R version 2.8.0 (2008-10-20)
Copyright (C) 2008 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> x <- c(29.59,30.7,30.52,32.67,33.19,37.13,35.54,37.75,41.84,42.94,49.14,44.61,40.22,44.23,45.85,53.38,53.26,51.8,55.3,57.81,63.96,63.77,59.15,56.12,57.42,63.52,61.71,63.01,68.18,72.03,69.75,74.41,74.33,64.24,60.03,59.44,62.5,55.04,58.34,61.92,67.65,67.68,70.3,75.26,71.44,76.36,81.71,92.6,90.6,92.23,94.09,102.79,109.65,124.05,132.69,135.81,116.07,101.42,75.73,55.48)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '1'
> par6 = '2'
> par5 = '12'
> par4 = '0'
> par3 = '1'
> par2 = '-0.2'
> par1 = '12'
> #'GNU S' R Code compiled by R2WASP v. 1.0.44 ()
> #Author: Prof. Dr. P. Wessa
> #To cite this work: AUTHOR(S), (YEAR), YOUR SOFTWARE TITLE (vNUMBER) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_YOURPAGE.wasp/
> #Source of accompanying publication: Office for Research, Development, and Education
> #Technical description: Write here your technical program description (don't use hard returns!)
> par1 <- as.numeric(par1) #cut off periods
> 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
> par7 <- as.numeric(par7) #q
> 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     ma1
      0.0482  0.012  0.0481
s.e.     NaN    NaN     NaN

sigma^2 estimated as 4.312e-05:  log likelihood = 169.51,  aic = -331.03
Warning message:
In sqrt(diag(x$var.coef)) : NaNs produced
> (forecast <- predict(arima.out,fx))
$pred
Time Series:
Start = 49 
End = 60 
Frequency = 1 
 [1] 0.4032498 0.4030776 0.4030570 0.4030539 0.4030535 0.4030535 0.4030535
 [8] 0.4030535 0.4030535 0.4030535 0.4030535 0.4030535

$se
Time Series:
Start = 49 
End = 60 
Frequency = 1 
 [1] 0.006566888 0.009744437 0.012180658 0.014211641 0.015987535 0.017585091
 [7] 0.019049150 0.020408450 0.021682703 0.022886117 0.024029338 0.025120586

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 49 
End = 60 
Frequency = 1 
 [1] 0.3903787 0.3839785 0.3791829 0.3751991 0.3717180 0.3685867 0.3657171
 [8] 0.3630529 0.3605554 0.3581967 0.3559560 0.3538171
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 49 
End = 60 
Frequency = 1 
 [1] 0.4161209 0.4221767 0.4269311 0.4309087 0.4343891 0.4375203 0.4403898
 [8] 0.4430540 0.4455516 0.4479103 0.4501510 0.4522898
> 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$pred))
 [1] 29.59000 30.70000 30.52000 32.67000 33.19000 37.13000 35.54000 37.75000
 [9] 41.84000 42.94000 49.14000 44.61000 40.22000 44.23000 45.85000 53.38000
[17] 53.26000 51.80000 55.30000 57.81000 63.96000 63.77000 59.15000 56.12000
[25] 57.42000 63.52000 61.71000 63.01000 68.18000 72.03000 69.75000 74.41000
[33] 74.33000 64.24000 60.03000 59.44000 62.50000 55.04000 58.34000 61.92000
[41] 67.65000 67.68000 70.30000 75.26000 71.44000 76.36000 81.71000 92.60000
[49] 93.78404 93.98460 94.00863 94.01220 94.01266 94.01272 94.01273 94.01273
[57] 94.01273 94.01273 94.01273 94.01273
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 49 
End = 60 
Frequency = 1 
 [1] 0.08984139 0.14015423 0.18215675 0.21967464 0.25449371 0.28753156
 [7] 0.31932324 0.35021029 0.38042607 0.41013839 0.43947279 0.46852620
> postscript(file="/var/www/html/rcomp/tmp/1yqkq1229951135.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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.se <- array(0, dim=fx)
> perf.mse <- 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$pred[i]
+ perf.mape[i] = perf.mape[i] + abs(perf.pe[i])
+ perf.se[i] = (x[nx+i] - forecast$pred[i])^2
+ perf.mse[i] = perf.mse[i] + perf.se[i]
+ 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 = perf.mape / fx
> perf.mse = perf.mse / fx
> perf.rmse = sqrt(perf.mse)
> postscript(file="/var/www/html/rcomp/tmp/25vuc1229951135.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[1:12] <- 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/3uzcc1229951135.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.mape[i],4))
+ a<-table.element(a,round(perf.se[i],4))
+ a<-table.element(a,round(perf.mse[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/4fckz1229951135.tab") 
> 
> system("convert tmp/1yqkq1229951135.ps tmp/1yqkq1229951135.png")
> system("convert tmp/25vuc1229951135.ps tmp/25vuc1229951135.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.602   0.326   0.765