R version 2.12.0 (2010-10-15)
Copyright (C) 2010 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: i486-pc-linux-gnu (32-bit)

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> x <- c(7.14,7.24,7.33,7.61,7.66,7.69,7.7,7.68,7.71,7.71,7.72,7.68,7.72,7.74,7.76,7.9,7.97,7.96,7.95,7.97,7.93,7.99,7.96,7.92,7.97,7.98,8,8.04,8.17,8.29,8.26,8.3,8.32,8.28,8.27,8.32,8.31,8.34,8.32,8.36,8.33,8.35,8.34,8.37,8.31,8.33,8.34,8.25,8.27,8.31,8.25,8.3,8.3,8.35,8.78,8.9)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '0'
> par6 = '0'
> par5 = '12'
> par4 = '1'
> 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
      -0.3250  0.4938  0.420  0.3767  0.3726  0.9931
s.e.   0.2637  0.2517  0.319  0.2833  0.3543  0.4673

sigma^2 estimated as 0.001258:  log likelihood = 24.99,  aic = -35.97
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 29 
End = 56 
Frequency = 1 
 [1] 8.119159 8.021801 7.943586 7.946459 7.841651 7.885607 7.821623 7.757527
 [9] 7.791837 7.780765 7.789745 7.816331 7.885558 7.780175 7.694030 7.691346
[17] 7.581057 7.620720 7.553091 7.485758 7.517517 7.504144 7.511252 7.536239
[25] 7.604095 7.497582 7.410456 7.406956

$se
Time Series:
Start = 29 
End = 56 
Frequency = 1 
 [1] 0.03862829 0.05543110 0.09015664 0.14231721 0.18195777 0.23246841
 [7] 0.27802534 0.32421163 0.37041445 0.41424970 0.45807003 0.50005204
[13] 0.55693542 0.61098603 0.67458037 0.75039673 0.82155806 0.90031707
[19] 0.97648080 1.05297163 1.12920633 1.20317114 1.27651204 1.34774642
[25] 1.42991512 1.50974662 1.59666178 1.69295693

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 29 
End = 56 
Frequency = 1 
 [1] 8.043447 7.913156 7.766879 7.667517 7.485014 7.429969 7.276693 7.122073
 [9] 7.065825 6.968836 6.891928 6.836229 6.793964 6.582642 6.371852 6.220568
[17] 5.970804 5.856098 5.639188 5.421933 5.304272 5.145928 5.009289 4.894656
[25] 4.801461 4.538478 4.280998 4.088761
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 29 
End = 56 
Frequency = 1 
 [1]  8.194870  8.130446  8.120293  8.225401  8.198288  8.341245  8.366553
 [8]  8.392982  8.517850  8.592694  8.687563  8.796433  8.977151  8.977707
[15]  9.016207  9.162123  9.191311  9.385341  9.466993  9.549582  9.730761
[22]  9.862359 10.013216 10.177822 10.406728 10.456685 10.539913 10.725152
> 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$pred))
 [1] 7.140000 7.240000 7.330000 7.610000 7.660000 7.690000 7.700000 7.680000
 [9] 7.710000 7.710000 7.720000 7.680000 7.720000 7.740000 7.760000 7.900000
[17] 7.970000 7.960000 7.950000 7.970000 7.930000 7.990000 7.960000 7.920000
[25] 7.970000 7.980000 8.000000 8.040000 8.119159 8.021801 7.943586 7.946459
[33] 7.841651 7.885607 7.821623 7.757527 7.791837 7.780765 7.789745 7.816331
[41] 7.885558 7.780175 7.694030 7.691346 7.581057 7.620720 7.553091 7.485758
[49] 7.517517 7.504144 7.511252 7.536239 7.604095 7.497582 7.410456 7.406956
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 29 
End = 56 
Frequency = 1 
 [1] 0.004757671 0.006910058 0.011349614 0.017909514 0.023204012 0.029480092
 [7] 0.035545735 0.041793166 0.047538782 0.053240228 0.058804236 0.063975291
[13] 0.070627270 0.078531144 0.087675818 0.097563775 0.108369851 0.118140690
[19] 0.129282280 0.140663334 0.150210024 0.160334234 0.169946633 0.178835420
[25] 0.188045408 0.201364482 0.215460679 0.228563104
> postscript(file="/var/www/rcomp/tmp/1tnf81293194155.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/rcomp/tmp/2pxvz1293194155.ps",horizontal=F,onefile=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/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/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/rcomp/tmp/3egst1293194155.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/rcomp/tmp/40yrh1293194155.tab") 
> 
> try(system("convert tmp/1tnf81293194155.ps tmp/1tnf81293194155.png",intern=TRUE))
character(0)
> try(system("convert tmp/2pxvz1293194155.ps tmp/2pxvz1293194155.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  0.850   0.460   1.308