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(128.6,128.9,129.06,129.23,129.27,129.33,129.35,129.31,129.4,129.49,129.47,129.46,129.45,129.28,129.2,129.25,129.14,129.11,129.02,129.08,128.99,129.11,129.08,129.19,129.23,129.25,129.31,129.33,129.39,129.55,129.43,129.45,129.57,129.76,129.92,130.08,130.41,130.84,131.24,131.49,131.74,132.34,133.5,134.43,136.5,137.41,138.02,138.15,138.24,138.2,138.31,138.65,139.3,139.8,140.52,141.57,141.77,141.66,141.36,141.17)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '2'
> par7 = '0'
> par6 = '3'
> par5 = '12'
> par4 = '0'
> par3 = '1'
> par2 = '1'
> par1 = '1'
> 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     sar1     sar2
      -0.1483  0.2770  -0.5746  0.2785  0.2934  0.9913  -0.6154  -0.3650
s.e.   0.2010  0.1908   0.1766  0.1272  0.1340  0.1334   0.2747   0.2909

sigma^2 estimated as 0.004177:  log likelihood = 35.17,  aic = -52.35
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1] 129.3699 129.2760 129.2351 129.2435 129.1860 129.2995 129.2306 129.2477
 [9] 129.1903 129.1602 129.2141 129.2385 129.2644 129.3332 129.3120 129.3227
[17] 129.2878 129.2674 129.2318 129.2700 129.2270 129.2432 129.1977 129.2317
[25] 129.1888 129.2369 129.2087 129.2552

$se
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1] 0.06735632 0.09982185 0.15005639 0.19899517 0.24046376 0.26758740
 [7] 0.28951092 0.30769474 0.32789791 0.34721350 0.36743590 0.38480758
[13] 0.39202974 0.39748185 0.40022191 0.40149266 0.40294510 0.40498799
[19] 0.40791949 0.41074150 0.41339538 0.41552711 0.41772616 0.41984601
[25] 0.42236732 0.42476739 0.42735972 0.42972334

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1] 129.2378 129.0803 128.9410 128.8534 128.7146 128.7750 128.6631 128.6447
 [9] 128.5476 128.4796 128.4939 128.4843 128.4960 128.5542 128.5275 128.5358
[17] 128.4980 128.4736 128.4323 128.4649 128.4167 128.4288 128.3789 128.4088
[25] 128.3610 128.4044 128.3711 128.4130
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1] 129.5019 129.4716 129.5292 129.6335 129.6573 129.8239 129.7980 129.8508
 [9] 129.8330 129.8407 129.9343 129.9927 130.0328 130.1123 130.0964 130.1096
[17] 130.0775 130.0611 130.0313 130.0750 130.0372 130.0577 130.0164 130.0546
[25] 130.0167 130.0695 130.0463 130.0975
> 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$pred))
 [1] 128.6000 128.9000 129.0600 129.2300 129.2700 129.3300 129.3500 129.3100
 [9] 129.4000 129.4900 129.4700 129.4600 129.4500 129.2800 129.2000 129.2500
[17] 129.1400 129.1100 129.0200 129.0800 128.9900 129.1100 129.0800 129.1900
[25] 129.2300 129.2500 129.3100 129.3300 129.3900 129.5500 129.4300 129.4500
[33] 129.3699 129.2760 129.2351 129.2435 129.1860 129.2995 129.2306 129.2477
[41] 129.1903 129.1602 129.2141 129.2385 129.2644 129.3332 129.3120 129.3227
[49] 129.2878 129.2674 129.2318 129.2700 129.2270 129.2432 129.1977 129.2317
[57] 129.1888 129.2369 129.2087 129.2552
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1] 0.0005206493 0.0007721610 0.0011611120 0.0015396923 0.0018613770
 [6] 0.0020695165 0.0022402669 0.0023806586 0.0025381002 0.0026882397
[11] 0.0028436204 0.0029774997 0.0030327744 0.0030733154 0.0030950105
[16] 0.0031045800 0.0031166533 0.0031329487 0.0031564945 0.0031773925
[21] 0.0031989864 0.0032150784 0.0032332331 0.0032487857 0.0032693792
[26] 0.0032867335 0.0033075145 0.0033246111
> postscript(file="/var/www/html/rcomp/tmp/19veb1260432431.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/28pla1260432431.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/30bol1260432431.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/4ja6z1260432431.tab") 
> 
> system("convert tmp/19veb1260432431.ps tmp/19veb1260432431.png")
> system("convert tmp/28pla1260432431.ps tmp/28pla1260432431.png")
> 
> 
> proc.time()
   user  system elapsed 
  2.943   1.020   3.785