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(117.09,116.77,119.39,122.49,124.08,118.29,112.94,113.79,114.43,118.70,120.36,118.27,118.34,117.82,117.65,118.18,121.02,124.78,131.16,130.14,131.75,134.73,135.35,140.32,136.35,131.60,128.90,133.89,138.25,146.23,144.76,149.30,156.80,159.08,165.12,163.14,153.43,151.01,154.72,154.58,155.63,161.67,163.51,162.91,164.80,164.98,154.54,148.60,149.19,150.61)
> 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
      -0.3088  -0.4957  -0.5420  0.8123  0.9333  0.8873
s.e.   0.3900   0.2691   0.3656  0.3702  0.2873  0.3795

sigma^2 estimated as 5.203:  log likelihood = -48.9,  aic = 111.81
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 23 
End = 50 
Frequency = 1 
 [1] 136.1297 138.4780 137.4139 135.8198 135.5665 137.0117 137.5551 136.8082
 [9] 135.9862 136.3156 137.0262 137.0891 136.5389 136.2924 136.6072 136.9304
[17] 136.8082 136.5151 136.4910 136.7099 136.8131 136.6858 136.5553 136.6028
[25] 136.7218 136.7323 136.6443 136.6018

$se
Time Series:
Start = 23 
End = 50 
Frequency = 1 
 [1]  2.365847  4.276607  5.900484  7.116934  7.766500  8.380566  9.126648
 [8]  9.934297 10.558184 11.055362 11.558947 12.130937 12.682663 13.154057
[15] 13.581240 14.026828 14.490583 14.929429 15.328113 15.714163 16.109794
[22] 16.505459 16.881235 17.237986 17.590981 17.946518 18.296172 18.632613

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 23 
End = 50 
Frequency = 1 
 [1] 131.4926 130.0959 125.8490 121.8706 120.3442 120.5858 119.6669 117.3370
 [9] 115.2921 114.6471 114.3707 113.3125 111.6809 110.5105 109.9879 109.4378
[17] 108.4066 107.2534 106.4479 105.9102 105.2380 104.3351 103.4681 102.8163
[25] 102.2435 101.5571 100.7838 100.0818
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 23 
End = 50 
Frequency = 1 
 [1] 140.7667 146.8602 148.9789 149.7690 150.7889 153.4376 155.4433 156.2795
 [9] 156.6802 157.9842 159.6818 160.8657 161.3969 162.0744 163.2264 164.4230
[17] 165.2097 165.7768 166.5341 167.5097 168.3883 169.0365 169.6425 170.3892
[25] 171.2001 171.9075 172.5048 173.1217
> 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$pred))
 [1] 117.0900 116.7700 119.3900 122.4900 124.0800 118.2900 112.9400 113.7900
 [9] 114.4300 118.7000 120.3600 118.2700 118.3400 117.8200 117.6500 118.1800
[17] 121.0200 124.7800 131.1600 130.1400 131.7500 134.7300 136.1297 138.4780
[25] 137.4139 135.8198 135.5665 137.0117 137.5551 136.8082 135.9862 136.3156
[33] 137.0262 137.0891 136.5389 136.2924 136.6072 136.9304 136.8082 136.5151
[41] 136.4910 136.7099 136.8131 136.6858 136.5553 136.6028 136.7218 136.7323
[49] 136.6443 136.6018
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 23 
End = 50 
Frequency = 1 
 [1] 0.01737936 0.03088292 0.04293949 0.05239984 0.05728921 0.06116679
 [7] 0.06634904 0.07261475 0.07764160 0.08110119 0.08435574 0.08848943
[13] 0.09288682 0.09651347 0.09941820 0.10243765 0.10591899 0.10936100
[19] 0.11230129 0.11494529 0.11775033 0.12075472 0.12362197 0.12619061
[25] 0.12866257 0.13125297 0.13389633 0.13640097
> postscript(file="/var/www/html/rcomp/tmp/18gkv1260360651.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/24vf81260360651.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/3btt01260360651.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/4c9mb1260360651.tab") 
> 
> system("convert tmp/18gkv1260360651.ps tmp/18gkv1260360651.png")
> system("convert tmp/24vf81260360651.ps tmp/24vf81260360651.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.773   0.314   1.003