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(7.1,6.9,6.8,7.5,7.6,7.8,8.0,8.1,8.2,8.3,8.2,8.0,7.9,7.6,7.6,8.3,8.4,8.4,8.4,8.4,8.6,8.9,8.8,8.3,7.5,7.2,7.4,8.8,9.3,9.3,8.7,8.2,8.3,8.5,8.6,8.5,8.2,8.1,7.9,8.6,8.7,8.7,8.5,8.4,8.5,8.7,8.7,8.6,8.5,8.3,8.0,8.2,8.1,8.1,8.0,7.9,7.9,8.0,8.0,7.9,8.0,7.7,7.2,7.5,7.3,7.0,7.0,7.0,7.2,7.3,7.1,6.8,6.4,6.1,6.5,7.7,7.9,7.5,6.9,6.6,6.9,7.7,8.0,8.0,7.7,7.3,7.4,8.1,8.3,8.2)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '2'
> par7 = '1'
> 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    sar1     sar2
      0.6027  0.0427  -0.6025  -1.2240  -0.1645  0.3897  0.0385  -0.5150
s.e.  0.2924  0.3631   0.2395   0.3564   0.5433  0.2878  0.3763   0.1638
         sma1
      -0.2265
s.e.   0.5020

sigma^2 estimated as 0.01908:  log likelihood = 15.69,  aic = -11.38
Warning messages:
1: In log(s2) : NaNs produced
2: In arima(x[1:nx], order = c(par6, par3, par7), seasonal = list(order = c(par8,  :
  possible convergence problem: optim gave code=1
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 63 
End = 90 
Frequency = 1 
 [1] 7.358200 7.519499 7.308357 7.200795 7.065262 7.018439 7.193789 7.286346
 [9] 7.121569 6.717908 6.425061 6.106375 5.925659 6.536964 6.543849 6.403010
[17] 6.042916 5.779193 5.848726 5.945382 5.828448 5.500262 5.130198 4.815684
[25] 4.541501 5.048059 5.015560 4.890165

$se
Time Series:
Start = 63 
End = 90 
Frequency = 1 
 [1] 0.1411569 0.2452444 0.3114446 0.3289020 0.3289024 0.3289805 0.3282021
 [8] 0.3331749 0.3577360 0.3939887 0.4221193 0.4343351 0.4671790 0.5079902
[15] 0.5488057 0.5760742 0.5931469 0.6044419 0.6171340 0.6358213 0.6629354
[22] 0.6947050 0.7250746 0.7496872 0.7802245 0.8120050 0.8434604 0.8712183

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 63 
End = 90 
Frequency = 1 
 [1] 7.081532 7.038820 6.697925 6.556147 6.420613 6.373637 6.550512 6.633324
 [9] 6.420406 5.945690 5.597707 5.255079 5.009988 5.541303 5.468190 5.273904
[17] 4.880348 4.594487 4.639144 4.699172 4.529094 4.138641 3.709051 3.346297
[25] 3.012261 3.456530 3.362378 3.182577
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 63 
End = 90 
Frequency = 1 
 [1] 7.634868 8.000178 7.918788 7.845443 7.709911 7.663241 7.837065 7.939369
 [9] 7.822732 7.490126 7.252415 6.957672 6.841329 7.532625 7.619508 7.532115
[17] 7.205484 6.963900 7.058309 7.191592 7.127801 6.861884 6.551344 6.285070
[25] 6.070741 6.639589 6.668743 6.597753
> 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$pred))
 [1] 7.100000 6.900000 6.800000 7.500000 7.600000 7.800000 8.000000 8.100000
 [9] 8.200000 8.300000 8.200000 8.000000 7.900000 7.600000 7.600000 8.300000
[17] 8.400000 8.400000 8.400000 8.400000 8.600000 8.900000 8.800000 8.300000
[25] 7.500000 7.200000 7.400000 8.800000 9.300000 9.300000 8.700000 8.200000
[33] 8.300000 8.500000 8.600000 8.500000 8.200000 8.100000 7.900000 8.600000
[41] 8.700000 8.700000 8.500000 8.400000 8.500000 8.700000 8.700000 8.600000
[49] 8.500000 8.300000 8.000000 8.200000 8.100000 8.100000 8.000000 7.900000
[57] 7.900000 8.000000 8.000000 7.900000 8.000000 7.700000 7.358200 7.519499
[65] 7.308357 7.200795 7.065262 7.018439 7.193789 7.286346 7.121569 6.717908
[73] 6.425061 6.106375 5.925659 6.536964 6.543849 6.403010 6.042916 5.779193
[81] 5.848726 5.945382 5.828448 5.500262 5.130198 4.815684 4.541501 5.048059
[89] 5.015560 4.890165
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 63 
End = 90 
Frequency = 1 
 [1] 0.01918362 0.03261447 0.04261486 0.04567579 0.04655205 0.04687374
 [7] 0.04562299 0.04572592 0.05023276 0.05864753 0.06569888 0.07112813
[13] 0.07884002 0.07771042 0.08386589 0.08996928 0.09815574 0.10458932
[19] 0.10551597 0.10694374 0.11374133 0.12630397 0.14133464 0.15567617
[25] 0.17179880 0.16085489 0.16816873 0.17815725
> postscript(file="/var/www/html/rcomp/tmp/11os41260538713.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2ztxc1260538713.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/3vdzo1260538713.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/43ip01260538713.tab") 
> 
> system("convert tmp/11os41260538713.ps tmp/11os41260538713.png")
> system("convert tmp/2ztxc1260538713.ps tmp/2ztxc1260538713.png")
> 
> 
> proc.time()
   user  system elapsed 
  8.965   1.378  10.196