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(2.83,2.72,2.73,2.72,2.77,2.61,2.47,2.30,2.38,2.43,2.39,2.60,2.84,2.87,2.92,2.08,3.33,3.48,3.57,3.66,3.77,3.75,3.75,3.81,3.82,3.89,4.05,4.10,4.07,4.26,4.40,4.61,4.63,4.48,4.46,4.45,4.32,4.52,4.21,3.97,4.12,4.50,4.73,5.26,4.52,4.94,4.95,3.52,3.85,2.41,2.95,2.68,2.53,2.44,2.16,2.20,2.10,2.29,2.03,2.05,2.07)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '2'
> par6 = '3'
> par5 = '12'
> par4 = '0'
> par3 = '2'
> par2 = '1'
> par1 = '13'
> 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
      -0.0682  -0.1506  -0.1276  -1.2192  0.4047  -0.0624
s.e.   1.7331   0.6688   0.2926   1.7364  2.2021   0.8117

sigma^2 estimated as 0.07504:  log likelihood = -5.08,  aic = 24.16
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 34 
End = 61 
Frequency = 1 
 [1] 4.720195 4.814434 4.922198 5.019478 5.114919 5.210340 5.307376 5.404539
 [9] 5.501454 5.598160 5.694901 5.791704 5.888523 5.985328 6.082123 6.178919
[17] 6.275718 6.372518 6.469317 6.566116 6.662915 6.759714 6.856513 6.953312
[25] 7.050111 7.146910 7.243709 7.340509

$se
Time Series:
Start = 34 
End = 61 
Frequency = 1 
 [1] 0.2739317 0.3363678 0.3966015 0.4533956 0.5229303 0.5970505 0.6739179
 [8] 0.7526934 0.8344359 0.9192450 1.0069277 1.0972366 1.1900904 1.2854495
[15] 1.3832640 1.4834669 1.5859956 1.6907965 1.7978219 1.9070265 2.0183667
[22] 2.1318017 2.2472929 2.3648040 2.4843006 2.6057499 2.7291208 2.8543836

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 34 
End = 61 
Frequency = 1 
 [1] 4.183289 4.155153 4.144859 4.130822 4.089976 4.040121 3.986497 3.929260
 [9] 3.865959 3.796440 3.721323 3.641120 3.555946 3.465846 3.370925 3.271324
[17] 3.167166 3.058557 2.945586 2.828344 2.706916 2.581383 2.451819 2.318296
[25] 2.180882 2.039641 1.894633 1.745917
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 34 
End = 61 
Frequency = 1 
 [1]  5.257101  5.473715  5.699537  5.908133  6.139862  6.380559  6.628255
 [8]  6.879818  7.136948  7.399880  7.668480  7.942287  8.221100  8.504809
[15]  8.793320  9.086514  9.384269  9.686479  9.993048 10.303888 10.618914
[22] 10.938045 11.261207 11.588328 11.919341 12.254180 12.592786 12.935100
> 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$pred))
 [1] 2.830000 2.720000 2.730000 2.720000 2.770000 2.610000 2.470000 2.300000
 [9] 2.380000 2.430000 2.390000 2.600000 2.840000 2.870000 2.920000 2.080000
[17] 3.330000 3.480000 3.570000 3.660000 3.770000 3.750000 3.750000 3.810000
[25] 3.820000 3.890000 4.050000 4.100000 4.070000 4.260000 4.400000 4.610000
[33] 4.630000 4.720195 4.814434 4.922198 5.019478 5.114919 5.210340 5.307376
[41] 5.404539 5.501454 5.598160 5.694901 5.791704 5.888523 5.985328 6.082123
[49] 6.178919 6.275718 6.372518 6.469317 6.566116 6.662915 6.759714 6.856513
[57] 6.953312 7.050111 7.146910 7.243709 7.340509
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 34 
End = 61 
Frequency = 1 
 [1] 0.05803397 0.06986652 0.08057406 0.09032724 0.10223628 0.11458956
 [7] 0.12697762 0.13927058 0.15167552 0.16420486 0.17681213 0.18944972
[13] 0.20210338 0.21476678 0.22743112 0.24008519 0.25271939 0.26532629
[19] 0.27789979 0.29043447 0.30292548 0.31536862 0.32776031 0.34009749
[25] 0.35237750 0.36459810 0.37675736 0.38885366
> postscript(file="/var/www/html/rcomp/tmp/1ie091260450508.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2me621260450508.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/3jy9u1260450508.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/4ofdm1260450508.tab") 
> 
> system("convert tmp/1ie091260450508.ps tmp/1ie091260450508.png")
> system("convert tmp/2me621260450508.ps tmp/2me621260450508.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.809   0.339   0.946