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(6.9,6.8,6.7,6.6,6.5,6.5,7.0,7.5,7.6,7.6,7.6,7.8,8.0,8.0,8.0,7.9,7.9,8.0,8.5,9.2,9.4,9.5,9.5,9.6,9.7,9.7,9.6,9.5,9.4,9.3,9.6,10.2,10.2,10.1,9.9,9.8,9.8,9.7,9.5,9.3,9.1,9.0,9.5,10.0,10.2,10.1,10.0,9.9,10.0,9.9,9.7,9.5,9.2,9.0,9.3,9.8,9.8,9.6,9.4,9.3,9.2,9.2,9.0,8.8,8.7,8.7,9.1,9.7,9.8,9.6,9.4,9.4,9.5,9.4,9.3,9.2,9.0,8.9,9.2,9.8,9.9,9.6,9.2,9.1,9.1,9.0,8.9,8.7,8.5,8.3,8.5,8.7,8.4,8.1,7.8,7.7,7.5,7.2,6.8,6.7,6.4,6.3,6.8,7.3,7.1,7.0,6.8,6.6,6.3,6.1,6.1,6.3,6.3,6.0,6.2,6.4,6.8,7.5,7.5,7.6,7.6,7.4,7.3,7.1,6.9,6.8,7.5,7.6,7.8,8.0,8.1,8.2,8.3,8.2,8.0,7.9,7.6,7.6,8.3,8.4,8.4,8.4,8.4,8.6,8.9,8.8,8.3,7.5,7.2,7.4,8.8,9.3,9.3,8.7,8.2,8.3,8.5,8.6,8.5,8.2,8.1,7.9,8.6,8.7,8.7,8.5,8.4,8.5,8.7,8.7,8.6,8.5,8.3,8.0,8.2,8.1,8.1,8.0,7.9,7.9)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '0'
> par6 = '0'
> par5 = '12'
> par4 = '0'
> par3 = '1'
> par2 = '1'
> par1 = '12'
> #'GNU S' R Code compiled by R2WASP v. 1.0.44 ()
> #Author: Prof. Dr. P. Wessa
> #To cite this work: Wessa P., (2009), ARIMA Forecasting (v1.0.5) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_arimaforecasting.wasp/
> #Source of accompanying publication: 
> #Technical description: 
> 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")


sigma^2 estimated as 0.08132:  log likelihood = -27.43,  aic = 56.86
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 169 
End = 180 
Frequency = 1 
 [1] 8.5 8.5 8.5 8.5 8.5 8.5 8.5 8.5 8.5 8.5 8.5 8.5

$se
Time Series:
Start = 169 
End = 180 
Frequency = 1 
 [1] 0.2851620 0.4032800 0.4939151 0.5703240 0.6376416 0.6985014 0.7544677
 [8] 0.8065599 0.8554860 0.9017614 0.9457754 0.9878301

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 169 
End = 180 
Frequency = 1 
 [1] 7.941082 7.709571 7.531926 7.382165 7.250222 7.130937 7.021243 6.919143
 [9] 6.823247 6.732548 6.646280 6.563853
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 169 
End = 180 
Frequency = 1 
 [1]  9.058918  9.290429  9.468074  9.617835  9.749778  9.869063  9.978757
 [8] 10.080857 10.176753 10.267452 10.353720 10.436147
> 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$pred))
  [1]  6.9  6.8  6.7  6.6  6.5  6.5  7.0  7.5  7.6  7.6  7.6  7.8  8.0  8.0  8.0
 [16]  7.9  7.9  8.0  8.5  9.2  9.4  9.5  9.5  9.6  9.7  9.7  9.6  9.5  9.4  9.3
 [31]  9.6 10.2 10.2 10.1  9.9  9.8  9.8  9.7  9.5  9.3  9.1  9.0  9.5 10.0 10.2
 [46] 10.1 10.0  9.9 10.0  9.9  9.7  9.5  9.2  9.0  9.3  9.8  9.8  9.6  9.4  9.3
 [61]  9.2  9.2  9.0  8.8  8.7  8.7  9.1  9.7  9.8  9.6  9.4  9.4  9.5  9.4  9.3
 [76]  9.2  9.0  8.9  9.2  9.8  9.9  9.6  9.2  9.1  9.1  9.0  8.9  8.7  8.5  8.3
 [91]  8.5  8.7  8.4  8.1  7.8  7.7  7.5  7.2  6.8  6.7  6.4  6.3  6.8  7.3  7.1
[106]  7.0  6.8  6.6  6.3  6.1  6.1  6.3  6.3  6.0  6.2  6.4  6.8  7.5  7.5  7.6
[121]  7.6  7.4  7.3  7.1  6.9  6.8  7.5  7.6  7.8  8.0  8.1  8.2  8.3  8.2  8.0
[136]  7.9  7.6  7.6  8.3  8.4  8.4  8.4  8.4  8.6  8.9  8.8  8.3  7.5  7.2  7.4
[151]  8.8  9.3  9.3  8.7  8.2  8.3  8.5  8.6  8.5  8.2  8.1  7.9  8.6  8.7  8.7
[166]  8.5  8.4  8.5  8.5  8.5  8.5  8.5  8.5  8.5  8.5  8.5  8.5  8.5  8.5  8.5
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 169 
End = 180 
Frequency = 1 
 [1] 0.03354847 0.04744470 0.05810766 0.06709694 0.07501666 0.08217663
 [7] 0.08876091 0.09488940 0.10064541 0.10608958 0.11126769 0.11621531
> postscript(file="/var/www/html/rcomp/tmp/1um911260645937.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/20szv1260645937.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/3cyoz1260645937.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/48oln1260645937.tab") 
> 
> try(system("convert tmp/1um911260645937.ps tmp/1um911260645937.png",intern=TRUE))
character(0)
> try(system("convert tmp/20szv1260645937.ps tmp/20szv1260645937.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  0.550   0.294   0.671