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(15.89,16.93,20.28,22.52,23.51,22.59,23.51,24.76,26.08,25.29,23.38,25.29,28.42,31.85,30.1,25.45,24.95,26.84,27.52,27.94,25.23,26.53,27.21,28.53,30.35,31.21,32.86,33.2,35.73,34.53,36.54,40.1,40.56,46.14,42.85,38.22,40.18,42.19,47.56,47.26,44.03,49.83,53.35,58.9,59.64,56.99,53.2,53.24,57.85,55.69,55.64,62.52,64.4,64.65,67.71,67.21,59.37,53.26,52.42,55.03)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '1'
> par7 = '0'
> par6 = '2'
> par5 = '12'
> par4 = '0'
> par3 = '1'
> par2 = '0.1'
> 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     sar1    sma1
      0.1010  -0.4964  -0.0666  0.4966  0.9032  -0.1497  -0.9960  0.9538
s.e.  0.6747   0.1993   0.4001  0.6765  0.4852   0.6739   0.0766  0.4413

sigma^2 estimated as 4.624e-05:  log likelihood = 105.66,  aic = -193.32
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1] 1.463517 1.468405 1.457150 1.453422 1.458011 1.462138 1.455186 1.447200
 [9] 1.444431 1.448664 1.447216 1.443761 1.437955 1.439491 1.443226 1.442262
[17] 1.440503 1.439496 1.445649 1.451798 1.454550 1.451281 1.452942 1.455935
[25] 1.461502 1.460158 1.456594 1.457492

$se
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1] 0.007460768 0.013927264 0.020305301 0.023299662 0.025097560 0.027179180
 [7] 0.029637917 0.031787139 0.033535316 0.035191302 0.036895317 0.038557826
[13] 0.039801130 0.040824043 0.041721002 0.042738181 0.043806890 0.044822389
[19] 0.045778803 0.046729583 0.047682899 0.048614464 0.049516866 0.050403456
[25] 0.051501231 0.052710572 0.053980884 0.055122085

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1] 1.448894 1.441107 1.417352 1.407755 1.408819 1.408867 1.397096 1.384897
 [9] 1.378701 1.379689 1.374901 1.368188 1.359944 1.359476 1.361452 1.358495
[17] 1.354642 1.351644 1.355923 1.360208 1.361092 1.355996 1.355889 1.357145
[25] 1.360560 1.356845 1.350791 1.349453
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1] 1.478140 1.495702 1.496949 1.499089 1.507202 1.515409 1.513276 1.509502
 [9] 1.510160 1.517639 1.519530 1.519334 1.515965 1.519506 1.524999 1.526029
[17] 1.526365 1.527348 1.535376 1.543388 1.548009 1.546565 1.549995 1.554726
[25] 1.562444 1.563470 1.562397 1.565531
> 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$pred))
 [1] 15.89000 16.93000 20.28000 22.52000 23.51000 22.59000 23.51000 24.76000
 [9] 26.08000 25.29000 23.38000 25.29000 28.42000 31.85000 30.10000 25.45000
[17] 24.95000 26.84000 27.52000 27.94000 25.23000 26.53000 27.21000 28.53000
[25] 30.35000 31.21000 32.86000 33.20000 35.73000 34.53000 36.54000 40.10000
[33] 45.07925 46.60767 43.15626 42.06469 43.41173 44.65634 42.57796 40.29807
[41] 39.53362 40.70776 40.30252 39.35078 37.79651 38.20228 39.20505 38.94402
[49] 38.47184 38.20368 39.86848 41.59709 42.39235 41.44898 41.92604 42.79778
[57] 44.46255 44.05520 42.99175 43.25753
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1] 0.05333265 0.10318694 0.15778531 0.18498313 0.20076579 0.21952135
 [7] 0.24443833 0.26747005 0.28596672 0.30216217 0.32061330 0.33961091
[13] 0.35512920 0.36614866 0.37510847 0.38707958 0.40009638 0.41240758
[19] 0.42146395 0.43045678 0.44081819 0.45342892 0.46380770 0.47349431
[25] 0.48473279 0.50054421 0.51845492 0.53283276
> postscript(file="/var/www/html/rcomp/tmp/1lxo81260483838.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2annz1260483838.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/3v2ic1260483839.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/42byj1260483839.tab") 
> 
> system("convert tmp/1lxo81260483838.ps tmp/1lxo81260483838.png")
> system("convert tmp/2annz1260483838.ps tmp/2annz1260483838.png")
> 
> 
> proc.time()
   user  system elapsed 
  1.514   0.324   1.625