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(10.92,10.98,11.15,11.19,11.33,11.38,11.4,11.45,11.56,11.61,11.82,11.77,11.85,11.82,11.92,11.86,11.87,11.94,11.86,11.92,11.83,11.91,11.93,11.99,11.96,12.12,11.85,12.01,12.1,12.21,12.31,12.31,12.39,12.35,12.41,12.51,12.27,12.51,12.44,12.47,12.51,12.58,12.5,12.52,12.59,12.51,12.67,12.64,12.54,12.66,12.67,12.62,12.72,12.85,12.85,12.82)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '0'
> par6 = '1'
> par5 = '12'
> par4 = '0'
> par3 = '2'
> 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
      0.3567  0.015  -0.8275  -1.7951  1.7535  -0.6693
s.e.  0.1376  0.168   0.1360   0.2025  0.2701   0.2021

sigma^2 estimated as 0.00434:  log likelihood = 30.88,  aic = -47.76
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 29 
End = 56 
Frequency = 1 
 [1] 11.83879 11.98515 11.89634 12.00246 11.91181 11.94848 11.86634 11.90653
 [9] 11.88322 11.93742 11.91708 11.92386 11.87506 11.86851 11.85378 11.88274
[17] 11.89220 11.90214 11.87579 11.85265 11.82971 11.83692 11.85223 11.87072
[25] 11.86551 11.84520 11.81651 11.80421

$se
Time Series:
Start = 29 
End = 56 
Frequency = 1 
 [1] 0.06797268 0.07916342 0.12255415 0.14353595 0.18119460 0.20615381
 [7] 0.24324270 0.27545841 0.31804674 0.35746401 0.40204083 0.44295855
[13] 0.48707352 0.53053697 0.57854245 0.62768560 0.67976459 0.73123164
[19] 0.78347688 0.83551419 0.88964441 0.94559567 1.00406340 1.06342575
[25] 1.12330634 1.18298597 1.24342957 1.30522668

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 29 
End = 56 
Frequency = 1 
 [1] 11.705567 11.829994 11.656138 11.721125 11.556665 11.544417 11.389580
 [8] 11.366627 11.259852 11.236790 11.129083 11.055656 10.920392 10.828660
[15] 10.719836 10.652477 10.559863 10.468922 10.340177 10.215041 10.086010
[22]  9.983552  9.884269  9.786403  9.663832  9.526543  9.379387  9.245970
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 29 
End = 56 
Frequency = 1 
 [1] 11.97202 12.14031 12.13655 12.28379 12.26695 12.35254 12.34309 12.44642
 [9] 12.50660 12.63805 12.70508 12.79205 12.82972 12.90836 12.98772 13.11300
[17] 13.22454 13.33535 13.41141 13.49026 13.57342 13.69029 13.82020 13.95503
[25] 14.06719 14.16385 14.25363 14.36246
> 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$pred))
 [1] 10.92000 10.98000 11.15000 11.19000 11.33000 11.38000 11.40000 11.45000
 [9] 11.56000 11.61000 11.82000 11.77000 11.85000 11.82000 11.92000 11.86000
[17] 11.87000 11.94000 11.86000 11.92000 11.83000 11.91000 11.93000 11.99000
[25] 11.96000 12.12000 11.85000 12.01000 11.83879 11.98515 11.89634 12.00246
[33] 11.91181 11.94848 11.86634 11.90653 11.88322 11.93742 11.91708 11.92386
[41] 11.87506 11.86851 11.85378 11.88274 11.89220 11.90214 11.87579 11.85265
[49] 11.82971 11.83692 11.85223 11.87072 11.86551 11.84520 11.81651 11.80421
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 29 
End = 56 
Frequency = 1 
 [1] 0.005741521 0.006605124 0.010301833 0.011958882 0.015211345 0.017253562
 [7] 0.020498553 0.023135078 0.026764348 0.029944831 0.033736514 0.037148937
[13] 0.041016524 0.044701218 0.048806581 0.052823301 0.057160533 0.061437007
[19] 0.065972600 0.070491770 0.075204225 0.079885283 0.084715126 0.089583951
[25] 0.094669857 0.099870533 0.105228164 0.110572942
> postscript(file="/var/www/rcomp/tmp/1j1cq1293187840.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2q2911293187840.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/3f3ov1293187840.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/4i3m11293187840.tab") 
> 
> try(system("convert tmp/1j1cq1293187840.ps tmp/1j1cq1293187840.png",intern=TRUE))
character(0)
> try(system("convert tmp/2q2911293187840.ps tmp/2q2911293187840.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  0.830   0.460   1.285