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(8.2,8,7.5,6.8,6.5,6.6,7.6,8,8.1,7.7,7.5,7.6,7.8,7.8,7.8,7.5,7.5,7.1,7.5,7.5,7.6,7.7,7.7,7.9,8.1,8.2,8.2,8.2,7.9,7.3,6.9,6.6,6.7,6.9,7,7.1,7.2,7.1,6.9,7,6.8,6.4,6.7,6.6,6.4,6.3,6.2,6.5,6.8,6.8,6.4,6.1,5.8,6.1,7.2,7.3,6.9,6.1,5.8,6.2,7.1,7.7,7.9,7.7,7.4,7.5,8,8.1)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '0'
> par7 = '1'
> par6 = '3'
> par5 = '12'
> par4 = '0'
> 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    sma1
      0.2479  -0.261  -0.2007  -0.6235  0.3969  -0.7734  1.0000
s.e.  0.2255   0.205   0.2003   0.2360  0.1822   0.3052  0.4321

sigma^2 estimated as 0.02278:  log likelihood = 7.13,  aic = 1.75
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 41 
End = 68 
Frequency = 1 
 [1] 6.876668 6.847035 6.547545 6.299151 6.269013 6.266002 6.304804 6.292018
 [9] 6.283156 6.142351 6.051272 6.129604 6.250813 6.383503 6.316718 6.188876
[17] 6.095663 6.067001 6.057555 6.029075 5.977906 5.922225 5.875167 5.835978
[25] 5.797394 5.755175 5.710319 5.665636

$se
Time Series:
Start = 41 
End = 68 
Frequency = 1 
 [1] 0.1712697 0.3287000 0.5152019 0.6332265 0.7067261 0.7632968 0.8226900
 [8] 0.8894095 0.9564212 1.0178003 1.0750352 1.1306680 1.2347816 1.3692411
[15] 1.5333371 1.6739119 1.7895395 1.8935844 1.9988494 2.1072761 2.2147732
[22] 2.3180129 2.4172638 2.5144611 2.6108926 2.7065913 2.8010808 2.8941572

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 41 
End = 68 
Frequency = 1 
 [1]  6.540979408  6.202782815  5.537748981  5.058027208  4.883830080
 [6]  4.769940032  4.692331782  4.548774995  4.408570735  4.147462345
[11]  3.944203415  3.913494889  3.830641440  3.699790575  3.311377129
[16]  2.908008942  2.588165704  2.355575309  2.139809848  1.898813317
[21]  1.636950502  1.378919610  1.137329822  0.907633864  0.680044178
[26]  0.450256452  0.220201027 -0.006911806
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 41 
End = 68 
Frequency = 1 
 [1]  7.212357  7.491287  7.557340  7.540275  7.654197  7.762063  7.917276
 [8]  8.035260  8.157742  8.137240  8.158341  8.345713  8.670985  9.067216
[15]  9.322058  9.469743  9.603160  9.778426  9.975300 10.159336 10.318861
[22] 10.465530 10.613004 10.764321 10.914743 11.060095 11.200438 11.338184
> 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$pred))
 [1] 8.200000 8.000000 7.500000 6.800000 6.500000 6.600000 7.600000 8.000000
 [9] 8.100000 7.700000 7.500000 7.600000 7.800000 7.800000 7.800000 7.500000
[17] 7.500000 7.100000 7.500000 7.500000 7.600000 7.700000 7.700000 7.900000
[25] 8.100000 8.200000 8.200000 8.200000 7.900000 7.300000 6.900000 6.600000
[33] 6.700000 6.900000 7.000000 7.100000 7.200000 7.100000 6.900000 7.000000
[41] 6.876668 6.847035 6.547545 6.299151 6.269013 6.266002 6.304804 6.292018
[49] 6.283156 6.142351 6.051272 6.129604 6.250813 6.383503 6.316718 6.188876
[57] 6.095663 6.067001 6.057555 6.029075 5.977906 5.922225 5.875167 5.835978
[65] 5.797394 5.755175 5.710319 5.665636
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 41 
End = 68 
Frequency = 1 
 [1] 0.02490592 0.04800618 0.07868628 0.10052569 0.11273323 0.12181560
 [7] 0.13048621 0.14135521 0.15221986 0.16570208 0.17765440 0.18446020
[13] 0.19753935 0.21449682 0.24274269 0.27047105 0.29357585 0.31211211
[19] 0.32997629 0.34951900 0.37049315 0.39140913 0.41143747 0.43085516
[25] 0.45035627 0.47028824 0.49052962 0.51082651
> postscript(file="/var/www/html/rcomp/tmp/1jl4b1260987696.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2smtr1260987696.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/3aadg1260987696.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/42ea61260987696.tab") 
> 
> try(system("convert tmp/1jl4b1260987696.ps tmp/1jl4b1260987696.png",intern=TRUE))
character(0)
> try(system("convert tmp/2smtr1260987696.ps tmp/2smtr1260987696.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.068   0.352   2.038