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(116222,110924,103753,99983,93302,91496,119321,139261,133739,123913,113438,109416,109406,105645,101328,97686,93093,91382,122257,139183,139887,131822,116805,113706,113012,110452,107005,102841,98173,98181,137277,147579,146571,138920,130340,128140,127059,122860,117702,113537,108366,111078,150739,159129,157928,147768,137507,136919,136151,133001,125554,119647,114158,116193,152803,161761,160942,149470,139208,134588,130322,126611,122401,117352,112135,112879,148729,157230,157221,146681,136524,132111)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '0'
> par6 = '0'
> par5 = '12'
> par4 = '1'
> par3 = '1'
> par2 = '1'
> par1 = '24'
> par1 <- as.numeric(par1) #cut off periods
> par1 <- 28
> 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
> par6 <- 3
> par7 <- as.numeric(par7) #q
> par7 <- 3
> 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     ma3
      0.4554  0.1594  -0.4401  -0.8998  -0.1186  0.6994
s.e.     NaN     NaN      NaN      NaN      NaN     NaN

sigma^2 estimated as 6424568:  log likelihood = -288.66,  aic = 591.32
Warning message:
In sqrt(diag(x$var.coef)) : NaNs produced
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 45 
End = 72 
Frequency = 1 
 [1] 157749.1 149948.3 141423.0 139387.7 138456.4 134327.7 129153.1 124925.9
 [9] 119693.0 122374.2 162038.6 170452.6 169097.7 161310.6 152785.0 150740.7
[17] 149799.2 145664.6 140489.6 136265.8 131036.9 133720.7 173385.5 181798.2
[25] 180441.7 172653.5 164127.7 162083.8

$se
Time Series:
Start = 45 
End = 72 
Frequency = 1 
 [1]  2600.633  3024.724  3222.751  3489.206  3940.975  4553.191  5178.669
 [8]  5710.797  6124.264  6452.332  6738.928  7018.734  8411.880  9173.080
[15]  9737.221 10341.581 11069.902 11900.313 12736.015 13500.063 14166.095
[22] 14754.175 15298.455 15828.684 17201.234 18137.212 18911.429 19715.157

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 45 
End = 72 
Frequency = 1 
 [1] 152651.9 144019.9 135106.5 132548.9 130732.1 125403.4 119002.9 113732.7
 [9] 107689.4 109727.6 148830.3 156695.8 152610.4 143331.3 133700.0 130471.2
[17] 128102.2 122340.0 115527.0 109805.7 103271.4 104802.5 143400.5 150774.0
[25] 146727.2 137104.5 127061.3 123442.1
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 45 
End = 72 
Frequency = 1 
 [1] 162846.4 155876.8 147739.6 146226.6 146180.7 143251.9 139303.3 136119.1
 [9] 131696.5 135020.7 175246.9 184209.3 185585.0 179289.8 171869.9 171010.2
[17] 171496.2 168989.2 165452.2 162725.9 158802.5 162638.9 203370.5 212822.4
[25] 214156.1 208202.4 201194.1 200725.5
> 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$pred))
 [1] 116222.0 110924.0 103753.0  99983.0  93302.0  91496.0 119321.0 139261.0
 [9] 133739.0 123913.0 113438.0 109416.0 109406.0 105645.0 101328.0  97686.0
[17]  93093.0  91382.0 122257.0 139183.0 139887.0 131822.0 116805.0 113706.0
[25] 113012.0 110452.0 107005.0 102841.0  98173.0  98181.0 137277.0 147579.0
[33] 146571.0 138920.0 130340.0 128140.0 127059.0 122860.0 117702.0 113537.0
[41] 108366.0 111078.0 150739.0 159129.0 157749.1 149948.3 141423.0 139387.7
[49] 138456.4 134327.7 129153.1 124925.9 119693.0 122374.2 162038.6 170452.6
[57] 169097.7 161310.6 152785.0 150740.7 149799.2 145664.6 140489.6 136265.8
[65] 131036.9 133720.7 173385.5 181798.2 180441.7 172653.5 164127.7 162083.8
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 45 
End = 72 
Frequency = 1 
 [1] 0.01648588 0.02017177 0.02278802 0.02503238 0.02846366 0.03389614
 [7] 0.04009714 0.04571347 0.05116644 0.05272625 0.04158840 0.04117705
[13] 0.04974568 0.05686595 0.06373154 0.06860510 0.07389828 0.08169668
[19] 0.09065449 0.09907155 0.10810764 0.11033577 0.08823377 0.08706734
[25] 0.09532850 0.10504979 0.11522390 0.12163556
> postscript(file="/var/www/html/rcomp/tmp/1d7w71260459002.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2saf31260459002.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/39f5k1260459002.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/47bfq1260459002.tab") 
> 
> system("convert tmp/1d7w71260459002.ps tmp/1d7w71260459002.png")
> system("convert tmp/2saf31260459002.ps tmp/2saf31260459002.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.898   0.362   3.076