R version 2.7.0 (2008-04-22)
Copyright (C) 2008 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> x <- c(105.2,91.5,75.3,60.5,80.4,84.5,93.9,78,92.3,90,72.1,76.9,76,88.7,55.4,46.6,90.9,84.9,89,90.2,72.3,83,71.6,75.4,85.1,81.2,68.7,68.4,93.7,96.6,101.8,93.6,88.9,114.1,82.3,96.4,104,88.2,85.2,87.1,85.5,89.1,105.2,82.9,86.8,112,97.4,88.9,109.4,87.8,90.5,79.3,114.9,118.8,125,96.1,116.7,119.5,104.1,121,127.3,117.7,108,89.4,137.4,142,137.3,122.8,126.1,147.6,115.7,139.2,151.2,123.8,109,112.1,136.4,135.5,138.7,137.5,141.5,143.6,146.5,200.7,196.2)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '2'
> par7 = '0'
> par6 = '3'
> par5 = '12'
> par4 = '1'
> par3 = '0'
> par2 = '0.1'
> 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     ar3     sar1     sar2
      0.2359  0.2706  0.4292  -0.4042  -0.5427
s.e.  0.1150  0.1160  0.1151   0.1255   0.1209

sigma^2 estimated as 0.0002621:  log likelihood = 159.76,  aic = -307.52
> (forecast <- predict(arima.out,fx))
$pred
Time Series:
Start = 74 
End = 85 
Frequency = 1 
 [1] 1.627416 1.615737 1.603525 1.631867 1.637429 1.646719 1.619859 1.621343
 [9] 1.657249 1.623606 1.629602 1.653598

$se
Time Series:
Start = 74 
End = 85 
Frequency = 1 
 [1] 0.01619043 0.01663477 0.01745313 0.01974232 0.02042711 0.02129025
 [7] 0.02234821 0.02300963 0.02370651 0.02439245 0.02495092 0.02549545

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 74 
End = 85 
Frequency = 1 
 [1] 1.595683 1.583133 1.569316 1.593172 1.597392 1.604990 1.576056 1.576244
 [9] 1.610784 1.575797 1.580698 1.603627
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 74 
End = 85 
Frequency = 1 
 [1] 1.659149 1.648341 1.637733 1.670562 1.677466 1.688448 1.663661 1.666442
 [9] 1.703714 1.671415 1.678505 1.703569
> 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$pred))
 [1] 105.2000  91.5000  75.3000  60.5000  80.4000  84.5000  93.9000  78.0000
 [9]  92.3000  90.0000  72.1000  76.9000  76.0000  88.7000  55.4000  46.6000
[17]  90.9000  84.9000  89.0000  90.2000  72.3000  83.0000  71.6000  75.4000
[25]  85.1000  81.2000  68.7000  68.4000  93.7000  96.6000 101.8000  93.6000
[33]  88.9000 114.1000  82.3000  96.4000 104.0000  88.2000  85.2000  87.1000
[41]  85.5000  89.1000 105.2000  82.9000  86.8000 112.0000  97.4000  88.9000
[49] 109.4000  87.8000  90.5000  79.3000 114.9000 118.8000 125.0000  96.1000
[57] 116.7000 119.5000 104.1000 121.0000 127.3000 117.7000 108.0000  89.4000
[65] 137.4000 142.0000 137.3000 122.8000 126.1000 147.6000 115.7000 139.2000
[73] 151.2000 130.3123 121.2572 112.3973 133.9206 138.5556 146.6209 124.3859
[81] 125.5306 156.2707 127.2934 132.0732 152.8621
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 74 
End = 85 
Frequency = 1 
 [1] 0.1086847 0.1128248 0.1199083 0.1347401 0.1394120 0.1450739 0.1560217
 [8] 0.1610649 0.1625132 0.1717906 0.1755319 0.1769308
> postscript(file="/var/www/html/rcomp/tmp/1hizp1229362323.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2g7iv1229362323.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/3w74b1229362323.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/4jgts1229362323.tab") 
> 
> system("convert tmp/1hizp1229362323.ps tmp/1hizp1229362323.png")
> system("convert tmp/2g7iv1229362323.ps tmp/2g7iv1229362323.png")
> 
> 
> proc.time()
   user  system elapsed 
  2.870   0.678   3.108