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(62,64,62,64,64,69,69,65,56,58,53,62,55,60,59,58,53,57,57,53,54,53,57,57,55,49,50,49,54,58,58,52,56,52,59,53,52,53,51,50,56,52,46,48,46,48,48,49,53,48,51,48,50,55,52,53,52,55,53,53,56,54,52,55,54,59,56,56,51,53,52,51,46,49,46,55,57,53,52,53,50,54,53,50,51,52,47,51,49,53,52,45,53,51,48,48,48,48,40,43,40,39,39,36,41,39,40,39,46,40,37,37,44,41,40,36,38,43,42,45,46)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '2'
> par7 = '2'
> par6 = '3'
> par5 = '12'
> par4 = '0'
> par3 = '1'
> 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      ar2      ar3      ma1     ma2     sar1    sar2    sma1
      1.0673  -0.3317  -0.4147  -1.5737  1.0000  -0.6417  0.0754  1.0000
s.e.  0.0908   0.1358   0.0942   0.0497  0.0581   0.1148  0.1289  0.1509

sigma^2 estimated as 8.624:  log likelihood = -277.05,  aic = 572.1
> (forecast <- predict(arima.out,fx))
$pred
Time Series:
Start = 110 
End = 121 
Frequency = 1 
 [1] 42.18161 43.36295 44.29296 45.16086 43.71455 43.96674 43.39683 43.17170
 [9] 43.49691 44.65293 44.39997 47.40326

$se
Time Series:
Start = 110 
End = 121 
Frequency = 1 
 [1] 3.053329 3.421176 3.926922 4.229166 4.553332 4.885714 5.268396 5.674236
 [9] 6.068559 6.411730 6.691565 6.916273

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 110 
End = 121 
Frequency = 1 
 [1] 36.19709 36.65744 36.59619 36.87170 34.79002 34.39074 33.07077 32.05019
 [9] 31.60254 32.08594 31.28451 33.84737
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 110 
End = 121 
Frequency = 1 
 [1] 48.16614 50.06845 51.98972 53.45003 52.63908 53.54274 53.72288 54.29320
 [9] 55.39129 57.21992 57.51544 60.95916
> 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$pred))
  [1] 62.00000 64.00000 62.00000 64.00000 64.00000 69.00000 69.00000 65.00000
  [9] 56.00000 58.00000 53.00000 62.00000 55.00000 60.00000 59.00000 58.00000
 [17] 53.00000 57.00000 57.00000 53.00000 54.00000 53.00000 57.00000 57.00000
 [25] 55.00000 49.00000 50.00000 49.00000 54.00000 58.00000 58.00000 52.00000
 [33] 56.00000 52.00000 59.00000 53.00000 52.00000 53.00000 51.00000 50.00000
 [41] 56.00000 52.00000 46.00000 48.00000 46.00000 48.00000 48.00000 49.00000
 [49] 53.00000 48.00000 51.00000 48.00000 50.00000 55.00000 52.00000 53.00000
 [57] 52.00000 55.00000 53.00000 53.00000 56.00000 54.00000 52.00000 55.00000
 [65] 54.00000 59.00000 56.00000 56.00000 51.00000 53.00000 52.00000 51.00000
 [73] 46.00000 49.00000 46.00000 55.00000 57.00000 53.00000 52.00000 53.00000
 [81] 50.00000 54.00000 53.00000 50.00000 51.00000 52.00000 47.00000 51.00000
 [89] 49.00000 53.00000 52.00000 45.00000 53.00000 51.00000 48.00000 48.00000
 [97] 48.00000 48.00000 40.00000 43.00000 40.00000 39.00000 39.00000 36.00000
[105] 41.00000 39.00000 40.00000 39.00000 46.00000 42.18161 43.36295 44.29296
[113] 45.16086 43.71455 43.96674 43.39683 43.17170 43.49691 44.65293 44.39997
[121] 47.40326
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 110 
End = 121 
Frequency = 1 
 [1] 0.07238531 0.07889631 0.08865794 0.09364670 0.10416057 0.11112294
 [7] 0.12140048 0.13143417 0.13951701 0.14359034 0.15071101 0.14590290
> postscript(file="/var/www/html/rcomp/tmp/1h3361259962898.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2xfo61259962898.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/3xheg1259962898.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/4p22d1259962898.tab") 
> 
> system("convert tmp/1h3361259962898.ps tmp/1h3361259962898.png")
> system("convert tmp/2xfo61259962898.ps tmp/2xfo61259962898.png")
> 
> 
> proc.time()
   user  system elapsed 
  6.503   0.909   7.542