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(14929387.5,14717825.3,15826281.2,16301309.6,15033016.9,16998460.6,14066462.7,13328937.3,17319718.2,17586426.8,15887037.4,17935679.1,15869489,15892510.9,17556558.1,16791643,15953688.5,18144913.6,14390881,13885708.7,17332571.5,17152595.8,16003877.1,16841467.1,14783398.1,14667847.5,17714362.2,16282088,15014866.2,17722582.4,13876509.4,15495489.6,17799521.1,17920079.1,17248022.4,18813782.4,16249688.3,17823358.5,20424438.3,17814218.7,19699959.6,19776328.1,15679833.1,17119266.5,20092613,20863688.3,20925203.1,21032593,20664684.3,19711511.4,22553293.4,19498332.9,20722827.8,21321275,17960847.7,17789654.9,20003708.5,21169851.7,20422839.4,19810562.3)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '0'
> par7 = '1'
> par6 = '2'
> par5 = '12'
> par4 = '1'
> par3 = '1'
> par2 = '1.0'
> par1 = '21'
> #'GNU S' R Code compiled by R2WASP v. 1.0.44 ()
> #Author: Prof. Dr. P. Wessa
> #To cite this work: AUTHOR(S), (YEAR), YOUR SOFTWARE TITLE (vNUMBER) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_YOURPAGE.wasp/
> #Source of accompanying publication: Office for Research, Development, and Education
> #Technical description: Write here your technical program description (don't use hard returns!)
> 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     ma1     sma1
      -0.7063  -0.1934  0.2502  -0.0013
s.e.   1.4426   0.6457  1.4412   0.3065

sigma^2 estimated as 5.56e+11:  log likelihood = -388.57,  aic = 787.14
> (forecast <- predict(arima.out,fx))
$pred
Time Series:
Start = 40 
End = 60 
Frequency = 1 
 [1] 19048153 17828352 20491639 16667531 18276819 20583012 20704042 20030633
 [9] 21595817 19032264 20603773 23205438 21829069 20609214 23272555 19448420
[17] 21057717 23363909 23484938 22811530 24376713

$se
Time Series:
Start = 40 
End = 60 
Frequency = 1 
 [1]  745640.0  848792.1  985892.6 1105215.9 1205898.0 1303491.2 1392323.6
 [8] 1476308.5 1555773.8 1631281.9 1703506.4 1772766.3 2160758.0 2339061.3
[15] 2540561.7 2726484.5 2894717.9 3057694.3 3210729.9 3357226.0 3497598.2

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 40 
End = 60 
Frequency = 1 
 [1] 17586698 16164719 18559289 14501308 15913259 18028170 17975088 17137069
 [9] 18546500 15834951 17264901 19730816 17593984 16024654 18293054 14104510
[17] 15384070 17370828 17191908 16231367 17521421
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 40 
End = 60 
Frequency = 1 
 [1] 20509607 19491984 22423988 18833754 20640379 23137855 23432997 22924198
 [9] 24645133 22229576 23942646 26680060 26064155 25193774 28252056 24792329
[17] 26731364 29356990 29777969 29391693 31232006
> 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$pred))
 [1] 14929388 14717825 15826281 16301310 15033017 16998461 14066463 13328937
 [9] 17319718 17586427 15887037 17935679 15869489 15892511 17556558 16791643
[17] 15953688 18144914 14390881 13885709 17332572 17152596 16003877 16841467
[25] 14783398 14667848 17714362 16282088 15014866 17722582 13876509 15495490
[33] 17799521 17920079 17248022 18813782 16249688 17823358 20424438 19048153
[41] 17828352 20491639 16667531 18276819 20583012 20704042 20030633 21595817
[49] 19032264 20603773 23205438 21829069 20609214 23272555 19448420 21057717
[57] 23363909 23484938 22811530 24376713
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 40 
End = 60 
Frequency = 1 
 [1] 0.03914500 0.04760912 0.04811194 0.06630952 0.06597964 0.06332850
 [7] 0.06724888 0.07370254 0.07204051 0.08571140 0.08267934 0.07639443
[13] 0.09898534 0.11349590 0.10916557 0.14019054 0.13746589 0.13087255
[19] 0.13671443 0.14717233 0.14348112
> postscript(file="/var/www/html/rcomp/tmp/1s2zb1260547179.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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.se <- array(0, dim=fx)
> perf.mse <- 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$pred[i]
+ perf.mape[i] = perf.mape[i] + abs(perf.pe[i])
+ perf.se[i] = (x[nx+i] - forecast$pred[i])^2
+ perf.mse[i] = perf.mse[i] + perf.se[i]
+ 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 = perf.mape / fx
> perf.mse = perf.mse / fx
> perf.rmse = sqrt(perf.mse)
> postscript(file="/var/www/html/rcomp/tmp/2wruo1260547179.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[1:12] <- x[(nx+1):lx]
Warning message:
In NextMethod("[<-") :
  number of items to replace is not a multiple of replacement length
> 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/3gj9y1260547179.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.mape[i],4))
+ a<-table.element(a,round(perf.se[i],4))
+ a<-table.element(a,round(perf.mse[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/4z1431260547179.tab") 
> 
> system("convert tmp/1s2zb1260547179.ps tmp/1s2zb1260547179.png")
> system("convert tmp/2wruo1260547179.ps tmp/2wruo1260547179.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.850   0.339   1.487