R version 2.8.0 (2008-10-20)
Copyright (C) 2008 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> x <- c(1.64,1.65,1.65,1.65,1.66,1.66,1.67,1.67,1.68,1.68,1.68,1.68,1.69,1.69,1.7,1.7,1.71,1.71,1.71,1.71,1.72,1.72,1.72,1.73,1.73,1.73,1.74,1.75,1.75,1.76,1.76,1.77,1.77,1.78,1.79,1.8,1.8,1.81,1.81,1.81,1.81,1.82,1.82,1.82,1.83,1.83,1.83,1.84,1.84,1.85,1.85,1.86,1.86,1.86,1.86,1.86)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '1'
> par6 = '1'
> par5 = '12'
> par4 = '0'
> par3 = '2'
> 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
      -0.6085  0.1859  -0.0412  -1.1543  -0.5615  0.7174
s.e.   0.5385  0.8314   0.4675   1.8511   0.6528  1.4912

sigma^2 estimated as 1.478e-05:  log likelihood = 103.44,  aic = -192.88
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 29 
End = 56 
Frequency = 1 
 [1] 1.749101 1.751816 1.755027 1.759057 1.762532 1.766477 1.769999 1.773889
 [9] 1.777456 1.781306 1.784909 1.788727 1.792357 1.796152 1.799803 1.803580
[17] 1.807246 1.811009 1.814688 1.818440 1.822128 1.825873 1.829568 1.833306
[25] 1.837006 1.840740 1.844444 1.848174

$se
Time Series:
Start = 29 
End = 56 
Frequency = 1 
 [1] 0.003997293 0.004180135 0.004300188 0.004318225 0.004411831 0.004442156
 [7] 0.004534020 0.004573944 0.004663582 0.004712005 0.004800502 0.004856504
[13] 0.004944642 0.005007309 0.005095647 0.005164134 0.005253069 0.005326621
[19] 0.005416431 0.005494389 0.005585260 0.005667057 0.005759108 0.005844257
[25] 0.005937555 0.006025644 0.006120218 0.006210895

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 29 
End = 56 
Frequency = 1 
 [1] 1.741267 1.743623 1.746599 1.750593 1.753885 1.757770 1.761113 1.764924
 [9] 1.768316 1.772070 1.775500 1.779209 1.782666 1.786338 1.789816 1.793458
[17] 1.796950 1.800569 1.804072 1.807671 1.811181 1.814765 1.818280 1.821851
[25] 1.825368 1.828929 1.832448 1.836000
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 29 
End = 56 
Frequency = 1 
 [1] 1.756936 1.760009 1.763455 1.767521 1.771180 1.775184 1.778886 1.782853
 [9] 1.786597 1.790541 1.794318 1.798246 1.802049 1.805967 1.809790 1.813702
[17] 1.817542 1.821450 1.825304 1.829209 1.833075 1.836980 1.840855 1.844760
[25] 1.848644 1.852550 1.856440 1.860347
> 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$pred))
 [1] 1.640000 1.650000 1.650000 1.650000 1.660000 1.660000 1.670000 1.670000
 [9] 1.680000 1.680000 1.680000 1.680000 1.690000 1.690000 1.700000 1.700000
[17] 1.710000 1.710000 1.710000 1.710000 1.720000 1.720000 1.720000 1.730000
[25] 1.730000 1.730000 1.740000 1.750000 1.749101 1.751816 1.755027 1.759057
[33] 1.762532 1.766477 1.769999 1.773889 1.777456 1.781306 1.784909 1.788727
[41] 1.792357 1.796152 1.799803 1.803580 1.807246 1.811009 1.814688 1.818440
[49] 1.822128 1.825873 1.829568 1.833306 1.837006 1.840740 1.844444 1.848174
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 29 
End = 56 
Frequency = 1 
 [1] 0.002285341 0.002386173 0.002450212 0.002454852 0.002503120 0.002514698
 [7] 0.002561595 0.002578484 0.002623739 0.002645253 0.002689494 0.002715061
[13] 0.002758737 0.002787798 0.002831225 0.002863269 0.002906670 0.002941244
[19] 0.002984773 0.003021484 0.003065240 0.003103752 0.003147797 0.003187824
[25] 0.003232191 0.003273491 0.003318191 0.003360558
> postscript(file="/var/www/html/freestat/rcomp/tmp/1xt0z1293188159.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/freestat/rcomp/tmp/2b3g71293188159.ps",horizontal=F,onefile=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/freestat/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/html/freestat/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/freestat/rcomp/tmp/3awxe1293188160.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/freestat/rcomp/tmp/4eeek1293188160.tab") 
> 
> try(system("convert tmp/1xt0z1293188159.ps tmp/1xt0z1293188159.png",intern=TRUE))
character(0)
> try(system("convert tmp/2b3g71293188159.ps tmp/2b3g71293188159.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.088   0.451   1.957