R version 2.6.0 (2007-10-03)
Copyright (C) 2007 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> x <- c(0.007850049,0.008671912,0.008391986,0.008691954,0.008724839,0.008949762,0.009344295,0.009971514,0.010388067,0.008884599,0.01000981,0.012393539,0.007933519,0.008087396,0.008120881,0.008147148,0.00917087,0.009668358,0.009897495,0.011217878,0.010190084,0.009560637,0.011200671,0.013546776,0.008524882,0.009142143,0.008793047,0.009296235,0.009974995,0.009692013,0.010120046,0.011004981,0.010328492,0.009428406,0.011114429,0.011798579,0.008997058,0.008803914,0.007974159,0.008460945,0.009917747,0.009604284,0.011028851,0.011162991,0.010420855,0.009897095,0.010715298,0.012461041,0.008754735,0.009381664,0.008843755,0.009235122,0.009973356,0.009146341,0.011038445,0.010830104,0.010585414,0.010560523,0.010897526,0.014012667)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '2'
> par7 = '0'
> par6 = '2'
> par5 = '12'
> par4 = '1'
> par3 = '0'
> par2 = '1'
> par1 = '12'
> #'GNU S' R Code compiled by R2WASP v. 1.0.44 ()
> #Author: Prof. Dr. P. Wessa
> #To cite this work: AUTHOR(S), (YEAR), YOUR SOFTWARE TITLE (vNUMBER) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_YOURPAGE.wasp/
> #Source of accompanying publication: Office for Research, Development, and Education
> #Technical description: Write here your technical program description (don't use hard returns!)
> 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     ar2     sar1    sar2
      0.2221  0.3475  -0.3911  0.1417
s.e.  0.1538  0.1547   0.2053  0.3041

sigma^2 estimated as 2.68e-07:  log likelihood = 219.47,  aic = -428.95
> (forecast <- predict(arima.out,fx))
$pred
Time Series:
Start = 49 
End = 60 
Frequency = 1 
 [1] 0.008646058 0.008965928 0.008276172 0.008883668 0.009999806 0.009606650
 [7] 0.010678229 0.011052810 0.010391020 0.009685752 0.010852485 0.011949427

$se
Time Series:
Start = 49 
End = 60 
Frequency = 1 
 [1] 0.0005176994 0.0005303188 0.0005687323 0.0005751399 0.0005822055
 [6] 0.0005843350 0.0005858785 0.0005864895 0.0005868553 0.0005870199
[11] 0.0005871101 0.0005871532

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 49 
End = 60 
Frequency = 1 
 [1] 0.007631367 0.007926503 0.007161456 0.007756394 0.008858683 0.008461354
 [7] 0.009529907 0.009903291 0.009240783 0.008535193 0.009701749 0.010798606
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 49 
End = 60 
Frequency = 1 
 [1] 0.009660749 0.010005353 0.009390887 0.010010942 0.011140929 0.010751947
 [7] 0.011826551 0.012202330 0.011541256 0.010836311 0.012003221 0.013100247
> 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)
+ }
> (actandfor <- c(x[1:nx], forecast$pred))
 [1] 0.007850049 0.008671912 0.008391986 0.008691954 0.008724839 0.008949762
 [7] 0.009344295 0.009971514 0.010388067 0.008884599 0.010009810 0.012393539
[13] 0.007933519 0.008087396 0.008120881 0.008147148 0.009170870 0.009668358
[19] 0.009897495 0.011217878 0.010190084 0.009560637 0.011200671 0.013546776
[25] 0.008524882 0.009142143 0.008793047 0.009296235 0.009974995 0.009692013
[31] 0.010120046 0.011004981 0.010328492 0.009428406 0.011114429 0.011798579
[37] 0.008997058 0.008803914 0.007974159 0.008460945 0.009917747 0.009604284
[43] 0.011028851 0.011162991 0.010420855 0.009897095 0.010715298 0.012461041
[49] 0.008646058 0.008965928 0.008276172 0.008883668 0.009999806 0.009606650
[55] 0.010678229 0.011052810 0.010391020 0.009685752 0.010852485 0.011949427
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 49 
End = 60 
Frequency = 1 
 [1] 0.05987693 0.05914824 0.06871925 0.06474126 0.05822168 0.06082609
 [7] 0.05486664 0.05306248 0.05647716 0.06060654 0.05409914 0.04913652
> postscript(file="/var/www/html/rcomp/tmp/1wf131197320542.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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.se <- array(0, dim=fx)
> perf.mse <- 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$pred[i]
+ perf.mape[i] = perf.mape[i] + abs(perf.pe[i])
+ perf.se[i] = (x[nx+i] - forecast$pred[i])^2
+ perf.mse[i] = perf.mse[i] + perf.se[i]
+ 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 = perf.mape / fx
> perf.mse = perf.mse / fx
> perf.rmse = sqrt(perf.mse)
> postscript(file="/var/www/html/rcomp/tmp/24t261197320542.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[1:12] <- x[(nx+1):lx]
> lines(dum, lty=1)
> lines(ub,lty=3)
> lines(lb,lty=3)
> dev.off()
null device 
          1 
> 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/31au41197320542.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.mape[i],4))
+ a<-table.element(a,round(perf.se[i],4))
+ a<-table.element(a,round(perf.mse[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/4x9k71197320542.tab") 
> 
> system("convert tmp/1wf131197320542.ps tmp/1wf131197320542.png")
> system("convert tmp/24t261197320542.ps tmp/24t261197320542.png")
> 
> 
> proc.time()
   user  system elapsed 
  1.193   0.329   1.309