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(19,18,19,19,22,23,20,14,14,14,15,11,17,16,20,24,23,20,21,19,23,23,23,23,27,26,17,24,26,24,27,27,26,24,23,23,24,17,21,19,22,22,18,16,14,12,14,16,8,3,0,5,1,1,3,6,7,8,14,14,13)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '0'
> par6 = '0'
> par5 = '12'
> par4 = '0'
> par3 = '1'
> par2 = '1'
> par1 = '13'
> 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
      -0.2289  -0.5102  0.5913  -0.0255  0.3458  -0.8182
s.e.   0.3605   0.2439  0.2911   0.4441  0.4485   0.4531

sigma^2 estimated as 8.05:  log likelihood = -80.17,  aic = 174.34
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] 26.44840 26.82523 24.97229 25.46929 26.52368 24.93308 25.05312 26.46061
 [9] 25.13665 24.79260 26.37909 25.40860 24.61789 26.23213 25.69217 24.52465
[17] 26.02190 25.95555 24.51648 25.76509 26.17424 24.59262 25.48423 26.32900
[25] 24.74551 25.20420 26.40660 24.96102

$se
Time Series:
Start = 34 
End = 61 
Frequency = 1 
 [1] 2.898257 3.585877 3.982178 4.315448 4.539410 4.715153 4.917566 5.082816
 [9] 5.215589 5.381514 5.532186 5.649187 5.795024 5.939234 6.048135 6.178439
[17] 6.317696 6.422123 6.539282 6.673488 6.775722 6.881736 7.010303 7.111851
[25] 7.208678 7.330901 7.432659 7.522250

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 34 
End = 61 
Frequency = 1 
 [1] 20.76781 19.79691 17.16722 17.01101 17.62644 15.69138 15.41469 16.49830
 [9] 14.91410 14.24483 15.53601 14.33619 13.25964 14.59124 13.83783 12.41491
[17] 13.63922 13.36819 11.69949 12.68505 12.89382 11.10442 11.74403 12.38977
[25] 10.61650 10.83564 11.83859 10.21741
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 34 
End = 61 
Frequency = 1 
 [1] 32.12898 33.85355 32.77735 33.92757 35.42092 34.17478 34.69155 36.42293
 [9] 35.35921 35.34036 37.22218 36.48101 35.97614 37.87303 37.54652 36.63439
[17] 38.40459 38.54291 37.33348 38.84512 39.45465 38.08082 39.22442 40.26822
[25] 38.87452 39.57277 40.97462 39.70462
> 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$pred))
 [1] 19.00000 18.00000 19.00000 19.00000 22.00000 23.00000 20.00000 14.00000
 [9] 14.00000 14.00000 15.00000 11.00000 17.00000 16.00000 20.00000 24.00000
[17] 23.00000 20.00000 21.00000 19.00000 23.00000 23.00000 23.00000 23.00000
[25] 27.00000 26.00000 17.00000 24.00000 26.00000 24.00000 27.00000 27.00000
[33] 26.00000 26.44840 26.82523 24.97229 25.46929 26.52368 24.93308 25.05312
[41] 26.46061 25.13665 24.79260 26.37909 25.40860 24.61789 26.23213 25.69217
[49] 24.52465 26.02190 25.95555 24.51648 25.76509 26.17424 24.59262 25.48423
[57] 26.32900 24.74551 25.20420 26.40660 24.96102
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 34 
End = 61 
Frequency = 1 
 [1] 0.1095816 0.1336756 0.1594639 0.1694373 0.1711456 0.1891123 0.1962856
 [8] 0.1920899 0.2074894 0.2170613 0.2097186 0.2223337 0.2353989 0.2264106
[15] 0.2354077 0.2519277 0.2427838 0.2474277 0.2667300 0.2590128 0.2588699
[22] 0.2798293 0.2750840 0.2701148 0.2913126 0.2908603 0.2814697 0.3013599
> postscript(file="/var/www/html/rcomp/tmp/1les31260305515.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/22ji31260305515.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/3nmsb1260305515.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/4phf81260305515.tab") 
> 
> system("convert tmp/1les31260305515.ps tmp/1les31260305515.png")
> system("convert tmp/22ji31260305515.ps tmp/22ji31260305515.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.820   0.324   1.325