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)
> 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
      0.6665  -0.4510  0.2736  -0.5334  0.5334  -0.9999
s.e.  0.1994   0.2279  0.1841   0.1391  0.1379   0.1522

sigma^2 estimated as 30896792:  log likelihood = -385.01,  aic = 784.02
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 40 
End = 67 
Frequency = 1 
 [1] 254214.5 257801.9 266942.7 271148.0 270810.0 271189.5 272745.5 273519.0
 [9] 273436.6 273458.6 273722.1 273865.2 273847.8 273843.8 273888.1 273914.7
[17] 273911.3 273909.2 273916.6 273921.6 273920.9 273920.3 273921.6 273922.5
[25] 273922.4 273922.2 273922.4 273922.6

$se
Time Series:
Start = 40 
End = 67 
Frequency = 1 
 [1]  5751.238  8741.490 11498.426 12135.161 12197.063 12276.241 12391.774
 [8] 12435.297 12441.201 12448.516 12460.289 12466.016 12466.774 12467.690
[15] 12469.453 12470.409 12470.510 12470.622 12470.911 12471.080 12471.093
[22] 12471.105 12471.153 12471.183 12471.185 12471.186 12471.194 12471.199

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 40 
End = 67 
Frequency = 1 
 [1] 242942.0 240668.6 244405.8 247363.0 246903.8 247128.1 248457.7 249145.8
 [9] 249051.8 249059.5 249300.0 249431.8 249412.9 249407.1 249448.0 249472.7
[17] 249469.1 249466.8 249473.6 249478.2 249477.6 249477.0 249478.1 249479.0
[25] 249478.8 249478.7 249478.9 249479.0
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 40 
End = 67 
Frequency = 1 
 [1] 265486.9 274935.2 289479.7 294932.9 294716.3 295251.0 297033.4 297892.1
 [9] 297821.3 297857.7 298144.3 298298.6 298282.7 298280.5 298328.2 298356.7
[17] 298353.5 298351.6 298359.6 298364.9 298364.3 298363.7 298365.0 298366.0
[25] 298365.9 298365.7 298366.0 298366.1
> 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$pred))
 [1] 267413.0 267366.0 264777.0 258863.0 254844.0 254868.0 277267.0 285351.0
 [9] 286602.0 283042.0 276687.0 277915.0 277128.0 277103.0 275037.0 270150.0
[17] 267140.0 264993.0 287259.0 291186.0 292300.0 288186.0 281477.0 282656.0
[25] 280190.0 280408.0 276836.0 275216.0 274352.0 271311.0 289802.0 290726.0
[33] 292300.0 278506.0 269826.0 265861.0 269034.0 264176.0 255198.0 254214.5
[41] 257801.9 266942.7 271148.0 270810.0 271189.5 272745.5 273519.0 273436.6
[49] 273458.6 273722.1 273865.2 273847.8 273843.8 273888.1 273914.7 273911.3
[57] 273909.2 273916.6 273921.6 273920.9 273920.3 273921.6 273922.5 273922.4
[65] 273922.2 273922.4 273922.6
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 40 
End = 67 
Frequency = 1 
 [1] 0.02262357 0.03390778 0.04307450 0.04475476 0.04503919 0.04526812
 [7] 0.04543346 0.04546411 0.04549941 0.04552248 0.04552167 0.04551880
[13] 0.04552446 0.04552848 0.04552755 0.04552662 0.04552754 0.04552831
[19] 0.04552813 0.04552792 0.04552807 0.04552822 0.04552819 0.04552815
[25] 0.04552817 0.04552820 0.04552820 0.04552819
> postscript(file="/var/www/html/rcomp/tmp/1nswg1260541743.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2pbzs1260541743.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/3kqo41260541743.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/4pgwd1260541743.tab") 
> system("convert tmp/1nswg1260541743.ps tmp/1nswg1260541743.png")
> system("convert tmp/2pbzs1260541743.ps tmp/2pbzs1260541743.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.730   0.322   1.006