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(8.4,8.4,8.4,8.6,8.9,8.8,8.3,7.5,7.2,7.4,8.8,9.3,9.3,8.7,8.2,8.3,8.5,8.6,8.5,8.2,8.1,7.9,8.6,8.7,8.7,8.5,8.4,8.5,8.7,8.7,8.6,8.5,8.3,8,8.2,8.1,8.1,8,7.9,7.9,8,8,7.9,8,7.7,7.2,7.5,7.3,7,7,7,7.2,7.3,7.1,6.8,6.4,6.1,6.5,7.7,7.9,7.5,6.9)
> 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
      0.7791  -0.5704  -0.0985  -0.7136  0.3854  -0.6718
s.e.  0.2518   0.2623   0.2173   0.2202  0.2382   0.3139

sigma^2 estimated as 0.04611:  log likelihood = 1.4,  aic = 11.21
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 35 
End = 62 
Frequency = 1 
 [1] 8.008810 8.163254 8.494279 8.663224 8.590824 8.405436 8.285646 8.305191
 [9] 8.407011 8.486996 8.489312 8.435462 8.384304 8.374933 8.402117 8.433683
[17] 8.443694 8.430811 8.411954 8.403623 8.409158 8.420080 8.426253 8.424288
[25] 8.418159 8.413897 8.414266 8.417588

$se
Time Series:
Start = 35 
End = 62 
Frequency = 1 
 [1] 0.2178433 0.3228162 0.3880526 0.3882770 0.4049849 0.4201961 0.4202089
 [8] 0.4274412 0.4369370 0.4384676 0.4385278 0.4395056 0.4393723 0.4399978
[15] 0.4416543 0.4423997 0.4422668 0.4420452 0.4418455 0.4418764 0.4422071
[22] 0.4424769 0.4424955 0.4423812 0.4422667 0.4422369 0.4423080 0.4423989

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 35 
End = 62 
Frequency = 1 
 [1] 7.581837 7.530534 7.733696 7.902201 7.797053 7.581852 7.462037 7.467406
 [9] 7.550614 7.627600 7.629798 7.574031 7.523135 7.512538 7.536475 7.566579
[17] 7.576851 7.564403 7.545936 7.537545 7.542432 7.552825 7.558962 7.557221
[25] 7.551317 7.547113 7.547342 7.550486
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 35 
End = 62 
Frequency = 1 
 [1] 8.435783 8.795974 9.254862 9.424247 9.384594 9.229020 9.109256 9.142976
 [9] 9.263407 9.346393 9.348827 9.296893 9.245474 9.237329 9.267760 9.300786
[17] 9.310537 9.297220 9.277971 9.269701 9.275884 9.287334 9.293544 9.291355
[25] 9.285002 9.280681 9.281189 9.284690
> 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$pred))
 [1] 8.400000 8.400000 8.400000 8.600000 8.900000 8.800000 8.300000 7.500000
 [9] 7.200000 7.400000 8.800000 9.300000 9.300000 8.700000 8.200000 8.300000
[17] 8.500000 8.600000 8.500000 8.200000 8.100000 7.900000 8.600000 8.700000
[25] 8.700000 8.500000 8.400000 8.500000 8.700000 8.700000 8.600000 8.500000
[33] 8.300000 8.000000 8.008810 8.163254 8.494279 8.663224 8.590824 8.405436
[41] 8.285646 8.305191 8.407011 8.486996 8.489312 8.435462 8.384304 8.374933
[49] 8.402117 8.433683 8.443694 8.430811 8.411954 8.403623 8.409158 8.420080
[57] 8.426253 8.424288 8.418159 8.413897 8.414266 8.417588
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 35 
End = 62 
Frequency = 1 
 [1] 0.02720046 0.03954504 0.04568399 0.04481900 0.04714157 0.04999099
 [7] 0.05071528 0.05146675 0.05197293 0.05166346 0.05165646 0.05210214
[13] 0.05240415 0.05253747 0.05256464 0.05245629 0.05237836 0.05243211
[19] 0.05252591 0.05258165 0.05258638 0.05255020 0.05251391 0.05251259
[25] 0.05253723 0.05256029 0.05256644 0.05255649
> postscript(file="/var/www/html/rcomp/tmp/1rmv61260564504.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2ua8q1260564504.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/3kniy1260564504.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/42epj1260564504.tab") 
> system("convert tmp/1rmv61260564504.ps tmp/1rmv61260564504.png")
> system("convert tmp/2ua8q1260564504.ps tmp/2ua8q1260564504.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.739   0.334   0.881