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(104.2,103.2,112.7,106.4,102.6,110.6,95.2,89.0,112.5,116.8,107.2,113.6,101.8,102.6,122.7,110.3,110.5,121.6,100.3,100.7,123.4,127.1,124.1,131.2,111.6,114.2,130.1,125.9,119.0,133.8,107.5,113.5,134.4,126.8,135.6,139.9,129.8,131.0,153.1,134.1,144.1,155.9,123.3,128.1,144.3,153.0,149.9,150.9,141.0,138.9,157.4,142.9,151.7,161.0,138.5,135.9,151.5,164.0,159.1,157.0,142.1,144.8,152.1,154.6,148.7,157.7,146.7)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '0'
> par7 = '1'
> par6 = '3'
> par5 = '12'
> par4 = '1'
> par3 = '0'
> par2 = '0.5'
> 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     ma1     sma1
      0.0997  0.4906  0.4086  0.1592  -0.8642
s.e.  0.6676  0.3201  0.4056  0.7393   2.0613

sigma^2 estimated as 0.03706:  log likelihood = 2.31,  aic = 7.37
Warning message:
In arima(x[1:nx], order = c(par6, par3, par7), seasonal = list(order = c(par8,  :
  possible convergence problem: optim gave code=1
> (forecast <- predict(arima.out,fx))
$pred
Time Series:
Start = 56 
End = 67 
Frequency = 1 
 [1] 11.74636 12.69354 12.82691 12.72274 12.91262 12.37171 12.37540 13.14341
 [9] 12.63962 12.71244 13.18999 12.12586

$se
Time Series:
Start = 56 
End = 67 
Frequency = 1 
 [1] 0.2030307 0.2096275 0.2341703 0.2624808 0.2754956 0.2955364 0.3115699
 [8] 0.3260081 0.3414307 0.3550311 0.3684093 0.3814144

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 56 
End = 67 
Frequency = 1 
 [1] 11.34842 12.28267 12.36794 12.20828 12.37265 11.79246 11.76472 12.50443
 [9] 11.97042 12.01658 12.46791 11.37829
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 56 
End = 67 
Frequency = 1 
 [1] 12.14430 13.10441 13.28588 13.23720 13.45259 12.95096 12.98608 13.78239
 [9] 13.30883 13.40830 13.91207 12.87343
> 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$pred))
 [1] 104.2000 103.2000 112.7000 106.4000 102.6000 110.6000  95.2000  89.0000
 [9] 112.5000 116.8000 107.2000 113.6000 101.8000 102.6000 122.7000 110.3000
[17] 110.5000 121.6000 100.3000 100.7000 123.4000 127.1000 124.1000 131.2000
[25] 111.6000 114.2000 130.1000 125.9000 119.0000 133.8000 107.5000 113.5000
[33] 134.4000 126.8000 135.6000 139.9000 129.8000 131.0000 153.1000 134.1000
[41] 144.1000 155.9000 123.3000 128.1000 144.3000 153.0000 149.9000 150.9000
[49] 141.0000 138.9000 157.4000 142.9000 151.7000 161.0000 138.5000 137.9770
[57] 161.1259 164.5296 161.8681 166.7357 153.0591 153.1505 172.7492 159.7601
[65] 161.6062 173.9758 147.0365
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 56 
End = 67 
Frequency = 1 
 [1] 0.03515468 0.03356356 0.03716559 0.04209591 0.04356295 0.04889463
 [7] 0.05159547 0.05081370 0.05545565 0.05738441 0.05739102 0.06484845
> postscript(file="/var/www/html/rcomp/tmp/12gis1228854265.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/22i4n1228854265.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/30vd21228854265.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/4jr3e1228854265.tab") 
> 
> system("convert tmp/12gis1228854265.ps tmp/12gis1228854265.png")
> system("convert tmp/22i4n1228854265.ps tmp/22i4n1228854265.png")
> 
> 
> proc.time()
   user  system elapsed 
  3.446   0.535   3.571