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(593530.00,610943.00,612613.00,611324.00,594167.00,595454.00,590865.00,589379.00,584428.00,573100.00,567456.00,569028.00,620735.00,628884.00,628232.00,612117.00,595404.00,597141.00,593408.00,590072.00,579799.00,574205.00,572775.00,572942.00,619567.00,625809.00,619916.00,587625.00,565742.00,557274.00,560576.00,548854.00,531673.00,525919.00,511038.00,498662.00,555362.00,564591.00,541657.00,527070.00,509846.00,514258.00,516922.00,507561.00,492622.00,490243.00,469357.00,477580.00,528379.00,533590.00,517945.00,506174.00,501866.00,516141.00,528222.00,532638.00,536322.00,536535.00,523597.00,536214.00,586570.00,596594.00,580523.00)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '1'
> par6 = '1'
> par5 = '12'
> par4 = '1'
> par3 = '1'
> par2 = '1'
> par1 = '2'
> 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
      0.1741  0.3642  0.4610  -0.0879  0.1133  -0.9864
s.e.  0.3263  0.2536  0.2561   0.2267  0.2251   0.2108

sigma^2 estimated as 28004572:  log likelihood = -222.51,  aic = 459.02
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 36 
End = 63 
Frequency = 1 
 [1] 512130.2 549465.8 555090.7 546133.8 508802.0 484641.0 472528.2 472042.1
 [9] 457282.9 436513.3 427282.0 409088.5 406683.2 440600.3 442829.2 430423.7
[17] 389678.7 362101.9 346561.5 342661.1 324484.5 300296.2 287651.1 266042.7
[25] 260223.5 290728.8 289546.0 273730.2

$se
Time Series:
Start = 36 
End = 63 
Frequency = 1 
 [1]  5569.113  8192.714 11895.098 13721.431 15714.671 17794.443 19479.959
 [8] 21241.714 22961.263 24572.617 26200.071 27790.461 31677.904 35413.358
[15] 40022.956 43487.270 47073.252 50721.805 54033.533 57393.869 60702.596
[22] 63901.369 67100.941 70254.644 75316.889 80318.767 86070.321 90949.854

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 36 
End = 63 
Frequency = 1 
 [1] 501214.75 533408.04 531776.27 519239.79 478001.23 449763.91 434347.45
 [8] 430408.30 412278.87 388350.94 375929.86 354619.18 344594.46 371190.12
[15] 364384.17 345188.63 297415.15 262687.20 240655.76 230169.11 205507.42
[22] 175049.53 156133.26 128343.59 112602.41 133304.02 120848.21  95468.46
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 36 
End = 63 
Frequency = 1 
 [1] 523045.7 565523.5 578405.0 573027.8 539602.7 519518.1 510708.9 513675.8
 [9] 502287.0 484675.6 478634.1 463557.8 468771.8 510010.5 521274.2 515658.7
[17] 481942.3 461516.7 452467.2 455153.1 443461.6 425542.9 419168.9 403741.8
[25] 407844.6 448153.6 458243.9 451991.9
> 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$pred))
 [1] 593530.0 610943.0 612613.0 611324.0 594167.0 595454.0 590865.0 589379.0
 [9] 584428.0 573100.0 567456.0 569028.0 620735.0 628884.0 628232.0 612117.0
[17] 595404.0 597141.0 593408.0 590072.0 579799.0 574205.0 572775.0 572942.0
[25] 619567.0 625809.0 619916.0 587625.0 565742.0 557274.0 560576.0 548854.0
[33] 531673.0 525919.0 511038.0 512130.2 549465.8 555090.7 546133.8 508802.0
[41] 484641.0 472528.2 472042.1 457282.9 436513.3 427282.0 409088.5 406683.2
[49] 440600.3 442829.2 430423.7 389678.7 362101.9 346561.5 342661.1 324484.5
[57] 300296.2 287651.1 266042.7 260223.5 290728.8 289546.0 273730.2
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 36 
End = 63 
Frequency = 1 
 [1] 0.01087441 0.01491033 0.02142911 0.02512467 0.03088563 0.03671675
 [7] 0.04122497 0.04499962 0.05021238 0.05629295 0.06131799 0.06793264
[13] 0.07789333 0.08037525 0.09038013 0.10103364 0.12080016 0.14007604
[19] 0.15591327 0.16749456 0.18707394 0.21279446 0.23327197 0.26407282
[25] 0.28943153 0.27626698 0.29725954 0.33226098
> postscript(file="/var/www/html/rcomp/tmp/1109x1260458654.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2zddh1260458654.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/3kz7j1260458654.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/45u0b1260458654.tab") 
> 
> system("convert tmp/1109x1260458654.ps tmp/1109x1260458654.png")
> system("convert tmp/2zddh1260458654.ps tmp/2zddh1260458654.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.936   0.338   2.155