R version 2.12.0 (2010-10-15)
Copyright (C) 2010 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: i486-pc-linux-gnu (32-bit)

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> x <- c(10.81,9.12,11.03,12.74,9.98,11.62,9.40,9.27,7.76,8.78,10.65,10.95,12.36,10.85,11.84,12.14,11.65,8.86,7.63,7.38,7.25,8.03,7.75,7.16,7.18,7.51,7.07,7.11,8.98,9.53,10.54,11.31,10.36,11.44,10.45,10.69,11.28,11.96,13.52,12.89,14.03,16.27,16.17,17.25,19.38,26.20,33.53,32.20,38.45,44.86,41.67,36.06,39.76,36.81,42.65,46.89,53.61,57.59,67.82,71.89,75.51,68.49,62.72,70.39,59.77,57.27,67.96,67.85,76.98,81.08,91.66,84.84,85.73,84.61,92.91,99.80,121.19,122.04,131.76,138.48,153.47,189.95,182.22,198.08,135.36,125.02,143.50,173.95,188.75,167.44,158.95,169.53,113.66,107.59,92.67,85.35,90.13,89.31,105.12,125.83,135.81,142.43,163.39,168.21,185.35,188.50,199.91,210.73,192.06,204.62,235.00,261.09,256.88,251.53,257.25,243.10,283.75)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '1'
> par6 = '1'
> par5 = '12'
> par4 = '0'
> par3 = '1'
> par2 = '-0.1'
> 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")

Coefficients:
         ar1      ma1
      0.7087  -0.5974
s.e.  0.4311   0.4927

sigma^2 estimated as 8.075e-05:  log likelihood = 342.47,  aic = -678.93
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 106 
End = 117 
Frequency = 1 
 [1] 0.5918421 0.5908801 0.5901984 0.5897153 0.5893729 0.5891302 0.5889583
 [8] 0.5888364 0.5887501 0.5886889 0.5886455 0.5886148

$se
Time Series:
Start = 106 
End = 117 
Frequency = 1 
 [1] 0.008986281 0.013433940 0.017170837 0.020498633 0.023529628 0.026324542
 [7] 0.028923517 0.031356160 0.033645640 0.035810684 0.037866718 0.039826610

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 106 
End = 117 
Frequency = 1 
 [1] 0.5742289 0.5645496 0.5565435 0.5495379 0.5432548 0.5375341 0.5322682
 [8] 0.5273784 0.5228046 0.5184999 0.5144267 0.5105546
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 106 
End = 117 
Frequency = 1 
 [1] 0.6094552 0.6172106 0.6238532 0.6298926 0.6354909 0.6407263 0.6456484
 [8] 0.6502945 0.6546955 0.6588778 0.6628643 0.6666749
> 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$pred))
  [1]  10.8100   9.1200  11.0300  12.7400   9.9800  11.6200   9.4000   9.2700
  [9]   7.7600   8.7800  10.6500  10.9500  12.3600  10.8500  11.8400  12.1400
 [17]  11.6500   8.8600   7.6300   7.3800   7.2500   8.0300   7.7500   7.1600
 [25]   7.1800   7.5100   7.0700   7.1100   8.9800   9.5300  10.5400  11.3100
 [33]  10.3600  11.4400  10.4500  10.6900  11.2800  11.9600  13.5200  12.8900
 [41]  14.0300  16.2700  16.1700  17.2500  19.3800  26.2000  33.5300  32.2000
 [49]  38.4500  44.8600  41.6700  36.0600  39.7600  36.8100  42.6500  46.8900
 [57]  53.6100  57.5900  67.8200  71.8900  75.5100  68.4900  62.7200  70.3900
 [65]  59.7700  57.2700  67.9600  67.8500  76.9800  81.0800  91.6600  84.8400
 [73]  85.7300  84.6100  92.9100  99.8000 121.1900 122.0400 131.7600 138.4800
 [81] 153.4700 189.9500 182.2200 198.0800 135.3600 125.0200 143.5000 173.9500
 [89] 188.7500 167.4400 158.9500 169.5300 113.6600 107.5900  92.6700  85.3500
 [97]  90.1300  89.3100 105.1200 125.8300 135.8100 142.4300 163.3900 168.2100
[105] 185.3500 189.6452 192.7553 194.9934 196.5968 197.7418 198.5577 199.1382
[113] 199.5507 199.8436 200.0515 200.1989 200.3035
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 106 
End = 117 
Frequency = 1 
 [1] 0.1799584 0.2946492 0.4075633 0.5230111 0.6422128 0.7656370 0.8935277
 [8] 1.0260662 1.1634262 1.3057930 1.4533683 1.6063698
> postscript(file="/var/www/rcomp/tmp/17ez01292345259.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/rcomp/tmp/2lox81292345259.ps",horizontal=F,onefile=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/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/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/rcomp/tmp/3spck1292345259.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/rcomp/tmp/4d8tq1292345259.tab") 
> 
> try(system("convert tmp/17ez01292345259.ps tmp/17ez01292345259.png",intern=TRUE))
character(0)
> try(system("convert tmp/2lox81292345259.ps tmp/2lox81292345259.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  0.700   0.440   1.125