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(31.514,27.071,29.462,26.105,22.397,23.843,21.705,18.089,20.764,25.316,17.704,15.548,28.029,29.383,36.438,32.034,22.679,24.319,18.004,17.537,20.366,22.782,19.169,13.807,29.743,25.591,29.096,26.482,22.405,27.044,17.970,18.730,19.684,19.785,18.479,10.698,31.956,29.506,34.506,27.165,26.736,23.691,18.157,17.328,18.205,20.995,17.382,9.367,31.124,26.551,30.651,25.859,25.100,25.778,20.418,18.688,20.424,24.776,19.814,12.738,31.566,30.111,30.019,31.934,25.826,26.835,20.205,17.789,20.520,22.518,15.572,11.509,25.447,24.090,27.786,26.195,20.516,22.759,19.028,16.971,20.036,22.485,18.730,14.538)
> par10 = 'TRUE'
> par9 = '1'
> par8 = '1'
> par7 = '1'
> par6 = '3'
> par5 = '12'
> 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: 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     ar2      ar3      ma1     sar1     sma1
      1.0913  0.0714  -0.2411  -1.0000  -0.0072  -1.0000
s.e.  0.1331  0.1951   0.1271   0.1032   0.1860   0.4422

sigma^2 estimated as 3.193:  log likelihood = -132.45,  aic = 278.89
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 73 
End = 84 
Frequency = 1 
 [1] 29.46800 27.36683 31.12835 27.83519 23.85822 25.00206 19.21577 17.88727
 [9] 19.88638 22.61094 18.01346 12.22057

$se
Time Series:
Start = 73 
End = 84 
Frequency = 1 
 [1] 1.961901 1.976374 2.016314 2.016313 2.016731 2.021765 2.027691 2.034667
 [9] 2.040897 2.046264 2.049545 2.052577

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 73 
End = 84 
Frequency = 1 
 [1] 25.622673 23.493133 27.176379 23.883212 19.905428 21.039401 15.241499
 [8] 13.899323 15.886218 18.600261 13.996350  8.197523
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 73 
End = 84 
Frequency = 1 
 [1] 33.31332 31.24052 35.08033 31.78716 27.81101 28.96472 23.19005 21.87522
 [9] 23.88653 26.62162 22.03056 16.24362
> 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$pred))
 [1] 31.51400 27.07100 29.46200 26.10500 22.39700 23.84300 21.70500 18.08900
 [9] 20.76400 25.31600 17.70400 15.54800 28.02900 29.38300 36.43800 32.03400
[17] 22.67900 24.31900 18.00400 17.53700 20.36600 22.78200 19.16900 13.80700
[25] 29.74300 25.59100 29.09600 26.48200 22.40500 27.04400 17.97000 18.73000
[33] 19.68400 19.78500 18.47900 10.69800 31.95600 29.50600 34.50600 27.16500
[41] 26.73600 23.69100 18.15700 17.32800 18.20500 20.99500 17.38200  9.36700
[49] 31.12400 26.55100 30.65100 25.85900 25.10000 25.77800 20.41800 18.68800
[57] 20.42400 24.77600 19.81400 12.73800 31.56600 30.11100 30.01900 31.93400
[65] 25.82600 26.83500 20.20500 17.78900 20.52000 22.51800 15.57200 11.50900
[73] 29.46800 27.36683 31.12835 27.83519 23.85822 25.00206 19.21577 17.88727
[81] 19.88638 22.61094 18.01346 12.22057
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 73 
End = 84 
Frequency = 1 
 [1] 0.06657734 0.07221788 0.06477419 0.07243757 0.08452981 0.08086393
 [7] 0.10552220 0.11374946 0.10262790 0.09049886 0.11377852 0.16796075
> postscript(file="/var/www/html/rcomp/tmp/1a3hs1292691393.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/html/rcomp/tmp/2h5em1292691393.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/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/3n6bx1292691393.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/4rorl1292691393.tab") 
> 
> try(system("convert tmp/1a3hs1292691393.ps tmp/1a3hs1292691393.png",intern=TRUE))
character(0)
> try(system("convert tmp/2h5em1292691393.ps tmp/2h5em1292691393.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.766   0.366   4.860