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(25.22,27.63,27.47,22.54,27.4,29.68,28.51,29.89,32.62,30.93,32.52,25.28,25.64,27.41,24.4,25.55,28.45,27.72,24.54,25.67,25.54,20.48,18.94,18.6,19.49,20.29,23.69,25.65,25.43,24.13,25.77,26.63,28.34,27.55,24.5,28.52,31.29,32.65,30.34,25.02,25.81,27.55,28.4,29.83,27.1,29.59,28.77,29.88,31.18,30.87,33.8,33.36,37.92,35.19,38.37,43.03,43.38,49.77,43.05,39.65,44.28,45.56,53.08,51.86,48.67,54.31,57.58,64.09,62.98,58.52,55.54,56.75,63.57,59.92,62.25,70.44,70.19,68.86,73.9,73.61,62.77,58.38,58.48,62.31,54.3,57.76,62.14,67.4,67.48,71.32,77.2,70.8,77.13,83.04,92.53,91.45,91.92,94.82,103.28,110.44,123.94,133.05,133.9,113.85,99.06,72.84,53.24,41.58,44.86,43.24,46.84,50.85,57.94,68.59,64.92,72.5,67.69,73.19,77.04,74.67)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '1'
> par6 = '1'
> par5 = '12'
> par4 = '1'
> par3 = '1'
> par2 = '-0.5'
> 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
      -0.7828  0.9345
s.e.   0.1362  0.0990

sigma^2 estimated as 0.0001073:  log likelihood = 299.14,  aic = -592.27
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 109 
End = 120 
Frequency = 1 
 [1] 0.1568438 0.1536467 0.1505953 0.1463780 0.1418088 0.1380822 0.1382738
 [8] 0.1452092 0.1522486 0.1687208 0.1887772 0.2066700

$se
Time Series:
Start = 109 
End = 120 
Frequency = 1 
 [1] 0.01036034 0.01580209 0.01908486 0.02236730 0.02488660 0.02741558
 [7] 0.02955459 0.03167724 0.03357152 0.03543477 0.03715232 0.03883321

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 109 
End = 120 
Frequency = 1 
 [1] 0.13653757 0.12267463 0.11318893 0.10253807 0.09303105 0.08434764
 [7] 0.08034684 0.08312184 0.08644845 0.09926863 0.11595867 0.13055688
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 109 
End = 120 
Frequency = 1 
 [1] 0.1771501 0.1846188 0.1880016 0.1902179 0.1905865 0.1918167 0.1962008
 [8] 0.2072966 0.2180488 0.2381729 0.2615958 0.2827830
> 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$pred))
  [1]  25.22000  27.63000  27.47000  22.54000  27.40000  29.68000  28.51000
  [8]  29.89000  32.62000  30.93000  32.52000  25.28000  25.64000  27.41000
 [15]  24.40000  25.55000  28.45000  27.72000  24.54000  25.67000  25.54000
 [22]  20.48000  18.94000  18.60000  19.49000  20.29000  23.69000  25.65000
 [29]  25.43000  24.13000  25.77000  26.63000  28.34000  27.55000  24.50000
 [36]  28.52000  31.29000  32.65000  30.34000  25.02000  25.81000  27.55000
 [43]  28.40000  29.83000  27.10000  29.59000  28.77000  29.88000  31.18000
 [50]  30.87000  33.80000  33.36000  37.92000  35.19000  38.37000  43.03000
 [57]  43.38000  49.77000  43.05000  39.65000  44.28000  45.56000  53.08000
 [64]  51.86000  48.67000  54.31000  57.58000  64.09000  62.98000  58.52000
 [71]  55.54000  56.75000  63.57000  59.92000  62.25000  70.44000  70.19000
 [78]  68.86000  73.90000  73.61000  62.77000  58.38000  58.48000  62.31000
 [85]  54.30000  57.76000  62.14000  67.40000  67.48000  71.32000  77.20000
 [92]  70.80000  77.13000  83.04000  92.53000  91.45000  91.92000  94.82000
 [99] 103.28000 110.44000 123.94000 133.05000 133.90000 113.85000  99.06000
[106]  72.84000  53.24000  41.58000  40.65042  42.35975  44.09379  46.67115
[113]  49.72717  52.44750  52.30220  47.42546  43.14130  35.12876  28.06085
[120]  23.41236
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 109 
End = 120 
Frequency = 1 
 [1] 0.1630431 0.2901478 0.3929432 0.5295369 0.6752761 0.8571258 1.0008720
 [8] 1.0468441 1.0722691 0.9636586 0.8419827 0.7682912
> postscript(file="/var/www/rcomp/tmp/15jhs1293302105.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2jtei1293302105.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/3j3tx1293302105.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/4xdq61293302105.tab") 
> 
> try(system("convert tmp/15jhs1293302105.ps tmp/15jhs1293302105.png",intern=TRUE))
character(0)
> try(system("convert tmp/2jtei1293302105.ps tmp/2jtei1293302105.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  0.770   0.200   0.958