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(133.91,133.14,135.31,133.09,135.39,131.85,130.25,127.65,118.30,119.73,122.51,123.28,133.52,153.20,163.63,168.45,166.26,162.31,161.56,156.59,157.97,158.68,163.55,162.89,164.95,159.82,159.05,166.76,164.55,163.22,160.68,155.24,157.60,156.56,154.82,151.11,149.65,148.99,148.53,146.70,145.11,142.70,143.59,140.96,140.77,139.81,140.58,139.59,138.05,136.06,135.98,134.75,132.22,135.37,138.84,138.83,136.55,135.63,139.14,136.09)
> 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
      0.4270  0.0087  -0.5293  -0.0350  0.0946  0.9341
s.e.  0.2248  0.2597   0.2225   0.1934  0.2069  0.2228

sigma^2 estimated as 17.09:  log likelihood = -90.26,  aic = 194.52
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1] 150.4021 148.2322 148.1545 150.6630 152.8818 153.8923 153.0154 151.4755
 [9] 150.2755 150.2137 150.9919 151.9588 152.4111 152.2008 151.6033 151.1069
[17] 151.0010 151.2677 151.6434 151.8622 151.8177 151.6018 151.3934 151.3261
[25] 151.4098 151.5553 151.6537 151.6527

$se
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1]  4.247528  7.367750 10.231081 13.676707 16.366527 18.397014 19.721428
 [8] 20.793692 21.837568 23.053484 24.391347 25.725725 26.909477 27.926494
[15] 28.832739 29.716257 30.629546 31.577583 32.521838 33.421510 34.260375
[22] 35.052484 35.824190 36.596198 37.372612 38.143439 38.894998 39.620502

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1] 142.07691 133.79141 128.10158 123.85661 120.80342 117.83413 114.36145
 [8] 110.71986 107.47386 105.02890 103.18489 101.53639  99.66856  97.46491
[15]  95.09109  92.86299  90.96707  89.37566  87.90062  86.35605  84.66740
[22]  82.89893  81.17800  79.59755  78.15950  76.79413  75.41954  73.99656
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1] 158.7272 162.6730 168.2074 177.4693 184.9602 189.9504 191.6694 192.2311
 [9] 193.0771 195.3986 198.7990 202.3812 205.1537 206.9368 208.1154 209.3507
[17] 211.0349 213.1598 215.3862 217.3684 218.9681 220.3047 221.6088 223.0546
[25] 224.6601 226.3164 227.8879 229.3089
> 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$pred))
 [1] 133.9100 133.1400 135.3100 133.0900 135.3900 131.8500 130.2500 127.6500
 [9] 118.3000 119.7300 122.5100 123.2800 133.5200 153.2000 163.6300 168.4500
[17] 166.2600 162.3100 161.5600 156.5900 157.9700 158.6800 163.5500 162.8900
[25] 164.9500 159.8200 159.0500 166.7600 164.5500 163.2200 160.6800 155.2400
[33] 150.4021 148.2322 148.1545 150.6630 152.8818 153.8923 153.0154 151.4755
[41] 150.2755 150.2137 150.9919 151.9588 152.4111 152.2008 151.6033 151.1069
[49] 151.0010 151.2677 151.6434 151.8622 151.8177 151.6018 151.3934 151.3261
[57] 151.4098 151.5553 151.6537 151.6527
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1] 0.02824115 0.04970411 0.06905684 0.09077684 0.10705346 0.11954475
 [7] 0.12888521 0.13727429 0.14531690 0.15347121 0.16154073 0.16929407
[13] 0.17655847 0.18348449 0.19018548 0.19665724 0.20284336 0.20875295
[19] 0.21446256 0.22007785 0.22566781 0.23121417 0.23662977 0.24183667
[25] 0.24683084 0.25168007 0.25647240 0.26125807
> postscript(file="/var/www/html/rcomp/tmp/1ke551260535683.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2efs21260535683.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/3z5851260535683.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/4029s1260535683.tab") 
> system("convert tmp/1ke551260535683.ps tmp/1ke551260535683.png")
> system("convert tmp/2efs21260535683.ps tmp/2efs21260535683.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.726   0.306   2.050