R version 2.13.0 (2011-04-13)
Copyright (C) 2011 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: i486-pc-linux-gnu (32-bit)

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> x <- c(12008.00,9169.00,8788.00,8417.00,8247.00,8197.00,8236.00,8253.00,7733.00,8366.00,8626.00,8863.00,10102.00,8463.00,9114.00,8563.00,8872.00,8301.00,8301.00,8278.00,7736.00,7973.00,8268.00,9476.00,11100.00,8962.00,9173.00,8738.00,8459.00,8078.00,8411.00,8291.00,7810.00,8616.00,8312.00,9692.00,9911.00,8915.00,9452.00,9112.00,8472.00,8230.00,8384.00,8625.00,8221.00,8649.00,8625.00,10443.00,10357.00,8586.00,8892.00,8329.00,8101.00,7922.00,8120.00,7838.00,7735.00,8406.00,8209.00,9451.00,10041.00,9411.00,10405.00,8467.00,8464.00,8102.00,7627.00,7513.00,7510.00,8291.00,8064.00,9383.00,9706.00,8579.00,9474.00,8318.00,8213.00,8059.00,9111.00,7708.00,7680.00,8014.00,8007.00,8718.00,9486.00,9113.00,9025.00,8476.00,7952.00,7759.00,7835.00,7600.00,7651.00,8319.00,8812.00,8630.00)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '2'
> par7 = '1'
> par6 = '1'
> par5 = '12'
> par4 = '1'
> par3 = '0'
> par2 = '1'
> par1 = '12'
> 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      ma1     sar1     sar2    sma1
      0.4883  -0.0597  -0.9077  -0.0971  0.4068
s.e.  0.2085   0.2232   0.7351   0.4810  0.7213

sigma^2 estimated as 166658:  log likelihood = -538.02,  aic = 1088.04
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 85 
End = 96 
Frequency = 1 
 [1]  9544.168  8973.329 10074.507  8419.236  8385.546  8111.191  8322.143
 [8]  7614.194  7598.013  8145.227  8042.256  9101.769

$se
Time Series:
Start = 85 
End = 96 
Frequency = 1 
 [1] 408.2394 444.1512 452.2935 454.2135 454.6701 454.7789 454.8049 454.8110
 [9] 454.8125 454.8129 454.8129 454.8129

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 85 
End = 96 
Frequency = 1 
 [1] 8744.019 8102.793 9188.012 7528.977 7494.392 7219.825 7430.726 6722.764
 [9] 6706.580 7253.794 7150.823 8210.336
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 85 
End = 96 
Frequency = 1 
 [1] 10344.317  9843.866 10961.003  9309.494  9276.699  9002.558  9213.561
 [8]  8505.623  8489.445  9036.660  8933.689  9993.203
> 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$pred))
 [1] 12008.000  9169.000  8788.000  8417.000  8247.000  8197.000  8236.000
 [8]  8253.000  7733.000  8366.000  8626.000  8863.000 10102.000  8463.000
[15]  9114.000  8563.000  8872.000  8301.000  8301.000  8278.000  7736.000
[22]  7973.000  8268.000  9476.000 11100.000  8962.000  9173.000  8738.000
[29]  8459.000  8078.000  8411.000  8291.000  7810.000  8616.000  8312.000
[36]  9692.000  9911.000  8915.000  9452.000  9112.000  8472.000  8230.000
[43]  8384.000  8625.000  8221.000  8649.000  8625.000 10443.000 10357.000
[50]  8586.000  8892.000  8329.000  8101.000  7922.000  8120.000  7838.000
[57]  7735.000  8406.000  8209.000  9451.000 10041.000  9411.000 10405.000
[64]  8467.000  8464.000  8102.000  7627.000  7513.000  7510.000  8291.000
[71]  8064.000  9383.000  9706.000  8579.000  9474.000  8318.000  8213.000
[78]  8059.000  9111.000  7708.000  7680.000  8014.000  8007.000  8718.000
[85]  9544.168  8973.329 10074.507  8419.236  8385.546  8111.191  8322.143
[92]  7614.194  7598.013  8145.227  8042.256  9101.769
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 85 
End = 96 
Frequency = 1 
 [1] 0.04277370 0.04949681 0.04489485 0.05394949 0.05422069 0.05606808
 [7] 0.05464997 0.05973200 0.05985940 0.05583796 0.05655290 0.04996972
> postscript(file="/var/wessaorg/rcomp/tmp/1l3z91323528195.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/wessaorg/rcomp/tmp/20cux1323528195.ps",horizontal=F,onefile=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/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/wessaorg/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/wessaorg/rcomp/tmp/3x30m1323528195.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/wessaorg/rcomp/tmp/4971g1323528195.tab") 
> 
> try(system("convert tmp/1l3z91323528195.ps tmp/1l3z91323528195.png",intern=TRUE))
character(0)
> try(system("convert tmp/20cux1323528195.ps tmp/20cux1323528195.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  2.100   0.321   2.425