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(8.2,8.0,7.5,6.8,6.5,6.6,7.6,8.0,8.1,7.7,7.5,7.6,7.8,7.8,7.8,7.5,7.5,7.1,7.5,7.5,7.6,7.7,7.7,7.9,8.1,8.2,8.2,8.2,7.9,7.3,6.9,6.6,6.7,6.9,7.0,7.1,7.2,7.1,6.9,7.0,6.8,6.4,6.7,6.6,6.4,6.3,6.2,6.5,6.8,6.8,6.4,6.1,5.8,6.1,7.2,7.3,6.9,6.1,5.8,6.2,7.1,7.7,7.9,7.7,7.4,7.5,8.0,8.1)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '0'
> par7 = '0'
> par6 = '3'
> 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    sma1
      1.0224  -0.4645  0.1092  -0.4375  0.5258  -0.9412  0.9998
s.e.  0.2382   0.2774  0.2125   0.2272  0.4696   0.5766  1.1187

sigma^2 estimated as 0.01833:  log likelihood = 9.94,  aic = -3.88
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 41 
End = 68 
Frequency = 1 
 [1] 6.968173 7.045892 6.867744 6.701846 6.701497 6.660864 6.644319 6.609224
 [9] 6.618331 6.518098 6.457914 6.558115 6.773246 7.016352 7.075363 7.046277
[17] 7.015681 7.004354 7.003807 7.005167 7.005575 7.005301 7.004979 7.004822
[25] 7.004781 7.004777 7.004775 7.004770

$se
Time Series:
Start = 41 
End = 68 
Frequency = 1 
 [1] 0.1599273 0.2961832 0.4486234 0.5226719 0.5481636 0.5560936 0.5585831
 [8] 0.5619869 0.5661819 0.5703709 0.5743374 0.5781607 0.6099930 0.6653210
[15] 0.7451263 0.7962358 0.8209623 0.8346489 0.8449417 0.8543081 0.8632833
[22] 0.8719328 0.8803119 0.8885001 0.8965602 0.9045257 0.9124111 0.9202229

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 41 
End = 68 
Frequency = 1 
 [1] 6.654715 6.465373 5.988442 5.677409 5.627096 5.570921 5.549496 5.507730
 [9] 5.508615 5.400171 5.332212 5.424920 5.577660 5.712323 5.614916 5.485655
[17] 5.406595 5.368442 5.347721 5.330724 5.313540 5.296312 5.279568 5.263362
[25] 5.247523 5.231907 5.216449 5.201133
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 41 
End = 68 
Frequency = 1 
 [1] 7.281630 7.626411 7.747046 7.726283 7.775898 7.750807 7.739142 7.710719
 [9] 7.728048 7.636025 7.583615 7.691310 7.968832 8.320381 8.535811 8.606899
[17] 8.624767 8.640265 8.659893 8.679611 8.697610 8.714289 8.730390 8.746282
[25] 8.762039 8.777647 8.793101 8.808407
> 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$pred))
 [1] 8.200000 8.000000 7.500000 6.800000 6.500000 6.600000 7.600000 8.000000
 [9] 8.100000 7.700000 7.500000 7.600000 7.800000 7.800000 7.800000 7.500000
[17] 7.500000 7.100000 7.500000 7.500000 7.600000 7.700000 7.700000 7.900000
[25] 8.100000 8.200000 8.200000 8.200000 7.900000 7.300000 6.900000 6.600000
[33] 6.700000 6.900000 7.000000 7.100000 7.200000 7.100000 6.900000 7.000000
[41] 6.968173 7.045892 6.867744 6.701846 6.701497 6.660864 6.644319 6.609224
[49] 6.618331 6.518098 6.457914 6.558115 6.773246 7.016352 7.075363 7.046277
[57] 7.015681 7.004354 7.003807 7.005167 7.005575 7.005301 7.004979 7.004822
[65] 7.004781 7.004777 7.004775 7.004770
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 41 
End = 68 
Frequency = 1 
 [1] 0.02295111 0.04203630 0.06532325 0.07798924 0.08179719 0.08348670
 [7] 0.08406928 0.08503070 0.08554753 0.08750574 0.08893545 0.08815959
[13] 0.09005919 0.09482434 0.10531280 0.11300092 0.11701819 0.11916144
[19] 0.12064035 0.12195398 0.12322803 0.12446758 0.12566945 0.12684121
[25] 0.12799260 0.12912983 0.13025559 0.13137090
> postscript(file="/var/www/html/rcomp/tmp/1febd1260471517.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2d5l91260471517.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/3952o1260471518.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/4599w1260471518.tab") 
> 
> system("convert tmp/1febd1260471517.ps tmp/1febd1260471517.png")
> system("convert tmp/2d5l91260471517.ps tmp/2d5l91260471517.png")
> 
> 
> proc.time()
   user  system elapsed 
  1.165   0.330   1.247