8.300000 8.300000 8.400000 8.500000 8.400000
[17] 8.600000 8.500000 8.500000 8.400000 8.500000 8.500000 8.500000 8.500000
[25] 8.500000 8.500000 8.500000 8.500000 8.600000 8.400000 8.100000 8.000000
[33] 8.139230 8.490396 8.655533 8.612319 8.444067 8.308722 8.287011 8.358723
[41] 8.445516 8.483476 8.461930 8.414199 8.381057 8.380572 8.402866 8.425595
[49] 8.433105 8.425026 8.411747 8.403961 8.405267 8.411930 8.417727 8.418970
[57] 8.416234 8.412632 8.410893 8.411622
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1] 0.01418661 0.02109975 0.02614691 0.02639790 0.02768329 0.02935476
 [7] 0.02957872 0.02950607 0.02982175 0.03001100 0.03008463 0.03026774
[13] 0.03040431 0.03039170 0.03035452 0.03035388 0.03036503 0.03038865
[19] 0.03042069 0.03043472 0.03042645 0.03041403 0.03040843 0.03041043
[25] 0.03041750 0.03042423 0.03042587 0.03042300
> postscript(file="/var/www/html/rcomp/tmp/1w7fo1260522601.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2ujj71260522601.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/3c0pc1260522601.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/45cyq1260522601.tab") 
> 
> system("convert tmp/1w7fo1260522601.ps tmp/1w7fo1260522601.png")
> system("convert tmp/2ujj71260522601.ps tmp/2ujj71260522601.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.749   0.338   5.393