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(267413,267366,264777,258863,254844,254868,277267,285351,286602,283042,276687,277915,277128,277103,275037,270150,267140,264993,287259,291186,292300,288186,281477,282656,280190,280408,276836,275216,274352,271311,289802,290726,292300,278506,269826,265861,269034,264176,255198,253353,246057,235372,258556,260993,254663,250643,243422,247105,248541,245039,237080,237085,225554,226839,247934,248333,246969,245098,246263,255765,264319,268347,273046,273963,267430,271993,292710,295881,293299)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '0'
> par6 = '3'
> par5 = '12'
> par4 = '1'
> 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
      -0.2099  0.5835  0.5444  0.3212  -0.0430  -0.8731
s.e.   0.2955  0.1729  0.2482  0.2492   0.2139   0.2069

sigma^2 estimated as 6951031:  log likelihood = -262.67,  aic = 539.34
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 42 
End = 69 
Frequency = 1 
 [1] 244795.4 256948.5 259576.8 258063.8 242461.8 233288.0 226691.1 229144.3
 [9] 222632.9 212149.1 209263.6 200407.4 198046.5 208953.5 210352.6 207772.0
[17] 190998.5 180778.6 173136.6 174561.0 167086.3 155635.5 151830.8 142078.9
[25] 138843.2 148910.9 149488.1 146114.1

$se
Time Series:
Start = 42 
End = 69 
Frequency = 1 
 [1]  2720.010  3990.350  5845.804  6741.038  8075.451  9205.483 10274.043
 [8] 11474.437 12541.909 13682.938 14805.709 15911.830 18203.735 20389.352
[15] 23059.468 25153.569 27579.956 29876.900 32120.776 34474.979 36720.376
[22] 39023.808 41311.638 43581.137 46795.254 49971.154 53552.608 56713.535

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 42 
End = 69 
Frequency = 1 
 [1] 239464.20 249127.43 248119.07 244851.35 226633.94 215245.28 206554.01
 [8] 206654.36 198050.77 185330.56 180244.45 169220.18 162367.15 168990.38
[15] 165156.01 158471.04 136941.84 122219.90 110179.92 106990.01  95114.35
[22]  79148.83  70860.03  56659.82  47124.53  50967.41  44525.01  34955.60
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 42 
End = 69 
Frequency = 1 
 [1] 250126.6 264769.6 271034.6 271276.2 258289.7 251330.8 246828.3 251634.2
 [9] 247215.0 238967.7 238282.8 231594.6 233725.8 248916.6 255549.1 257073.0
[17] 245055.3 239337.3 236093.4 242131.9 239058.2 232122.2 232801.7 227497.9
[25] 230561.9 246854.3 254451.2 257272.7
> 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$pred))
 [1] 267413.0 267366.0 264777.0 258863.0 254844.0 254868.0 277267.0 285351.0
 [9] 286602.0 283042.0 276687.0 277915.0 277128.0 277103.0 275037.0 270150.0
[17] 267140.0 264993.0 287259.0 291186.0 292300.0 288186.0 281477.0 282656.0
[25] 280190.0 280408.0 276836.0 275216.0 274352.0 271311.0 289802.0 290726.0
[33] 292300.0 278506.0 269826.0 265861.0 269034.0 264176.0 255198.0 253353.0
[41] 246057.0 244795.4 256948.5 259576.8 258063.8 242461.8 233288.0 226691.1
[49] 229144.3 222632.9 212149.1 209263.6 200407.4 198046.5 208953.5 210352.6
[57] 207772.0 190998.5 180778.6 173136.6 174561.0 167086.3 155635.5 151830.8
[65] 142078.9 138843.2 148910.9 149488.1 146114.1
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 42 
End = 69 
Frequency = 1 
 [1] 0.01111136 0.01552976 0.02252051 0.02612160 0.03330607 0.03945973
 [7] 0.04532177 0.05007517 0.05633448 0.06449679 0.07075147 0.07939743
[13] 0.09191649 0.09757841 0.10962295 0.12106330 0.14439877 0.16526788
[19] 0.18552270 0.19749534 0.21976894 0.25073848 0.27208990 0.30673908
[25] 0.33703663 0.33557761 0.35823990 0.38814546
> postscript(file="/var/www/html/rcomp/tmp/1fuqn1260377739.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2ocv91260377739.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/3flbz1260377739.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/4c76d1260377739.tab") 
> 
> system("convert tmp/1fuqn1260377739.ps tmp/1fuqn1260377739.png")
> system("convert tmp/2ocv91260377739.ps tmp/2ocv91260377739.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.876   0.364   1.011