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(17,14,15,16,16,15,13,12,13,13,12,10,14,14,15,16,16,15,15,13,15,15,15,13,16,16,14,16,15,14,15,15,14,13,12,13,12,9,10,8,11,8,8,8,4,6,8,10,5,6,5,9,8,6,9,11,11,8,11,11,13)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '0'
> par6 = '0'
> par5 = '12'
> par4 = '0'
> par3 = '1'
> par2 = '1'
> par1 = '24'
> 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
      -0.3138  -0.4502  0.5997  -0.1072  0.1072  -0.9999
s.e.   0.1839   0.1505  0.1619   0.1988  0.2045   0.2109

sigma^2 estimated as 1.392:  log likelihood = -53.52,  aic = 121.04
Warning message:
In arima(x[1:nx], order = c(par6, par3, par7), seasonal = list(order = c(par8,  :
  possible convergence problem: optim gave code=1
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 34 
End = 61 
Frequency = 1 
 [1] 14.88688 14.86943 13.96496 14.78848 14.92681 13.97025 14.70198 14.98598
 [9] 13.99380 14.61607 15.03782 14.03032 14.52976 15.07955 14.07800 14.44425
[17] 15.10994 14.13555 14.36123 15.12830 14.20167 14.28243 15.13427 14.27493
[25] 14.20950 15.12776 14.35374 14.14396

$se
Time Series:
Start = 34 
End = 61 
Frequency = 1 
 [1] 1.226537 1.417744 1.487954 1.531202 1.540734 1.546162 1.555093 1.553515
 [9] 1.553971 1.558711 1.555929 1.555502 1.559450 1.556741 1.555904 1.559579
[17] 1.557268 1.556092 1.559533 1.557757 1.556249 1.559415 1.558255 1.556411
[25] 1.559257 1.558763 1.556584 1.559079

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 34 
End = 61 
Frequency = 1 
 [1] 12.48286 12.09065 11.04857 11.78732 11.90697 10.93977 11.65399 11.94109
 [9] 10.94801 11.56100 11.98820 10.98154 11.47323 12.02833 11.02842 11.38747
[17] 12.05769 11.08561 11.30455 12.07510 11.15142 11.22598 12.08009 11.22436
[25] 11.15335 12.07258 11.30284 11.08817
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 34 
End = 61 
Frequency = 1 
 [1] 17.29089 17.64820 16.88135 17.78963 17.94664 17.00073 17.74996 18.03087
 [9] 17.03958 17.67115 18.08744 17.07911 17.58628 18.13076 17.12757 17.50102
[17] 18.16218 17.18549 17.41792 18.18151 17.25192 17.33888 18.18845 17.32549
[25] 17.26564 18.18293 17.40465 17.19976
> 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$pred))
 [1] 17.00000 14.00000 15.00000 16.00000 16.00000 15.00000 13.00000 12.00000
 [9] 13.00000 13.00000 12.00000 10.00000 14.00000 14.00000 15.00000 16.00000
[17] 16.00000 15.00000 15.00000 13.00000 15.00000 15.00000 15.00000 13.00000
[25] 16.00000 16.00000 14.00000 16.00000 15.00000 14.00000 15.00000 15.00000
[33] 14.00000 14.88688 14.86943 13.96496 14.78848 14.92681 13.97025 14.70198
[41] 14.98598 13.99380 14.61607 15.03782 14.03032 14.52976 15.07955 14.07800
[49] 14.44425 15.10994 14.13555 14.36123 15.12830 14.20167 14.28243 15.13427
[57] 14.27493 14.20950 15.12776 14.35374 14.14396
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 34 
End = 61 
Frequency = 1 
 [1] 0.08239046 0.09534628 0.10654908 0.10354021 0.10321927 0.11067536
 [7] 0.10577442 0.10366453 0.11104715 0.10664364 0.10346773 0.11086714
[13] 0.10732805 0.10323530 0.11052028 0.10797231 0.10306249 0.11008358
[19] 0.10859326 0.10296972 0.10958208 0.10918414 0.10296199 0.10903108
[25] 0.10973348 0.10303992 0.10844447 0.11022932
> postscript(file="/var/www/html/rcomp/tmp/1ef4d1260549421.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2pipe1260549421.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/394p11260549421.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/4a0ps1260549421.tab") 
> 
> system("convert tmp/1ef4d1260549421.ps tmp/1ef4d1260549421.png")
> system("convert tmp/2pipe1260549421.ps tmp/2pipe1260549421.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.870   0.338   1.018