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(1.19,1.18,1.18,1.33,1.3,1.25,1.22,1.17,1.18,1.19,1.21,1.21,1.2,1.2,1.29,1.83,1.85,1.54,1.52,1.43,1.4,1.4,1.39,1.37,1.33,1.36,1.34,1.75,1.84,1.73,1.63,1.5,1.45,1.38,1.38,1.27,1.31,1.29,1.32,1.48,1.39,1.45,1.44,1.44,1.42,1.39,1.4,1.39,1.3,1.32,1.35,1.51,1.37,1.25,1.15,1.09,1.09,1.06,1.02,1.01,1,1,1.05,1.3,1.34,1.24,1.22,1.06,1,1,1,1.01)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '1'
> par6 = '1'
> par5 = '12'
> par4 = '1'
> 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
      0.4854  -0.1410  -0.6623  -0.3551  -0.3551  1.000
s.e.  0.1630   0.1747   0.1589   0.1771   0.1678  0.204

sigma^2 estimated as 0.009414:  log likelihood = 25.29,  aic = -36.58
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 45 
End = 72 
Frequency = 1 
 [1] 1.3587373 1.2124082 1.1420451 1.0293578 1.1285257 1.1842257 1.2444080
 [8] 1.3691993 1.2077182 1.2179958 1.2172571 1.2761042 1.2550307 1.1234870
[15] 1.0128408 0.8386526 0.9038553 0.9784187 1.0932776 1.2644442 1.1052717
[22] 1.0739197 1.0219346 1.0602470 1.0640022 0.9813455 0.9045283 0.7234245

$se
Time Series:
Start = 45 
End = 72 
Frequency = 1 
 [1] 0.1010942 0.1533773 0.1702277 0.1869252 0.2016424 0.2260283 0.2525030
 [8] 0.2774410 0.2940583 0.3051642 0.3141212 0.3254665 0.3837020 0.4465057
[15] 0.4825365 0.5123091 0.5356464 0.5653115 0.6002945 0.6389569 0.6720191
[22] 0.6974914 0.7170681 0.7361595 0.7895661 0.8523939 0.8995973 0.9423625

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 45 
End = 72 
Frequency = 1 
 [1]  1.16059267  0.91178859  0.80839880  0.66298441  0.73330651  0.74121019
 [7]  0.74950217  0.82541504  0.63136399  0.61987397  0.60157956  0.63818985
[13]  0.50297479  0.24833580  0.06706928 -0.16547320 -0.14601153 -0.12959177
[19] -0.08329956  0.01208875 -0.21188570 -0.29316343 -0.38351898 -0.38262555
[25] -0.48354733 -0.68934649 -0.85868247 -1.12360603
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 45 
End = 72 
Frequency = 1 
 [1] 1.556882 1.513028 1.475691 1.395731 1.523745 1.627241 1.739314 1.912984
 [9] 1.784072 1.816118 1.832935 1.914018 2.007087 1.998638 1.958612 1.842778
[17] 1.953722 2.086429 2.269855 2.516800 2.422429 2.441003 2.427388 2.503120
[25] 2.611552 2.652037 2.667739 2.570455
> 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$pred))
 [1] 1.1900000 1.1800000 1.1800000 1.3300000 1.3000000 1.2500000 1.2200000
 [8] 1.1700000 1.1800000 1.1900000 1.2100000 1.2100000 1.2000000 1.2000000
[15] 1.2900000 1.8300000 1.8500000 1.5400000 1.5200000 1.4300000 1.4000000
[22] 1.4000000 1.3900000 1.3700000 1.3300000 1.3600000 1.3400000 1.7500000
[29] 1.8400000 1.7300000 1.6300000 1.5000000 1.4500000 1.3800000 1.3800000
[36] 1.2700000 1.3100000 1.2900000 1.3200000 1.4800000 1.3900000 1.4500000
[43] 1.4400000 1.4400000 1.3587373 1.2124082 1.1420451 1.0293578 1.1285257
[50] 1.1842257 1.2444080 1.3691993 1.2077182 1.2179958 1.2172571 1.2761042
[57] 1.2550307 1.1234870 1.0128408 0.8386526 0.9038553 0.9784187 1.0932776
[64] 1.2644442 1.1052717 1.0739197 1.0219346 1.0602470 1.0640022 0.9813455
[71] 0.9045283 0.7234245
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 45 
End = 72 
Frequency = 1 
 [1] 0.07440304 0.12650636 0.14905515 0.18159399 0.17867775 0.19086590
 [7] 0.20291012 0.20263008 0.24348251 0.25054619 0.25805657 0.25504696
[13] 0.30573117 0.39742847 0.47641889 0.61087163 0.59262400 0.57778072
[19] 0.54907781 0.50532626 0.60801257 0.64948188 0.70167715 0.69432826
[25] 0.74207186 0.86859712 0.99454856 1.30264114
> postscript(file="/var/www/html/rcomp/tmp/1tc561261337532.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2ruq01261337532.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/3zobh1261337532.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/4hah11261337532.tab") 
> 
> try(system("convert tmp/1tc561261337532.ps tmp/1tc561261337532.png",intern=TRUE))
character(0)
> try(system("convert tmp/2ruq01261337532.ps tmp/2ruq01261337532.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  0.919   0.338   2.359