R version 2.9.0 (2009-04-17)
Copyright (C) 2009 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> x <- c(100,99.93,100.89,101.61,107.26,109.16,106.62,103.56,102.64,104.71,105.95,107.59,107.72,108.29,107.38,109.85,114.94,118.38,117.76,115.87,114.03,114.36,125.35,125.35,122.21,122.16,119.34,122.70,128.63,132.16,127.14,125.11,123.70,121.88,123.10,122.37,122.52,124.67,127.33,129.43,133.76,135.29,126.37,121.33,121.32,113.43,120.76,118.63,122.22,121.04,122.52,123.02,128.80,126.41,119.65,117.56,119.35,116.78,120.19,114.26)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '2'
> par7 = '0'
> par6 = '0'
> par5 = '12'
> par4 = '0'
> par3 = '1'
> par2 = '1'
> par1 = '18'
> #'GNU S' R Code compiled by R2WASP v. 1.0.44 ()
> #Author: Prof. Dr. P. Wessa
> #To cite this work: Wessa P., (2009), ARIMA Forecasting (v1.0.5) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_arimaforecasting.wasp/
> #Source of accompanying publication: 
> #Technical description: 
> 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:
        sar1    sar2     sma1
      0.4287  0.5712  -0.4303
s.e.  0.1374  0.1374      NaN

sigma^2 estimated as 2.717:  log likelihood = -130.02,  aic = 268.04
Warning messages:
1: In log(s2) : NaNs produced
2: In sqrt(diag(x$var.coef)) : NaNs produced
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 43 
End = 60 
Frequency = 1 
 [1] 133.9349 131.7021 130.1452 130.8879 138.6626 139.1052 137.0440 137.1809
 [9] 135.3964 138.1747 143.8222 147.1154 143.6668 141.5500 140.0771 139.3558
[17] 143.3857 143.1585

$se
Time Series:
Start = 43 
End = 60 
Frequency = 1 
 [1] 1.663441 2.352461 2.881165 3.326883 3.719568 4.074582 4.401052 4.700560
 [9] 4.982095 5.248550 5.502116 5.744500 5.979950 6.206474 6.425016 6.636366
[17] 6.841189 7.040056

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 43 
End = 60 
Frequency = 1 
 [1] 130.6745 127.0913 124.4982 124.3672 131.3723 131.1190 128.4180 127.9678
 [9] 125.6315 127.8876 133.0380 135.8561 131.9461 129.3853 127.4841 126.3485
[17] 129.9770 129.3600
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 43 
End = 60 
Frequency = 1 
 [1] 137.1952 136.3129 135.7923 137.4086 145.9530 147.0913 145.6701 146.3939
 [9] 145.1614 148.4619 154.6063 158.3746 155.3875 153.7146 152.6701 152.3631
[17] 156.7945 156.9570
> 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$pred))
 [1] 100.0000  99.9300 100.8900 101.6100 107.2600 109.1600 106.6200 103.5600
 [9] 102.6400 104.7100 105.9500 107.5900 107.7200 108.2900 107.3800 109.8500
[17] 114.9400 118.3800 117.7600 115.8700 114.0300 114.3600 125.3500 125.3500
[25] 122.2100 122.1600 119.3400 122.7000 128.6300 132.1600 127.1400 125.1100
[33] 123.7000 121.8800 123.1000 122.3700 122.5200 124.6700 127.3300 129.4300
[41] 133.7600 135.2900 133.9349 131.7021 130.1452 130.8879 138.6626 139.1052
[49] 137.0440 137.1809 135.3964 138.1747 143.8222 147.1154 143.6668 141.5500
[57] 140.0771 139.3558 143.3857 143.1585
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 43 
End = 60 
Frequency = 1 
 [1] 0.01241978 0.01786199 0.02213807 0.02541780 0.02682459 0.02929138
 [7] 0.03211415 0.03426542 0.03679635 0.03798488 0.03825639 0.03904759
[13] 0.04162375 0.04384653 0.04586772 0.04762174 0.04771178 0.04917667
> postscript(file="/var/www/html/rcomp/tmp/1x5wg1260986419.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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.mape1 <- array(0, dim=fx)
> perf.se <- array(0, dim=fx)
> perf.mse <- array(0, dim=fx)
> perf.mse1 <- 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$pred[i]
+ perf.se[i] = (x[nx+i] - forecast$pred[i])^2
+ 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[1] = abs(perf.pe[1])
> perf.mse[1] = abs(perf.se[1])
> for (i in 2:fx) {
+ perf.mape[i] = perf.mape[i-1] + abs(perf.pe[i])
+ perf.mape1[i] = perf.mape[i] / i
+ perf.mse[i] = perf.mse[i-1] + perf.se[i]
+ perf.mse1[i] = perf.mse[i] / i
+ }
> perf.rmse = sqrt(perf.mse1)
> postscript(file="/var/www/html/rcomp/tmp/2urqk1260986419.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:par1] <- 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/3udmn1260986419.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.mape1[i],4))
+ a<-table.element(a,round(perf.se[i],4))
+ a<-table.element(a,round(perf.mse1[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/4w8ce1260986419.tab") 
> 
> try(system("convert tmp/1x5wg1260986419.ps tmp/1x5wg1260986419.png",intern=TRUE))
character(0)
> try(system("convert tmp/2urqk1260986419.ps tmp/2urqk1260986419.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  0.908   0.335   1.133