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(14.5,14.3,15.3,14.4,13.7,14.2,13.5,11.9,14.6,15.6,14.1,14.9,14.2,14.6,17.2,15.4,14.3,17.5,14.5,14.4,16.6,16.7,16.6,16.9,15.7,16.4,18.4,16.9,16.5,18.3,15.1,15.7,18.1,16.8,18.9,19,18.1,17.8,21.5,17.1,18.7,19,16.4,16.9,18.6,19.3,19.4,17.6,18.6,18.1,20.4,18.1,19.6,19.9,19.2,17.8,19.2,22,21.1,19.5,22.2,20.9,22.2,23.5,21.5,24.3,22.8,20.3,23.7,23.3,19.6,18,17.3,16.8,18.2,16.5,16,18.4)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '2'
> par7 = '0'
> par6 = '3'
> par5 = '12'
> par4 = '1'
> par3 = '1'
> par2 = '-0.2'
> par1 = '12'
> par1 <- as.numeric(par1) #cut off periods
> par1 <- 28
> 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
> par6 <- 3
> par7 <- as.numeric(par7) #q
> par7 <- 3
> 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      ma2     ma3     sar1     sar2
      -0.5229  0.2655  0.8568  -0.3427  -0.2665  -0.384  -0.6551  -0.9040
s.e.   0.2265  0.3256  0.2269   0.5279   0.3453   0.265   0.1105   0.0683
         sma1
      -0.8447
s.e.   2.6300

sigma^2 estimated as 3.501e-06:  log likelihood = 141.67,  aic = -263.34
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 51 
End = 78 
Frequency = 1 
 [1] 0.5469144 0.5501864 0.5669593 0.5439845 0.5584695 0.5713620 0.5445988
 [8] 0.5437848 0.5513368 0.5413003 0.5560655 0.5461919 0.5317924 0.5451961
[15] 0.5454692 0.5327859 0.5563790 0.5485244 0.5374859 0.5406269 0.5290382
[22] 0.5308714 0.5328491 0.5356133 0.5171911 0.5360753 0.5320427 0.5266724

$se
Time Series:
Start = 51 
End = 78 
Frequency = 1 
 [1] 0.002377060 0.002257100 0.002686459 0.003066141 0.003035955 0.003617386
 [7] 0.003557637 0.003596253 0.004067686 0.003987682 0.004175377 0.004274695
[13] 0.004249649 0.004524970 0.004404132 0.004394970 0.004629965 0.004556613
[19] 0.004666208 0.004691039 0.004663756 0.004907840 0.004825903 0.004822332
[25] 0.004837222 0.004791734 0.004814811 0.004772920

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 51 
End = 78 
Frequency = 1 
 [1] 0.5422554 0.5457625 0.5616938 0.5379748 0.5525190 0.5642719 0.5376259
 [8] 0.5367361 0.5433641 0.5334844 0.5478818 0.5378135 0.5234631 0.5363271
[15] 0.5368371 0.5241717 0.5473042 0.5395935 0.5283402 0.5314324 0.5198972
[22] 0.5212521 0.5233903 0.5261615 0.5077102 0.5266835 0.5226057 0.5173175
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 51 
End = 78 
Frequency = 1 
 [1] 0.5515734 0.5546103 0.5722248 0.5499941 0.5644199 0.5784520 0.5515718
 [8] 0.5508334 0.5593095 0.5491161 0.5642492 0.5545703 0.5401218 0.5540650
[15] 0.5541013 0.5414000 0.5654537 0.5574554 0.5466317 0.5498213 0.5381791
[22] 0.5404908 0.5423079 0.5450651 0.5266721 0.5454671 0.5414797 0.5360274
> 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$pred))
 [1] 14.50000 14.30000 15.30000 14.40000 13.70000 14.20000 13.50000 11.90000
 [9] 14.60000 15.60000 14.10000 14.90000 14.20000 14.60000 17.20000 15.40000
[17] 14.30000 17.50000 14.50000 14.40000 16.60000 16.70000 16.60000 16.90000
[25] 15.70000 16.40000 18.40000 16.90000 16.50000 18.30000 15.10000 15.70000
[33] 18.10000 16.80000 18.90000 19.00000 18.10000 17.80000 21.50000 17.10000
[41] 18.70000 19.00000 16.40000 16.90000 18.60000 19.30000 19.40000 17.60000
[49] 18.60000 18.10000 20.43635 19.83585 17.07028 20.99266 18.40784 16.42266
[57] 20.87452 21.03123 19.62976 21.51834 18.80920 20.57186 23.51198 20.76044
[65] 20.70851 23.29360 18.75627 20.13818 22.29279 21.65269 24.13042 23.71664
[73] 23.27978 22.68523 27.02369 22.58765 23.45673 24.67727
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 51 
End = 78 
Frequency = 1 
 [1] 0.02229817 0.02101637 0.02436648 0.02914089 0.02807193 0.03286927
 [7] 0.03395601 0.03439266 0.03854523 0.03848520 0.03926020 0.04099910
[13] 0.04190418 0.04360323 0.04235979 0.04332374 0.04372402 0.04364365
[19] 0.04571465 0.04568965 0.04645787 0.04884734 0.04779905 0.04750181
[25] 0.04945034 0.04714122 0.04775941 0.04783032
> postscript(file="/var/www/html/rcomp/tmp/1q8cr1260298380.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2mmag1260298380.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/3mt1d1260298380.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/4rtrq1260298380.tab") 
> 
> system("convert tmp/1q8cr1260298380.ps tmp/1q8cr1260298380.png")
> system("convert tmp/2mmag1260298380.ps tmp/2mmag1260298380.png")
> 
> 
> proc.time()
   user  system elapsed 
  4.937   0.893   5.783