R version 2.8.0 (2008-10-20)
Copyright (C) 2008 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> x <- c(98.5,97.0,103.3,99.6,100.1,102.9,95.9,94.5,107.4,116.0,102.8,99.8,109.6,103.0,111.6,106.3,97.9,108.8,103.9,101.2,122.9,123.9,111.7,120.9,99.6,103.3,119.4,106.5,101.9,124.6,106.5,107.8,127.4,120.1,118.5,127.7,107.7,104.5,118.8,110.3,109.6,119.1,96.5,106.7,126.3,116.2,118.8,115.2,110.0,111.4,129.6,108.1,117.8,122.9,100.6,111.8,127.0,128.6,124.8,118.5,114.7,112.6,128.7,111.0,115.8,126.0,111.1,113.2,120.1,130.6,124.0,119.4,116.7,116.5,119.6,126.5,111.3,123.5,114.2,103.7,129.5)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '2'
> par7 = '1'
> par6 = '3'
> par5 = '1'
> par4 = '1'
> par3 = '0'
> par2 = '1'
> 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      ma1    sar1     sar2     sma1
      -0.753  -0.5792  0.173  -0.3854  0.9292  -0.6228  -0.3854
s.e.     NaN      NaN    NaN      NaN  0.1660   0.0864      NaN

sigma^2 estimated as 50.16:  log likelihood = -230.72,  aic = 477.44
Warning message:
In sqrt(diag(x$var.coef)) : NaNs produced
> (forecast <- predict(arima.out,fx))
$pred
Time Series:
Start = 70 
End = 81 
Frequency = 1 
 [1] 112.5178 116.8602 120.4035 113.6389 116.4164 118.0798 113.9601 116.9808
 [9] 117.8075 114.8704 116.9966 117.0275

$se
Time Series:
Start = 70 
End = 81 
Frequency = 1 
 [1] 7.082630 7.642459 7.651710 8.176477 8.185023 8.198433 9.025197 9.175131
 [9] 9.266794 9.676061 9.727148 9.815282

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 70 
End = 81 
Frequency = 1 
 [1]  98.63586 101.88103 105.40617  97.61305 100.37379 102.01089  96.27074
 [8]  98.99750  99.64460  95.90530  97.93142  97.78957
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 70 
End = 81 
Frequency = 1 
 [1] 126.3998 131.8395 135.4009 129.6648 132.4591 134.1488 131.6495 134.9640
 [9] 135.9704 133.8355 136.0618 136.2655
> 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$pred))
 [1]  98.5000  97.0000 103.3000  99.6000 100.1000 102.9000  95.9000  94.5000
 [9] 107.4000 116.0000 102.8000  99.8000 109.6000 103.0000 111.6000 106.3000
[17]  97.9000 108.8000 103.9000 101.2000 122.9000 123.9000 111.7000 120.9000
[25]  99.6000 103.3000 119.4000 106.5000 101.9000 124.6000 106.5000 107.8000
[33] 127.4000 120.1000 118.5000 127.7000 107.7000 104.5000 118.8000 110.3000
[41] 109.6000 119.1000  96.5000 106.7000 126.3000 116.2000 118.8000 115.2000
[49] 110.0000 111.4000 129.6000 108.1000 117.8000 122.9000 100.6000 111.8000
[57] 127.0000 128.6000 124.8000 118.5000 114.7000 112.6000 128.7000 111.0000
[65] 115.8000 126.0000 111.1000 113.2000 120.1000 112.5178 116.8602 120.4035
[73] 113.6389 116.4164 118.0798 113.9601 116.9808 117.8075 114.8704 116.9966
[81] 117.0275
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 70 
End = 81 
Frequency = 1 
 [1] 0.06294674 0.06539828 0.06355055 0.07195136 0.07030814 0.06943128
 [7] 0.07919610 0.07843282 0.07866047 0.08423460 0.08314041 0.08387157
> postscript(file="/var/www/html/rcomp/tmp/1dd531229524356.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2m25o1229524356.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 
> 
> #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/3thxt1229524356.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/4down1229524357.tab") 
> 
> system("convert tmp/1dd531229524356.ps tmp/1dd531229524356.png")
> system("convert tmp/2m25o1229524356.ps tmp/2m25o1229524356.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.651   0.319   1.162