R version 2.13.0 (2011-04-13)
Copyright (C) 2011 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: i486-pc-linux-gnu (32-bit)

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> x <- c(41,39,50,40,43,38,44,35,39,35,29,49,50,59,63,32,39,47,53,60,57,52,70,90,74,62,55,84,94,70,108,139,120,97,126,149,158,124,140,109,114,77,120,133,110,92,97,78,99,107,112,90,98,125,155,190,236,189,174,178,136,161,171,149,184,155,276,224,213,279,268,287,238,213,257,293,212,246,353,339,308,247,257,322,298,273,312,249,286,279,309,401,309,328,353,354,327,324,285,243,241,287,355,460,364,487,452,391,500,451,375,372,302,316,398,394,431,431)
> par10 = 'TRUE'
> par9 = '1'
> par8 = '2'
> par7 = '2'
> par6 = '3'
> par5 = '2'
> par4 = '0'
> par3 = '1'
> par2 = '0.0'
> par1 = '12'
> 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
      -0.8370  -0.9956  -0.3077  0.5711  1.0000  -0.1443  -0.0630  -0.1765
s.e.   0.1109   0.0965   0.1196  0.0558  0.0678   0.5748   0.2437   0.5843

sigma^2 estimated as 0.03675:  log likelihood = 22.49,  aic = -26.99
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 107 
End = 118 
Frequency = 1 
 [1] 6.078528 6.062054 6.066835 6.015253 6.064100 6.080300 6.035013 6.046884
 [9] 6.076563 6.052642 6.039470 6.065029

$se
Time Series:
Start = 107 
End = 118 
Frequency = 1 
 [1] 0.1932504 0.2392011 0.2678320 0.2842139 0.2977000 0.3224074 0.3405986
 [8] 0.3525317 0.3704124 0.3886019 0.4004864 0.4135770

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 107 
End = 118 
Frequency = 1 
 [1] 5.699758 5.593220 5.541884 5.458194 5.480608 5.448382 5.367440 5.355922
 [9] 5.350555 5.290982 5.254517 5.254418
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 107 
End = 118 
Frequency = 1 
 [1] 6.457299 6.530888 6.591786 6.572312 6.647593 6.712219 6.702586 6.737846
 [9] 6.802571 6.814302 6.824423 6.875640
> 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$pred))
  [1]  41.0000  39.0000  50.0000  40.0000  43.0000  38.0000  44.0000  35.0000
  [9]  39.0000  35.0000  29.0000  49.0000  50.0000  59.0000  63.0000  32.0000
 [17]  39.0000  47.0000  53.0000  60.0000  57.0000  52.0000  70.0000  90.0000
 [25]  74.0000  62.0000  55.0000  84.0000  94.0000  70.0000 108.0000 139.0000
 [33] 120.0000  97.0000 126.0000 149.0000 158.0000 124.0000 140.0000 109.0000
 [41] 114.0000  77.0000 120.0000 133.0000 110.0000  92.0000  97.0000  78.0000
 [49]  99.0000 107.0000 112.0000  90.0000  98.0000 125.0000 155.0000 190.0000
 [57] 236.0000 189.0000 174.0000 178.0000 136.0000 161.0000 171.0000 149.0000
 [65] 184.0000 155.0000 276.0000 224.0000 213.0000 279.0000 268.0000 287.0000
 [73] 238.0000 213.0000 257.0000 293.0000 212.0000 246.0000 353.0000 339.0000
 [81] 308.0000 247.0000 257.0000 322.0000 298.0000 273.0000 312.0000 249.0000
 [89] 286.0000 279.0000 309.0000 401.0000 309.0000 328.0000 353.0000 354.0000
 [97] 327.0000 324.0000 285.0000 243.0000 241.0000 287.0000 355.0000 460.0000
[105] 364.0000 487.0000 436.3865 429.2563 431.3133 409.6295 430.1356 437.1604
[113] 417.8042 422.7935 435.5297 425.2350 419.6706 430.5353
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 107 
End = 118 
Frequency = 1 
 [1] 0.2349430 0.3051683 0.3522325 0.3803734 0.4042277 0.4496001 0.4844392
 [8] 0.5079768 0.5442929 0.5825654 0.6083186 0.6373886
> postscript(file="/var/wessaorg/rcomp/tmp/1xc5w1324645147.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/wessaorg/rcomp/tmp/2mo8n1324645147.ps",horizontal=F,onefile=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/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/wessaorg/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/wessaorg/rcomp/tmp/3h9qu1324645147.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/wessaorg/rcomp/tmp/4t0md1324645147.tab") 
> 
> try(system("convert tmp/1xc5w1324645147.ps tmp/1xc5w1324645147.png",intern=TRUE))
character(0)
> try(system("convert tmp/2mo8n1324645147.ps tmp/2mo8n1324645147.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.150   0.150   1.293