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(32.68,31.54,32.43,26.54,25.85,27.6,25.71,25.38,28.57,27.64,25.36,25.9,26.29,21.74,19.2,19.32,19.82,20.36,24.31,25.97,25.61,24.67,25.59,26.09,28.37,27.34,24.46,27.46,30.23,32.33,29.87,24.87,25.48,27.28,28.24,29.58,26.95,29.08,28.76,29.59,30.7,30.52,32.67,33.19,37.13,35.54,37.75,41.84,42.94,49.14,44.61,40.22,44.23,45.85,53.38,53.26,51.8,55.3,57.81,63.96,63.77,59.15,56.12,57.42,63.52,61.71,63.01,68.18,72.03,69.75,74.41,74.33,64.24,60.03,59.44,62.5,55.04,58.34,61.92,67.65,67.68,70.3,75.26,71.44,76.36,81.71,92.6,90.6,92.23,94.09,102.79,109.65,124.05,132.69,135.81,116.07,101.42,75.73,55.48)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '0'
> par6 = '1'
> par5 = '12'
> par4 = '0'
> par3 = '2'
> 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
      -0.3812
s.e.   0.1005

sigma^2 estimated as 17.20:  log likelihood = -241.59,  aic = 487.17
> (forecast <- predict(arima.out,fx))
$pred
Time Series:
Start = 88 
End = 99 
Frequency = 1 
 [1] 101.3783 110.9615 120.2379 129.6312 138.9800 148.3457 157.7050 167.0667
 [9] 176.4275 185.7887 195.1497 204.5108

$se
Time Series:
Start = 88 
End = 99 
Frequency = 1 
 [1]  4.146820  7.890492 12.645401 18.007611 23.987620 30.501852 37.518248
 [8] 45.000040 52.920999 61.257620 69.990280 79.101732

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 88 
End = 99 
Frequency = 1 
 [1] 93.25050 95.49611 95.45287 94.33628 91.96422 88.56208 84.16922 78.86665
 [9] 72.70238 65.72376 57.96877 49.47140
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 88 
End = 99 
Frequency = 1 
 [1] 109.5060 126.4268 145.0228 164.9261 185.9957 208.1293 231.2408 255.2668
 [9] 280.1527 305.8536 332.3307 359.5502
> 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$pred))
 [1]  32.6800  31.5400  32.4300  26.5400  25.8500  27.6000  25.7100  25.3800
 [9]  28.5700  27.6400  25.3600  25.9000  26.2900  21.7400  19.2000  19.3200
[17]  19.8200  20.3600  24.3100  25.9700  25.6100  24.6700  25.5900  26.0900
[25]  28.3700  27.3400  24.4600  27.4600  30.2300  32.3300  29.8700  24.8700
[33]  25.4800  27.2800  28.2400  29.5800  26.9500  29.0800  28.7600  29.5900
[41]  30.7000  30.5200  32.6700  33.1900  37.1300  35.5400  37.7500  41.8400
[49]  42.9400  49.1400  44.6100  40.2200  44.2300  45.8500  53.3800  53.2600
[57]  51.8000  55.3000  57.8100  63.9600  63.7700  59.1500  56.1200  57.4200
[65]  63.5200  61.7100  63.0100  68.1800  72.0300  69.7500  74.4100  74.3300
[73]  64.2400  60.0300  59.4400  62.5000  55.0400  58.3400  61.9200  67.6500
[81]  67.6800  70.3000  75.2600  71.4400  76.3600  81.7100  92.6000 101.3783
[89] 110.9615 120.2379 129.6312 138.9800 148.3457 157.7050 167.0667 176.4275
[97] 185.7887 195.1497 204.5108
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 88 
End = 99 
Frequency = 1 
 [1] 0.04090443 0.07111020 0.10516988 0.13891418 0.17259769 0.20561330
 [7] 0.23790147 0.26935368 0.29995885 0.32971661 0.35864914 0.38678511
> postscript(file="/var/www/html/rcomp/tmp/1hl8s1229294554.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2sa8q1229294554.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/3j4121229294554.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/4jaew1229294554.tab") 
> 
> system("convert tmp/1hl8s1229294554.ps tmp/1hl8s1229294554.png")
> system("convert tmp/2sa8q1229294554.ps tmp/2sa8q1229294554.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.588   0.323   0.688