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(91.98,91.72,90.27,91.89,92.07,92.92,93.34,93.6,92.41,93.6,93.77,93.6,93.6,93.51,92.66,94.2,94.37,94.45,94.62,94.37,93.43,94.79,94.88,94.79,94.62,94.71,93.77,95.73,95.99,95.82,95.47,95.82,94.71,96.33,96.5,96.16,96.33,96.33,95.05,96.84,96.92,97.44,97.78,97.69,96.67,98.29,98.2,98.71,98.54,98.2,96.92,99.06,99.65,99.82,99.99,100.33,99.31,101.1,101.1,100.93,100.85,100.93,99.6,101.88,101.81,102.38,102.74,102.82,101.72,103.47,102.98,102.68,102.9,103.03,101.29,103.69,103.68,104.2,104.08,104.16,103.05,104.66,104.46,104.95,105.85,106.23,104.86,107.44,108.23,108.45,109.39,110.15,109.13,110.28,110.17,109.99,109.26,109.11,107.06,109.53,108.92,109.24,109.12,109,107.23,109.49,109.04,109.02,109.23)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '0'
> par7 = '1'
> par6 = '1'
> par5 = '12'
> par4 = '1'
> par3 = '1'
> par2 = '1'
> par1 = '15'
> #'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     ma1     sma1
      0.0121  0.0852  -0.5976
s.e.  1.0232  1.0173   0.1214

sigma^2 estimated as 0.1086:  log likelihood = -27.68,  aic = 63.37
> (forecast <- predict(arima.out,fx))
$pred
Time Series:
Start = 95 
End = 109 
Frequency = 1 
 [1] 110.0421 110.1598 110.5520 110.7148 109.2984 111.6516 112.0281 112.3774
 [9] 112.8112 113.1834 112.1261 113.5746 113.3657 113.4839 113.8760

$se
Time Series:
Start = 95 
End = 109 
Frequency = 1 
 [1] 0.3296688 0.4894416 0.6088560 0.7083937 0.7955739 0.8741018 0.9461343
 [8] 1.0130579 1.0758264 1.1351293 1.1914842 1.2452915 1.3400225 1.4330145
[15] 1.5203790

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 95 
End = 109 
Frequency = 1 
 [1] 109.3959 109.2005 109.3586 109.3264 107.7391 109.9383 110.1737 110.3918
 [9] 110.7026 110.9586 109.7907 111.1338 110.7393 110.6752 110.8961
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 95 
End = 109 
Frequency = 1 
 [1] 110.6882 111.1191 111.7454 112.1033 110.8577 113.3648 113.8826 114.3630
 [9] 114.9199 115.4083 114.4614 116.0153 115.9922 116.2926 116.8560
> 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$pred))
  [1]  91.9800  91.7200  90.2700  91.8900  92.0700  92.9200  93.3400  93.6000
  [9]  92.4100  93.6000  93.7700  93.6000  93.6000  93.5100  92.6600  94.2000
 [17]  94.3700  94.4500  94.6200  94.3700  93.4300  94.7900  94.8800  94.7900
 [25]  94.6200  94.7100  93.7700  95.7300  95.9900  95.8200  95.4700  95.8200
 [33]  94.7100  96.3300  96.5000  96.1600  96.3300  96.3300  95.0500  96.8400
 [41]  96.9200  97.4400  97.7800  97.6900  96.6700  98.2900  98.2000  98.7100
 [49]  98.5400  98.2000  96.9200  99.0600  99.6500  99.8200  99.9900 100.3300
 [57]  99.3100 101.1000 101.1000 100.9300 100.8500 100.9300  99.6000 101.8800
 [65] 101.8100 102.3800 102.7400 102.8200 101.7200 103.4700 102.9800 102.6800
 [73] 102.9000 103.0300 101.2900 103.6900 103.6800 104.2000 104.0800 104.1600
 [81] 103.0500 104.6600 104.4600 104.9500 105.8500 106.2300 104.8600 107.4400
 [89] 108.2300 108.4500 109.3900 110.1500 109.1300 110.2800 110.0421 110.1598
 [97] 110.5520 110.7148 109.2984 111.6516 112.0281 112.3774 112.8112 113.1834
[105] 112.1261 113.5746 113.3657 113.4839 113.8760
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 95 
End = 109 
Frequency = 1 
 [1] 0.002995844 0.004443013 0.005507417 0.006398364 0.007278917 0.007828835
 [7] 0.008445506 0.009014783 0.009536517 0.010029113 0.010626293 0.010964528
[13] 0.011820349 0.012627473 0.013351175
> postscript(file="/var/www/html/rcomp/tmp/106lh1261304675.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2kkjc1261304675.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]
Warning message:
In NextMethod("[<-") :
  number of items to replace is not a multiple of replacement length
> 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/31xtm1261304675.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/4jj251261304675.tab") 
> 
> try(system("convert tmp/106lh1261304675.ps tmp/106lh1261304675.png",intern=TRUE))
character(0)
> try(system("convert tmp/2kkjc1261304675.ps tmp/2kkjc1261304675.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  0.833   0.312   1.264