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(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 = '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
      0.6108  -0.4517  0.3025  -0.4565  0.6171  -0.7501
s.e.  0.4771   0.3426  0.3804   0.4346  0.3190   0.4659

sigma^2 estimated as 35841270:  log likelihood = -324.78,  aic = 663.55
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 34 
End = 61 
Frequency = 1 
 [1] 250718.9 251444.4 252858.3 254804.5 255574.1 255592.8 255845.3 256224.0
 [9] 256346.8 256327.2 256374.3 256449.1 256467.6 256459.3 256468.6 256483.5
[17] 256486.0 256483.5 256485.5 256488.5 256488.7 256488.1 256488.5 256489.1
[25] 256489.1 256488.9 256489.0 256489.2

$se
Time Series:
Start = 34 
End = 61 
Frequency = 1 
 [1]  6006.443  9168.037 12466.756 13971.263 14705.638 15522.095 16410.796
 [8] 17114.166 17701.082 18298.354 18896.612 19451.295 19975.645 20493.695
[15] 21002.717 21494.639 21972.945 22442.731 22903.586 23354.302 23796.026
[22] 24230.082 24656.626 25075.696 25487.797 25893.426 26292.822 26686.193

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 34 
End = 61 
Frequency = 1 
 [1] 238946.2 233475.0 228423.4 227420.8 226751.1 225169.5 223680.2 222680.2
 [9] 221652.7 220462.5 219337.0 218324.6 217315.3 216291.7 215303.2 214354.0
[17] 213419.0 212495.8 211594.4 210714.0 209848.5 208997.1 208161.5 207340.7
[25] 206533.0 205737.8 204955.1 204184.2
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 34 
End = 61 
Frequency = 1 
 [1] 262491.5 269413.7 277293.1 282188.2 284397.2 286016.1 288010.5 289767.8
 [9] 291041.0 292192.0 293411.7 294573.6 295619.8 296627.0 297633.9 298613.0
[17] 299553.0 300471.3 301376.5 302262.9 303128.9 303979.0 304815.5 305637.5
[25] 306445.2 307240.1 308023.0 308794.1
> 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$pred))
 [1] 286602.0 283042.0 276687.0 277915.0 277128.0 277103.0 275037.0 270150.0
 [9] 267140.0 264993.0 287259.0 291186.0 292300.0 288186.0 281477.0 282656.0
[17] 280190.0 280408.0 276836.0 275216.0 274352.0 271311.0 289802.0 290726.0
[25] 292300.0 278506.0 269826.0 265861.0 269034.0 264176.0 255198.0 253353.0
[33] 246057.0 250718.9 251444.4 252858.3 254804.5 255574.1 255592.8 255845.3
[41] 256224.0 256346.8 256327.2 256374.3 256449.1 256467.6 256459.3 256468.6
[49] 256483.5 256486.0 256483.5 256485.5 256488.5 256488.7 256488.1 256488.5
[57] 256489.1 256489.1 256488.9 256489.0 256489.2
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 34 
End = 61 
Frequency = 1 
 [1] 0.02395689 0.03646149 0.04930334 0.05483130 0.05753962 0.06072979
 [7] 0.06414343 0.06679377 0.06905130 0.07138670 0.07370712 0.07584856
[13] 0.07788760 0.07991012 0.08189197 0.08380514 0.08566918 0.08750164
[19] 0.08929780 0.09105400 0.09277611 0.09446865 0.09613151 0.09776515
[25] 0.09937185 0.10095338 0.10251051 0.10404413
> postscript(file="/var/www/html/rcomp/tmp/11sql1260547516.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2fb4e1260547516.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/3s8ef1260547516.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/4o8ys1260547516.tab") 
> 
> system("convert tmp/11sql1260547516.ps tmp/11sql1260547516.png")
> system("convert tmp/2fb4e1260547516.ps tmp/2fb4e1260547516.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.768   0.336   3.135