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(13139.7,14532.2,15167,16071.1,14827.5,15082,14772.7,16083,14272.5,15223.3,14897.3,13062.6,12603.8,13629.8,14421.1,13978.3,12927.9,13429.9,13470.1,14785.8,14292,14308.8,14013,13240.9,12153.4,14289.7,15669.2,14169.5,14569.8,14469.1,14264.9,15320.9,14433.5,13691.5,14194.1,13519.2,11857.9,14616,15643.4,14077.2,14887.5,14159.9,14643,17192.5,15386.1,14287.1,17526.6,14497,14398.3,16629.6,16670.7,16614.8,16869.2,15663.9,16359.9,18447.7,16889,16505,18320.9,15052.1,15699.8,18135.3,16768.7,18883,19021,18101.9,17776.1,21489.9,17065.3,18690,18953.1,16398.9,16895.7,18553,19270,19422.1,17579.4,18637.3,18076.7,20438.6,18075.2,19563,19899.2,19227.5,17789.6,19220.8,21968.9,21131.5,19484.6,22404.1,21099,22486.5,23707.5,21897.5,23326.4,23765.4,20444)
> par20 = ''
> par19 = ''
> par18 = ''
> par17 = ''
> par16 = ''
> par15 = ''
> par14 = ''
> par13 = ''
> par12 = ''
> par11 = ''
> par10 = 'FALSE'
> par9 = '1'
> par8 = '2'
> par7 = '0'
> par6 = '3'
> par5 = '12'
> par4 = '1'
> par3 = '1'
> par2 = '-0.6'
> par1 = '12'
> ylab = ''
> xlab = ''
> main = ''
> #'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     ar3    sar1     sar2     sma1
      -0.6099  -0.1729  0.2440  0.3426  -0.3045  -0.9999
s.e.   0.1304   0.1524  0.1205  0.1357   0.1600   0.2583

sigma^2 estimated as 5.099e-09:  log likelihood = 572.52,  aic = -1131.05
> (forecast <- predict(arima.out,fx))
$pred
Time Series:
Start = 86 
End = 97 
Frequency = 1 
 [1] 0.002584372 0.002415355 0.002539643 0.002615211 0.002568102 0.002591951
 [7] 0.002403254 0.002541520 0.002533990 0.002436548 0.002588053 0.002718790

$se
Time Series:
Start = 86 
End = 97 
Frequency = 1 
 [1] 7.712222e-05 8.262048e-05 9.401182e-05 1.131869e-04 1.192388e-04
 [6] 1.308416e-04 1.411097e-04 1.478245e-04 1.573762e-04 1.648186e-04
[11] 1.716039e-04 1.794644e-04

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 86 
End = 97 
Frequency = 1 
 [1] 0.002433213 0.002253418 0.002355380 0.002393365 0.002334394 0.002335501
 [7] 0.002126679 0.002251784 0.002225533 0.002113503 0.002251710 0.002367039
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 86 
End = 97 
Frequency = 1 
 [1] 0.002735532 0.002577291 0.002723906 0.002837058 0.002801810 0.002848400
 [7] 0.002679829 0.002831256 0.002842448 0.002759592 0.002924397 0.003070540
> 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$pred))
 [1] 13139.70 14532.20 15167.00 16071.10 14827.50 15082.00 14772.70 16083.00
 [9] 14272.50 15223.30 14897.30 13062.60 12603.80 13629.80 14421.10 13978.30
[17] 12927.90 13429.90 13470.10 14785.80 14292.00 14308.80 14013.00 13240.90
[25] 12153.40 14289.70 15669.20 14169.50 14569.80 14469.10 14264.90 15320.90
[33] 14433.50 13691.50 14194.10 13519.20 11857.90 14616.00 15643.40 14077.20
[41] 14887.50 14159.90 14643.00 17192.50 15386.10 14287.10 17526.60 14497.00
[49] 14398.30 16629.60 16670.70 16614.80 16869.20 15663.90 16359.90 18447.70
[57] 16889.00 16505.00 18320.90 15052.10 15699.80 18135.30 16768.70 18883.00
[65] 19021.00 18101.90 17776.10 21489.90 17065.30 18690.00 18953.10 16398.90
[73] 16895.70 18553.00 19270.00 19422.10 17579.40 18637.30 18076.70 20438.60
[81] 18075.20 19563.00 19899.20 19227.50 17789.60 20546.67 22998.45 21153.34
[89] 20144.45 20764.09 20446.65 23191.77 21127.30 21232.04 22666.01 20497.99
[97] 18881.68
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 86 
End = 97 
Frequency = 1 
 [1] 0.05391257 0.06255987 0.06824276 0.08123092 0.08794226 0.09674882
 [7] 0.11531442 0.11404118 0.12322127 0.13648754 0.13324169 0.13252426
> postscript(file="/var/www/html/rcomp/tmp/1y38g1229943956.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2vv4n1229943957.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 
> 
> #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/3dvwn1229943957.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/4sd1i1229943957.tab") 
> 
> system("convert tmp/1y38g1229943956.ps tmp/1y38g1229943956.png")
> system("convert tmp/2vv4n1229943957.ps tmp/2vv4n1229943957.png")
> 
> 
> proc.time()
   user  system elapsed 
  2.192   0.370   2.389