R version 2.6.0 (2007-10-03)
Copyright (C) 2007 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> x <- c(7.4,7.2,7,6.6,6.4,6.4,6.8,7.3,7,7,6.7,6.7,6.3,6.2,6,6.3,6.2,6.1,6.2,6.6,6.6,7.8,7.4,7.4,7.5,7.4,7.4,7,6.9,6.9,7.6,7.7,7.6,8.2,8,8.1,8.3,8.2,8.1,7.7,7.6,7.7,8.2,8.4,8.4,8.6,8.4,8.5,8.7,8.7,8.6,7.4,7.3,7.4,9,9.2,9.2,8.5,8.3,8.3,8.6,8.6,8.5,8.1,8.1,8,8.6,8.7,8.7,8.6,8.4,8.4,8.7,8.7,8.5,8.3,8.3,8.3,8.1,8.2,8.1,8.1,7.9,7.7,8.1,8,7.7,7.8,7.6,7.4,7.7,7.9,7.6)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '2'
> par7 = '0'
> par6 = '3'
> par5 = '12'
> par4 = '0'
> par3 = '1'
> par2 = '0.0'
> par1 = '12'
> #'GNU S' R Code compiled by R2WASP v. 1.0.44 ()
> #Author: Prof. Dr. P. Wessa
> #To cite this work: AUTHOR(S), (YEAR), YOUR SOFTWARE TITLE (vNUMBER) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_YOURPAGE.wasp/
> #Source of accompanying publication: Office for Research, Development, and Education
> #Technical description: Write here your technical program description (don't use hard returns!)
> par1 <- as.numeric(par1) #cut off periods
> 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
> par7 <- as.numeric(par7) #q
> 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     sar1    sar2    sma1
      0.0278  0.0152  -0.4170  -0.4445  0.5531  0.9762
s.e.  0.1014  0.1008   0.1053   0.0935  0.0916  0.1517

sigma^2 estimated as 0.001152:  log likelihood = 151.05,  aic = -288.11
Warning messages:
1: In log(s2) : NaNs produced
2: In log(s2) : NaNs produced
> (forecast <- predict(arima.out,fx))
$pred
Time Series:
Start = 82 
End = 93 
Frequency = 1 
 [1] 2.098485 2.084713 2.087654 2.083154 2.083961 2.067853 2.088771 2.091325
 [9] 2.088315 2.050733 2.058447 2.057410

$se
Time Series:
Start = 82 
End = 93 
Frequency = 1 
 [1] 0.03510371 0.05032774 0.06224328 0.06602516 0.06933321 0.07235245
 [7] 0.07713098 0.08178798 0.08629067 0.08984085 0.09319278 0.09638360

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 82 
End = 93 
Frequency = 1 
 [1] 2.029682 1.986070 1.965657 1.953744 1.948067 1.926043 1.937594 1.931020
 [9] 1.919185 1.874644 1.875789 1.868498
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 82 
End = 93 
Frequency = 1 
 [1] 2.167288 2.183355 2.209651 2.212563 2.219854 2.209664 2.239948 2.251629
 [9] 2.257445 2.226821 2.241105 2.246322
> 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)
+ }
> (actandfor <- c(x[1:nx], forecast$pred))
 [1] 7.400000 7.200000 7.000000 6.600000 6.400000 6.400000 6.800000 7.300000
 [9] 7.000000 7.000000 6.700000 6.700000 6.300000 6.200000 6.000000 6.300000
[17] 6.200000 6.100000 6.200000 6.600000 6.600000 7.800000 7.400000 7.400000
[25] 7.500000 7.400000 7.400000 7.000000 6.900000 6.900000 7.600000 7.700000
[33] 7.600000 8.200000 8.000000 8.100000 8.300000 8.200000 8.100000 7.700000
[41] 7.600000 7.700000 8.200000 8.400000 8.400000 8.600000 8.400000 8.500000
[49] 8.700000 8.700000 8.600000 7.400000 7.300000 7.400000 9.000000 9.200000
[57] 9.200000 8.500000 8.300000 8.300000 8.600000 8.600000 8.500000 8.100000
[65] 8.100000 8.000000 8.600000 8.700000 8.700000 8.600000 8.400000 8.400000
[73] 8.700000 8.700000 8.500000 8.300000 8.300000 8.300000 8.100000 8.200000
[81] 8.100000 8.153809 8.042281 8.065970 8.029753 8.036234 7.907830 8.074984
[89] 8.095633 8.071304 7.773593 7.833794 7.825676
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 82 
End = 93 
Frequency = 1 
 [1] 0.03633951 0.05289363 0.06619925 0.07048771 0.07426500 0.07773399
 [7] 0.08326643 0.08870826 0.09401722 0.09823627 0.10224674 0.10608901
> postscript(file="/var/www/html/rcomp/tmp/137gx1197120941.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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.se <- array(0, dim=fx)
> perf.mse <- 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$pred[i]
+ perf.mape[i] = perf.mape[i] + abs(perf.pe[i])
+ perf.se[i] = (x[nx+i] - forecast$pred[i])^2
+ perf.mse[i] = perf.mse[i] + perf.se[i]
+ 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 = perf.mape / fx
> perf.mse = perf.mse / fx
> perf.rmse = sqrt(perf.mse)
> postscript(file="/var/www/html/rcomp/tmp/2516q1197120942.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[1:12] <- x[(nx+1):lx]
> lines(dum, lty=1)
> lines(ub,lty=3)
> lines(lb,lty=3)
> dev.off()
null device 
          1 
> 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/31oy61197120942.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.mape[i],4))
+ a<-table.element(a,round(perf.se[i],4))
+ a<-table.element(a,round(perf.mse[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/44jj51197120942.tab") 
> 
> system("convert tmp/137gx1197120941.ps tmp/137gx1197120941.png")
> system("convert tmp/2516q1197120942.ps tmp/2516q1197120942.png")
> 
> 
> proc.time()
   user  system elapsed 
  3.375   0.717   3.924