R version 2.15.2 (2012-10-26) -- "Trick or Treat"
Copyright (C) 2012 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: i686-pc-linux-gnu (32-bit)

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> x <- c(1.4761,1.4721,1.487,1.5167,1.5812,1.554,1.5508,1.5764,1.5611,1.4735,1.4303,1.2757,1.2727,1.3917,1.2816,1.2644,1.3308,1.3275,1.4098,1.4134,1.4138,1.4272,1.4643,1.48,1.5023,1.4406,1.3966,1.357,1.3479,1.3315,1.2307,1.2271,1.3028,1.268,1.3648,1.3857,1.2998,1.3362,1.3692,1.3834,1.4207,1.486,1.4385,1.4453,1.426,1.445,1.3503,1.4001,1.3418,1.2939,1.3176,1.3443,1.3356,1.3214,1.2403,1.259,1.2284,1.2611,1.293,1.2993,1.2986)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '1'
> par7 = '1'
> par6 = '1'
> par5 = '12'
> par4 = '0'
> par3 = '1'
> par2 = '-0.2'
> par1 = '12'
> par10 <- 'FALSE'
> par9 <- '1'
> par8 <- '1'
> par7 <- '1'
> par6 <- '1'
> par5 <- '12'
> par4 <- '0'
> par3 <- '1'
> par2 <- '-0.2'
> par1 <- '12'
> #'GNU S' R Code compiled by R2WASP v. 1.0.44 ()
> #Author: Prof. Dr. P. Wessa
> #To cite this work: Wessa P., (2009), ARIMA Forecasting (v1.0.5) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_arimaforecasting.wasp/
> #Source of accompanying publication: 
> #Technical description: 
> par1 <- as.numeric(par1) #cut off periods
> 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
> par7 <- as.numeric(par7) #q
> 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      ma1    sar1     sma1
      0.0903  -0.2297  0.5993  -0.9345
s.e.  0.5545   0.5308  0.6823   1.9339

sigma^2 estimated as 4.95e-05:  log likelihood = 167.06,  aic = -324.13
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 50 
End = 61 
Frequency = 1 
 [1] 0.9440054 0.9414754 0.9408164 0.9443971 0.9456618 0.9426640 0.9432115
 [8] 0.9448118 0.9433840 0.9431598 0.9433488 0.9389837

$se
Time Series:
Start = 50 
End = 61 
Frequency = 1 
 [1] 0.007260372 0.009578493 0.011386242 0.012940007 0.014325917 0.015589072
 [7] 0.016757278 0.017849190 0.018878054 0.019853707 0.020783991 0.021678151

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 50 
End = 61 
Frequency = 1 
 [1] 0.9297751 0.9227016 0.9184993 0.9190347 0.9175830 0.9121094 0.9103672
 [8] 0.9098274 0.9063830 0.9042465 0.9026122 0.8964945
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 50 
End = 61 
Frequency = 1 
 [1] 0.9582357 0.9602493 0.9631334 0.9697595 0.9737406 0.9732186 0.9760558
 [8] 0.9797962 0.9803850 0.9820730 0.9840855 0.9814729
> 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$pred))
 [1] 1.476100 1.472100 1.487000 1.516700 1.581200 1.554000 1.550800 1.576400
 [9] 1.561100 1.473500 1.430300 1.275700 1.272700 1.391700 1.281600 1.264400
[17] 1.330800 1.327500 1.409800 1.413400 1.413800 1.427200 1.464300 1.480000
[25] 1.502300 1.440600 1.396600 1.357000 1.347900 1.331500 1.230700 1.227100
[33] 1.302800 1.268000 1.364800 1.385700 1.299800 1.336200 1.369200 1.383400
[41] 1.420700 1.486000 1.438500 1.445300 1.426000 1.445000 1.350300 1.400100
[49] 1.341800 1.333913 1.351933 1.356675 1.331149 1.322272 1.343431 1.339536
[57] 1.328230 1.338312 1.339904 1.338562 1.369966
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 50 
End = 61 
Frequency = 1 
 [1] 0.04025727 0.05406019 0.06506896 0.07439434 0.08298939 0.09137654
 [7] 0.09892070 0.10593029 0.11299624 0.11964439 0.12600445 0.13292180
> postscript(file="/var/fisher/rcomp/tmp/1ovkh1356110851.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/fisher/rcomp/tmp/27b151356110851.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/fisher/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/fisher/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/fisher/rcomp/tmp/3npet1356110851.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/fisher/rcomp/tmp/4bpki1356110851.tab") 
> 
> try(system("convert tmp/1ovkh1356110851.ps tmp/1ovkh1356110851.png",intern=TRUE))
character(0)
> try(system("convert tmp/27b151356110851.ps tmp/27b151356110851.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.564   0.439   1.986