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(8.3,8.2,8,7.9,7.6,7.6,8.3,8.4,8.4,8.4,8.4,8.6,8.9,8.8,8.3,7.5,7.2,7.4,8.8,9.3,9.3,8.7,8.2,8.3,8.5,8.6,8.5,8.2,8.1,7.9,8.6,8.7,8.7,8.5,8.4,8.5,8.7,8.7,8.6,8.5,8.3,8,8.2,8.1,8.1,8,7.9,7.9,8,8,7.9,8,7.7,7.2,7.5,7.3,7,7,7,7.2,7.3,7.1,6.8,6.4,6.1,6.5,7.7,7.9,7.5,6.9,6.6,6.9)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '0'
> par7 = '0'
> par6 = '3'
> par5 = '12'
> par4 = '1'
> par3 = '2'
> par2 = '1'
> 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     sma1
      0.5113  0.0998  -0.6649  -1.3778  -0.1643  0.5845  -0.3953
s.e.  0.3650  0.4482   0.3064   0.4223   0.7801  0.3991   0.4451

sigma^2 estimated as 0.02485:  log likelihood = 4.06,  aic = 7.88
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 45 
End = 72 
Frequency = 1 
 [1] 8.211411 8.416758 8.664682 8.954856 8.960241 8.576160 8.068814 7.737034
 [9] 7.692941 7.767653 8.450946 8.492111 8.383965 8.149359 8.044400 8.244032
[17] 8.448226 8.379195 8.100799 7.773179 7.532438 7.342634 7.856117 7.902623
[25] 7.943947 7.887022 7.872106 8.023967

$se
Time Series:
Start = 45 
End = 72 
Frequency = 1 
 [1] 0.1613699 0.2491706 0.2844492 0.2847362 0.2927165 0.3032018 0.3031073
 [8] 0.3171446 0.3578150 0.3956854 0.4131622 0.4161638 0.4319482 0.4570102
[15] 0.4887330 0.5133611 0.5320466 0.5460230 0.5625591 0.5856260 0.6184086
[22] 0.6570662 0.6962198 0.7311902 0.7963556 0.8636010 0.9199369 0.9569999

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 45 
End = 72 
Frequency = 1 
 [1] 7.895126 7.928384 8.107161 8.396773 8.386516 7.981884 7.474724 7.115431
 [9] 6.991623 6.992109 7.641148 7.676430 7.537346 7.253619 7.086483 7.237845
[17] 7.405415 7.308989 6.998184 6.625352 6.320357 6.054784 6.491526 6.469491
[25] 6.383090 6.194364 6.069030 6.148247
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 45 
End = 72 
Frequency = 1 
 [1] 8.527696 8.905133 9.222202 9.512939 9.533965 9.170436 8.662904 8.358638
 [9] 8.394258 8.543196 9.260744 9.307792 9.230583 9.045099 9.002317 9.250220
[17] 9.491037 9.449400 9.203415 8.921006 8.744518 8.630483 9.220707 9.335756
[25] 9.504804 9.579680 9.675182 9.899687
> 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$pred))
 [1] 8.300000 8.200000 8.000000 7.900000 7.600000 7.600000 8.300000 8.400000
 [9] 8.400000 8.400000 8.400000 8.600000 8.900000 8.800000 8.300000 7.500000
[17] 7.200000 7.400000 8.800000 9.300000 9.300000 8.700000 8.200000 8.300000
[25] 8.500000 8.600000 8.500000 8.200000 8.100000 7.900000 8.600000 8.700000
[33] 8.700000 8.500000 8.400000 8.500000 8.700000 8.700000 8.600000 8.500000
[41] 8.300000 8.000000 8.200000 8.100000 8.211411 8.416758 8.664682 8.954856
[49] 8.960241 8.576160 8.068814 7.737034 7.692941 7.767653 8.450946 8.492111
[57] 8.383965 8.149359 8.044400 8.244032 8.448226 8.379195 8.100799 7.773179
[65] 7.532438 7.342634 7.856117 7.902623 7.943947 7.887022 7.872106 8.023967
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 45 
End = 72 
Frequency = 1 
 [1] 0.01965191 0.02960411 0.03282858 0.03179685 0.03266838 0.03535403
 [7] 0.03756529 0.04099047 0.04651212 0.05094014 0.04888946 0.04900593
[13] 0.05152075 0.05607928 0.06075444 0.06227063 0.06297731 0.06516414
[19] 0.06944488 0.07533932 0.08209940 0.08948644 0.08862136 0.09252499
[25] 0.10024683 0.10949646 0.11686033 0.11926768
> postscript(file="/var/www/html/rcomp/tmp/1gies1260475681.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2pcke1260475681.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/3sawt1260475681.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/47gys1260475681.tab") 
> system("convert tmp/1gies1260475681.ps tmp/1gies1260475681.png")
> system("convert tmp/2pcke1260475681.ps tmp/2pcke1260475681.png")
> 
> 
> proc.time()
   user  system elapsed 
  1.988   0.352   2.165