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(14.2,13.5,11.9,14.6,15.6,14.1,14.9,14.2,14.6,17.2,15.4,14.3,17.5,14.5,14.4,16.6,16.7,16.6,16.9,15.7,16.4,18.4,16.9,16.5,18.3,15.1,15.7,18.1,16.8,18.9,19,18.1,17.8,21.5,17.1,18.7,19,16.4,16.9,18.6,19.3,19.4,17.6,18.6,18.1,20.4,18.1,19.6,19.9,19.2,17.8,19.2,22,21.1,19.5,22.2,20.9,22.2,23.5,21.5,24.3,22.8,20.3,23.7,23.3,19.6,18,17.3,16.8,18.2,16.5,16,18.4)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '0'
> par6 = '0'
> par5 = '12'
> par4 = '0'
> 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
      -1.1112  -1.0026  -0.0149  0.5769  0.2433  -0.6280
s.e.   0.2512   0.2698   0.2508  0.2103  0.2151   0.1855

sigma^2 estimated as 1.21:  log likelihood = -69.45,  aic = 152.89
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 46 
End = 73 
Frequency = 1 
 [1] 18.20677 17.56429 18.91196 18.05695 17.66545 18.93768 17.92918 17.78015
 [9] 18.93795 17.81578 17.90418 18.91381 17.71995 18.03304 18.86706 17.64413
[17] 18.16224 18.80020 17.59001 18.28749 18.71627 17.55851 18.40477 18.61877
[25] 17.54974 18.51054 18.51149 17.56304

$se
Time Series:
Start = 46 
End = 73 
Frequency = 1 
 [1] 1.122595 1.226941 1.265615 1.343303 1.429746 1.462731 1.535721 1.606580
 [9] 1.636440 1.706266 1.765385 1.793613 1.860850 1.910738 1.938319 2.003085
[17] 2.045573 2.073200 2.135380 2.171900 2.200076 2.259446 2.291169 2.320255
[25] 2.376561 2.404468 2.434706 2.487713

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 46 
End = 73 
Frequency = 1 
 [1] 16.00648 15.15949 16.43136 15.42408 14.86315 16.07073 14.91916 14.63125
 [9] 15.73053 14.47150 14.44403 15.39833 14.07268 14.28799 15.06796 13.71808
[17] 14.15292 14.73673 13.40467 14.03056 14.40412 13.13000 13.91408 14.07107
[25] 12.89168 13.79778 13.73947 12.68712
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 46 
End = 73 
Frequency = 1 
 [1] 20.40706 19.96910 21.39257 20.68982 20.46776 21.80463 20.93919 20.92905
 [9] 22.14537 21.16007 21.36433 22.42929 21.36721 21.77808 22.66617 21.57017
[17] 22.17156 22.86367 21.77536 22.54441 23.02842 21.98703 22.89547 23.16647
[25] 22.20780 23.22329 23.28352 22.43896
> 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$pred))
 [1] 14.20000 13.50000 11.90000 14.60000 15.60000 14.10000 14.90000 14.20000
 [9] 14.60000 17.20000 15.40000 14.30000 17.50000 14.50000 14.40000 16.60000
[17] 16.70000 16.60000 16.90000 15.70000 16.40000 18.40000 16.90000 16.50000
[25] 18.30000 15.10000 15.70000 18.10000 16.80000 18.90000 19.00000 18.10000
[33] 17.80000 21.50000 17.10000 18.70000 19.00000 16.40000 16.90000 18.60000
[41] 19.30000 19.40000 17.60000 18.60000 18.10000 18.20677 17.56429 18.91196
[49] 18.05695 17.66545 18.93768 17.92918 17.78015 18.93795 17.81578 17.90418
[57] 18.91381 17.71995 18.03304 18.86706 17.64413 18.16224 18.80020 17.59001
[65] 18.28749 18.71627 17.55851 18.40477 18.61877 17.54974 18.51054 18.51149
[73] 17.56304
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 46 
End = 73 
Frequency = 1 
 [1] 0.06165812 0.06985426 0.06692142 0.07439256 0.08093456 0.07723917
 [7] 0.08565484 0.09035806 0.08641063 0.09577271 0.09860182 0.09483087
[13] 0.10501442 0.10595765 0.10273562 0.11352701 0.11262777 0.11027545
[19] 0.12139727 0.11876427 0.11754885 0.12868094 0.12448777 0.12461913
[25] 0.13541860 0.12989725 0.13152403 0.14164479
> postscript(file="/var/www/html/rcomp/tmp/1upog1260470305.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2zg851260470305.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/36gsz1260470305.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/4jzhw1260470305.tab") 
> 
> system("convert tmp/1upog1260470305.ps tmp/1upog1260470305.png")
> system("convert tmp/2zg851260470305.ps tmp/2zg851260470305.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.746   0.324   0.867