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(9487,8700,9627,8947,9283,8829,9947,9628,9318,9605,8640,9214,9567,8547,9185,9470,9123,9278,10170,9434,9655,9429,8739,9552,9687,9019,9672,9206,9069,9788,10312,10105,9863,9656,9295,9946,9701,9049,10190,9706,9765,9893,9994,10433,10073,10112,9266,9820,10097,9115,10411,9678,10408,10153,10368,10581,10597,10680,9738,9556)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '1'
> par7 = '1'
> par6 = '0'
> par5 = '12'
> par4 = '1'
> 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    sma1
      -1.1364  -0.7583  0.1572  0.3295  0.0373  -0.8300  -0.6915  0.5403
s.e.   0.3502   0.4353  0.3140  0.3956  0.3126   0.3057   2.6067  2.8237

sigma^2 estimated as 58295:  log likelihood = -134.2,  aic = 286.39
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1]  9774.873  9624.613  9188.304  9551.430  9944.562  9315.681  9595.692
 [8]  9671.663  9336.752  9832.361 10739.239 10145.621  9961.104  9994.477
[15]  9219.156  9863.278 10273.259  9392.433 10033.074  9818.804  9411.445
[22] 10251.430 10849.748 10396.342 10318.681 10078.736  9526.769 10132.762

$se
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1] 253.4658 255.8667 270.9781 273.2619 274.0230 288.0290 288.6028 291.1581
 [9] 301.5776 301.7269 308.3615 313.9377 386.9169 402.0955 417.9690 422.4023
[17] 434.1203 444.7191 449.0416 462.3816 469.5001 474.9412 487.9820 492.9573
[25] 591.8691 608.4829 626.6111 641.5255

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1]  9278.080  9123.115  8657.187  9015.836  9407.477  8751.144  9030.031
 [8]  9100.993  8745.660  9240.976 10134.851  9530.303  9202.747  9206.370
[15]  8399.937  9035.370  9422.383  8520.784  9152.953  8912.536  8491.225
[22]  9320.545  9893.303  9430.146  9158.618  8886.110  8298.611  8875.372
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1] 10271.666 10126.112  9719.422 10087.023 10481.647  9880.218 10161.354
 [8] 10242.333  9927.844 10423.746 11343.628 10760.939 10719.461 10782.584
[15] 10038.375 10691.187 11124.135 10264.083 10913.196 10725.072 10331.665
[22] 11182.314 11806.193 11362.538 11478.745 11271.363 10754.927 11390.152
> 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$pred))
 [1]  9487.000  8700.000  9627.000  8947.000  9283.000  8829.000  9947.000
 [8]  9628.000  9318.000  9605.000  8640.000  9214.000  9567.000  8547.000
[15]  9185.000  9470.000  9123.000  9278.000 10170.000  9434.000  9655.000
[22]  9429.000  8739.000  9552.000  9687.000  9019.000  9672.000  9206.000
[29]  9069.000  9788.000 10312.000 10105.000  9774.873  9624.613  9188.304
[36]  9551.430  9944.562  9315.681  9595.692  9671.663  9336.752  9832.361
[43] 10739.239 10145.621  9961.104  9994.477  9219.156  9863.278 10273.259
[50]  9392.433 10033.074  9818.804  9411.445 10251.430 10849.748 10396.342
[57] 10318.681 10078.736  9526.769 10132.762
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1] 0.02593034 0.02658462 0.02949164 0.02860953 0.02755506 0.03091873
 [7] 0.03007628 0.03010425 0.03230005 0.03068713 0.02871354 0.03094318
[13] 0.03884277 0.04023177 0.04533701 0.04282575 0.04225731 0.04734865
[19] 0.04475613 0.04709144 0.04988608 0.04632927 0.04497634 0.04741641
[25] 0.05735898 0.06037293 0.06577372 0.06331201
> postscript(file="/var/www/html/rcomp/tmp/132ob1260564592.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2i4nr1260564592.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/37xk71260564592.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/4jp5t1260564592.tab") 
> system("convert tmp/132ob1260564592.ps tmp/132ob1260564592.png")
> system("convert tmp/2i4nr1260564592.ps tmp/2i4nr1260564592.png")
> 
> 
> proc.time()
   user  system elapsed 
  2.351   0.362   2.713