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(325412,326011,328282,317480,317539,313737,312276,309391,302950,300316,304035,333476,337698,335932,323931,313927,314485,313218,309664,302963,298989,298423,310631,329765,335083,327616,309119,295916,291413,291542,284678,276475,272566,264981,263290,296806,303598,286994,276427,266424,267153,268381,262522,255542,253158,243803,250741,280445,285257,270976,261076,255603,260376,263903,264291,263276,262572,256167,264221,293860,300713,287224)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '1'
> par7 = '0'
> par6 = '3'
> par5 = '12'
> par4 = '0'
> par3 = '1'
> par2 = '1'
> par1 = '12'
> 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    sar1
      0.4162  -0.7024  0.1489  -0.1588  0.9433  -0.3305  0.7884
s.e.     NaN   0.0922     NaN      NaN     NaN      NaN  0.0944

sigma^2 estimated as 21281199:  log likelihood = -332.69,  aic = 681.37
Warning message:
In sqrt(diag(x$var.coef)) : NaNs produced
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 35 
End = 62 
Frequency = 1 
 [1] 275098.6 288258.8 292535.4 288108.9 273788.9 262476.2 258583.4 259216.4
 [9] 254132.6 247377.7 244025.3 238184.1 246365.2 256687.7 259914.2 256431.4
[17] 245239.1 236334.8 233204.6 233682.8 229711.3 224406.9 221743.9 217121.5
[25] 223581.0 231732.2 234271.8 231516.5

$se
Time Series:
Start = 35 
End = 62 
Frequency = 1 
 [1]  4760.266  7625.072 10567.618 12291.946 13295.254 14386.531 15733.794
 [8] 16930.746 17849.728 18712.664 19652.635 20578.519 22716.170 25005.440
[15] 27590.417 29680.006 31291.991 32904.371 34661.133 36322.566 37775.914
[22] 39157.232 40570.170 41961.817 44078.680 46289.632 48684.268 50803.929

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 35 
End = 62 
Frequency = 1 
 [1] 265768.5 273313.6 271822.9 264016.7 247730.2 234278.6 227745.2 226032.2
 [9] 219147.1 210700.9 205506.2 197850.2 201841.5 207677.1 205837.0 198258.6
[17] 183906.8 171842.2 165268.8 162490.5 155670.5 147658.7 142226.4 134876.3
[25] 137186.8 141004.5 138850.6 131940.8
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 35 
End = 62 
Frequency = 1 
 [1] 284428.7 303203.9 313248.0 312201.2 299847.6 290673.8 289421.6 292400.7
 [9] 289118.0 284054.5 282544.5 278518.0 290888.9 305698.4 313991.4 314604.2
[17] 306571.4 300827.4 301140.4 304875.0 303752.1 301155.0 301261.4 299366.6
[25] 309975.2 322459.9 329692.9 331092.2
> 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$pred))
 [1] 325412.0 326011.0 328282.0 317480.0 317539.0 313737.0 312276.0 309391.0
 [9] 302950.0 300316.0 304035.0 333476.0 337698.0 335932.0 323931.0 313927.0
[17] 314485.0 313218.0 309664.0 302963.0 298989.0 298423.0 310631.0 329765.0
[25] 335083.0 327616.0 309119.0 295916.0 291413.0 291542.0 284678.0 276475.0
[33] 272566.0 264981.0 275098.6 288258.8 292535.4 288108.9 273788.9 262476.2
[41] 258583.4 259216.4 254132.6 247377.7 244025.3 238184.1 246365.2 256687.7
[49] 259914.2 256431.4 245239.1 236334.8 233204.6 233682.8 229711.3 224406.9
[57] 221743.9 217121.5 223581.0 231732.2 234271.8 231516.5
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 35 
End = 62 
Frequency = 1 
 [1] 0.01730385 0.02645218 0.03612423 0.04266423 0.04856024 0.05481079
 [7] 0.06084611 0.06531510 0.07023786 0.07564409 0.08053522 0.08639754
[13] 0.09220528 0.09741579 0.10615201 0.11574247 0.12759787 0.13922780
[19] 0.14862973 0.15543537 0.16444950 0.17449214 0.18295957 0.19326424
[25] 0.19714863 0.19975488 0.20781107 0.21943977
> postscript(file="/var/www/html/rcomp/tmp/104a51260468962.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/21f4x1260468962.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/324121260468962.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/4z1jd1260468962.tab") 
> system("convert tmp/104a51260468962.ps tmp/104a51260468962.png")
> system("convert tmp/21f4x1260468962.ps tmp/21f4x1260468962.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.888   0.317   1.000