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 = '1'
> par7 = '0'
> par6 = '3'
> par5 = '12'
> par4 = '0'
> par3 = '1'
> 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    sar1    sma1
      0.4225  0.3471  -0.8938  -0.2095  -0.8393  0.2098  0.4653  0.9988
s.e.  0.3624  0.4982   0.3553   0.4032   0.4629  0.2343  0.1449  0.7258

sigma^2 estimated as 0.01652:  log likelihood = 12.86,  aic = -7.72
Warning message:
In arima(x[1:nx], order = c(par6, par3, par7), seasonal = list(order = c(par8,  :
  possible convergence problem: optim gave code=1
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 45 
End = 72 
Frequency = 1 
 [1] 8.227891 8.468022 8.676379 8.695904 8.806421 8.664176 8.476917 8.308317
 [9] 8.134049 8.067055 8.270988 8.252956 8.369745 8.495176 8.569676 8.522833
[17] 8.530581 8.446595 8.386779 8.352729 8.315798 8.294280 8.368885 8.315815
[25] 8.335609 8.381990 8.439538 8.454132

$se
Time Series:
Start = 45 
End = 72 
Frequency = 1 
 [1] 0.1450493 0.2266137 0.2538889 0.2520758 0.2637017 0.2845879 0.2898513
 [8] 0.2919345 0.3123460 0.3376571 0.3477808 0.3474203 0.3679671 0.3951026
[15] 0.4108590 0.4129782 0.4131593 0.4148446 0.4147685 0.4175913 0.4300892
[22] 0.4459412 0.4555020 0.4573075 0.4645022 0.4720597 0.4779237 0.4808341

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 45 
End = 72 
Frequency = 1 
 [1] 7.943594 8.023859 8.178756 8.201836 8.289566 8.106384 7.908808 7.736126
 [9] 7.521851 7.405248 7.589338 7.572012 7.648529 7.720775 7.764392 7.713395
[17] 7.720789 7.633499 7.573833 7.534250 7.472823 7.420235 7.476101 7.419492
[25] 7.425185 7.456753 7.502808 7.511697
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 45 
End = 72 
Frequency = 1 
 [1] 8.512187 8.912184 9.174001 9.189973 9.323276 9.221968 9.045026 8.880509
 [9] 8.746247 8.728863 8.952638 8.933899 9.090960 9.269577 9.374960 9.332270
[17] 9.340373 9.259690 9.199725 9.171208 9.158772 9.168324 9.261669 9.212137
[25] 9.246033 9.307227 9.376269 9.396566
> 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$pred))
 [1] 8.300000 8.200000 8.000000 7.900000 7.600000 7.600000 8.300000 8.400000
 [9] 8.400000 8.400000 8.400000 8.600000 8.900000 8.800000 8.300000 7.500000
[17] 7.200000 7.400000 8.800000 9.300000 9.300000 8.700000 8.200000 8.300000
[25] 8.500000 8.600000 8.500000 8.200000 8.100000 7.900000 8.600000 8.700000
[33] 8.700000 8.500000 8.400000 8.500000 8.700000 8.700000 8.600000 8.500000
[41] 8.300000 8.000000 8.200000 8.100000 8.227891 8.468022 8.676379 8.695904
[49] 8.806421 8.664176 8.476917 8.308317 8.134049 8.067055 8.270988 8.252956
[57] 8.369745 8.495176 8.569676 8.522833 8.530581 8.446595 8.386779 8.352729
[65] 8.315798 8.294280 8.368885 8.315815 8.335609 8.381990 8.439538 8.454132
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 45 
End = 72 
Frequency = 1 
 [1] 0.01762897 0.02676112 0.02926208 0.02898788 0.02994425 0.03284650
 [7] 0.03419301 0.03513763 0.03839981 0.04185630 0.04204827 0.04209647
[13] 0.04396396 0.04650906 0.04794335 0.04845551 0.04843272 0.04911383
[19] 0.04945504 0.04999460 0.05171954 0.05376491 0.05442804 0.05499250
[25] 0.05572505 0.05631833 0.05662913 0.05687563
> postscript(file="/var/www/html/rcomp/tmp/13h0b1260559279.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2om3f1260559279.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/30y1f1260559279.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/4psk61260559279.tab") 
> 
> system("convert tmp/13h0b1260559279.ps tmp/13h0b1260559279.png")
> system("convert tmp/2om3f1260559279.ps tmp/2om3f1260559279.png")
> 
> 
> proc.time()
   user  system elapsed 
  1.873   0.318   1.978