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(101.3,106.3,94,102.8,102,105.1,92.4,81.4,105.8,120.3,100.7,88.8,94.3,99.9,103.4,103.3,98.8,104.2,91.2,74.7,108.5,114.5,96.9,89.6,97.1,100.3,122.6,115.4,109,129.1,102.8,96.2,127.7,128.9,126.5,119.8,113.2,114.1,134.1,130,121.8,132.1,105.3,103,117.1,126.3,138.1,119.5,138,135.5,178.6,162.2,176.9,204.9,132.2,142.5,164.3,174.9,175.4,143)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '1'
> par6 = '3'
> par5 = '12'
> par4 = '0'
> par3 = '1'
> par2 = '-0.6'
> par1 = '12'
> 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
      0.1310  -0.2842  -0.3521  -0.7840  -0.1900  0.7672
s.e.  0.3579   0.2939   0.3329   0.3435   0.4282  0.3199

sigma^2 estimated as 1.197e-05:  log likelihood = 128.63,  aic = -243.26
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1] 0.05586030 0.05401598 0.05910892 0.06337031 0.06313059 0.06009486
 [7] 0.05826485 0.05897225 0.06065390 0.06131752 0.06067746 0.05981289
[13] 0.05964787 0.06009733 0.06050752 0.06049163 0.06021472 0.06003853
[19] 0.06009974 0.06025533 0.06032036 0.06026310 0.06018234 0.06016513
[25] 0.06020599 0.06024467 0.06024418 0.06021874

$se
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1] 0.003562828 0.003822439 0.003878210 0.004005430 0.004758192 0.005639583
 [7] 0.006002447 0.006130593 0.006258152 0.006520138 0.006877124 0.007181239
[13] 0.007391109 0.007565563 0.007760937 0.007989111 0.008219331 0.008424717
[19] 0.008608571 0.008788677 0.008975524 0.009165497 0.009349564 0.009524425
[25] 0.009693691 0.009861939 0.010030164 0.010196279

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1] 0.04887716 0.04652399 0.05150762 0.05551966 0.05380453 0.04904128
 [7] 0.04650005 0.04695629 0.04838792 0.04853804 0.04719829 0.04573767
[13] 0.04516130 0.04526882 0.04529608 0.04483297 0.04410483 0.04352608
[19] 0.04322694 0.04302953 0.04272833 0.04229873 0.04185719 0.04149726
[25] 0.04120636 0.04091527 0.04058506 0.04023404
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1] 0.06284345 0.06150796 0.06671021 0.07122095 0.07245664 0.07114844
 [7] 0.07002964 0.07098822 0.07291988 0.07409699 0.07415662 0.07388812
[13] 0.07413445 0.07492583 0.07571896 0.07615029 0.07632461 0.07655097
[19] 0.07697254 0.07748114 0.07791238 0.07822748 0.07850748 0.07883301
[25] 0.07920563 0.07957407 0.07990331 0.08020345
> 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$pred))
 [1] 101.3000 106.3000  94.0000 102.8000 102.0000 105.1000  92.4000  81.4000
 [9] 105.8000 120.3000 100.7000  88.8000  94.3000  99.9000 103.4000 103.3000
[17]  98.8000 104.2000  91.2000  74.7000 108.5000 114.5000  96.9000  89.6000
[25]  97.1000 100.3000 122.6000 115.4000 109.0000 129.1000 102.8000  96.2000
[33] 122.5071 129.5576 111.4923  99.2789  99.9080 108.4604 114.1972 111.9233
[41] 106.7994 104.8799 106.7303 109.3139 109.8184 108.4530 107.2304 107.2773
[49] 108.1008 108.6300 108.4457 107.9794 107.7855 107.9562 108.1978 108.2493
[57] 108.1269 108.0112 108.0127 108.0888
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1] 0.1271872 0.1441598 0.1315664 0.1258229 0.1557519 0.2057247 0.2328137
 [8] 0.2356728 0.2332946 0.2430030 0.2652910 0.2876901 0.3009901 0.3079539
[15] 0.3164524 0.3303652 0.3470405 0.3618526 0.3734333 0.3840456 0.3962043
[22] 0.4101414 0.4242877 0.4373842 0.4496453 0.4620937 0.4753008 0.4889690
> postscript(file="/var/www/html/rcomp/tmp/1y5so1260453608.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2x7ab1260453608.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/3gl2h1260453609.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/4d2521260453609.tab") 
> 
> system("convert tmp/1y5so1260453608.ps tmp/1y5so1260453608.png")
> system("convert tmp/2x7ab1260453608.ps tmp/2x7ab1260453608.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.723   0.319   1.729