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(2849.27,2921.44,2981.85,3080.58,3106.22,3119.31,3061.26,3097.31,3161.69,3257.16,3277.01,3295.32,3363.99,3494.17,3667.03,3813.06,3917.96,3895.51,3801.06,3570.12,3701.61,3862.27,3970.1,4138.52,4199.75,4290.89,4443.91,4502.64,4356.98,4591.27,4696.96,4621.4,4562.84,4202.52,4296.49,4435.23,4105.18,4116.68,3844.49,3720.98,3674.4,3857.62,3801.06,3504.37,3032.6,3047.03,2962.34,2197.82,2014.45,1862.83,1905.41,1810.99,1670.07,1864.44,2052.02,2029.6,2070.83,2293.41,2443.27,2513.17)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '0'
> par7 = '0'
> par6 = '3'
> par5 = '12'
> par4 = '1'
> par3 = '2'
> par2 = '1'
> par1 = '12'
> 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     sma1
      -0.0546  0.3531  -0.4753  -0.9382  -0.9450  0.9834  -0.0980
s.e.   0.2563  0.2707   0.2407   0.2902   0.2252  0.2843   0.3693

sigma^2 estimated as 11216:  log likelihood = -115.26,  aic = 246.52
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1] 4678.821 4709.712 4755.893 4926.891 5053.326 5200.743 5391.744 5470.041
 [9] 5360.718 5581.186 5691.253 5624.883 5716.095 5779.344 5854.110 6041.701
[17] 6184.732 6346.305 6557.296 6654.400 6567.169 6806.360 6937.055 6888.458
[25] 6999.874 7081.280 7176.529 7382.599

$se
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1]  110.7596  161.7068  175.5547  178.3571  179.7788  185.1797  197.7931
 [8]  217.5761  238.8384  260.6564  281.9268  304.9374  380.4004  452.7596
[15]  498.5309  531.4616  562.3212  601.2830  648.7121  703.6883  760.3562
[22]  818.5873  876.8004  937.4848 1040.7780 1145.5380 1230.1730 1303.8055

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1] 4461.732 4392.766 4411.805 4577.312 4700.959 4837.791 5004.069 5043.591
 [9] 4892.594 5070.299 5138.677 5027.206 4970.510 4891.935 4876.989 5000.036
[17] 5082.582 5167.790 5285.820 5275.171 5076.871 5201.929 5218.526 5050.988
[25] 4959.949 4836.025 4765.390 4827.140
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1] 4895.909 5026.657 5099.980 5276.471 5405.692 5563.695 5779.418 5896.490
 [9] 5828.841 6092.073 6243.830 6222.560 6461.680 6666.753 6831.230 7083.365
[17] 7286.882 7524.820 7828.771 8033.629 8057.467 8410.791 8655.584 8725.928
[25] 9039.799 9326.534 9587.668 9938.058
> 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$pred))
 [1] 2849.270 2921.440 2981.850 3080.580 3106.220 3119.310 3061.260 3097.310
 [9] 3161.690 3257.160 3277.010 3295.320 3363.990 3494.170 3667.030 3813.060
[17] 3917.960 3895.510 3801.060 3570.120 3701.610 3862.270 3970.100 4138.520
[25] 4199.750 4290.890 4443.910 4502.640 4356.980 4591.270 4696.960 4621.400
[33] 4678.821 4709.712 4755.893 4926.891 5053.326 5200.743 5391.744 5470.041
[41] 5360.718 5581.186 5691.253 5624.883 5716.095 5779.344 5854.110 6041.701
[49] 6184.732 6346.305 6557.296 6654.400 6567.169 6806.360 6937.055 6888.458
[57] 6999.874 7081.280 7176.529 7382.599
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1] 0.02367254 0.03433475 0.03691308 0.03620073 0.03557634 0.03560639
 [7] 0.03668444 0.03977596 0.04455344 0.04670269 0.04953685 0.05421222
[13] 0.06654900 0.07834100 0.08515914 0.08796556 0.09092087 0.09474537
[19] 0.09892983 0.10574781 0.11578142 0.12026800 0.12639374 0.13609503
[25] 0.14868525 0.16176991 0.17141615 0.17660521
> postscript(file="/var/www/html/rcomp/tmp/1wqfa1260553293.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2miuz1260553293.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/38sxo1260553293.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/4dj141260553293.tab") 
> system("convert tmp/1wqfa1260553293.ps tmp/1wqfa1260553293.png")
> system("convert tmp/2miuz1260553293.ps tmp/2miuz1260553293.png")
> 
> 
> proc.time()
   user  system elapsed 
  1.967   0.343   3.112