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(9051,8823,8776,8255,7969,8758,8693,8271,7790,7769,8170,8209,9395,9260,9018,8501,8500,9649,9319,8830,8436,8169,8269,7945,9144,8770,8834,7837,7792,8616,8518,7940,7545,7531,7665,7599,8444,8549,7986,7335,7287,7870,7839,7327,7259,6964,7271,6956,7608,7692,7255,6804,6655,7341,7602,7086,6625,6272,6576,6491,7649,7400,6913,6532,6486,7295,7556,7088,6952,6773,6917,7371,8221,7953,8027,7287,8076,8933,9433,9479,9199,9469,10015,10999,13009,13699,13895,13248,13973,15095,15201,14823,14538,14547,14407)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '1'
> par7 = '1'
> par6 = '3'
> 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
      -0.2946  -0.8677  -0.4800  -0.0035  0.9842  0.1240  -0.4326
s.e.   0.2784   0.0705   0.2858   0.3072  0.0999  0.3324   0.1385

sigma^2 estimated as 40584:  log likelihood = -365.99,  aic = 747.97
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 68 
End = 95 
Frequency = 1 
 [1] 6982.321 6789.661 6455.447 6705.803 6495.765 7493.086 7419.523 6906.645
 [9] 6454.185 6401.922 7204.962 7438.575 6838.534 6545.988 6256.546 6525.096
[17] 6316.950 7378.122 7278.033 6791.773 6325.562 6252.086 7096.107 7372.451
[25] 6752.876 6467.426 6181.278 6481.469

$se
Time Series:
Start = 68 
End = 95 
Frequency = 1 
 [1]  204.5503  250.0537  307.8113  341.5611  375.3065  409.3775  443.1784
 [8]  470.3034  494.1895  519.8102  546.6527  569.9855  629.9621  673.9501
[15]  725.9246  767.2767  804.6236  841.9987  881.7933  918.1539  949.7171
[22]  980.8880 1014.4472 1046.9632 1120.8851 1174.7963 1238.0368 1292.7151

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 68 
End = 95 
Frequency = 1 
 [1] 6581.402 6299.556 5852.137 6036.343 5760.165 6690.707 6550.894 5984.850
 [9] 5485.574 5383.094 6133.522 6321.403 5603.808 5225.046 4833.734 5021.234
[17] 4739.888 5727.804 5549.718 4992.191 4464.116 4329.546 5107.790 5320.403
[25] 4555.941 4164.825 3754.726 3947.748
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 68 
End = 95 
Frequency = 1 
 [1] 7383.239 7279.766 7058.757 7375.263 7231.366 8295.466 8288.153 7828.439
 [9] 7422.797 7420.750 8276.401 8555.746 8073.260 7866.930 7679.358 8028.958
[17] 7894.012 9028.439 9006.347 8591.355 8187.007 8174.627 9084.424 9424.499
[25] 8949.810 8770.027 8607.831 9015.191
> 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$pred))
 [1] 9051.000 8823.000 8776.000 8255.000 7969.000 8758.000 8693.000 8271.000
 [9] 7790.000 7769.000 8170.000 8209.000 9395.000 9260.000 9018.000 8501.000
[17] 8500.000 9649.000 9319.000 8830.000 8436.000 8169.000 8269.000 7945.000
[25] 9144.000 8770.000 8834.000 7837.000 7792.000 8616.000 8518.000 7940.000
[33] 7545.000 7531.000 7665.000 7599.000 8444.000 8549.000 7986.000 7335.000
[41] 7287.000 7870.000 7839.000 7327.000 7259.000 6964.000 7271.000 6956.000
[49] 7608.000 7692.000 7255.000 6804.000 6655.000 7341.000 7602.000 7086.000
[57] 6625.000 6272.000 6576.000 6491.000 7649.000 7400.000 6913.000 6532.000
[65] 6486.000 7295.000 7556.000 6982.321 6789.661 6455.447 6705.803 6495.765
[73] 7493.086 7419.523 6906.645 6454.185 6401.922 7204.962 7438.575 6838.534
[81] 6545.988 6256.546 6525.096 6316.950 7378.122 7278.033 6791.773 6325.562
[89] 6252.086 7096.107 7372.451 6752.876 6467.426 6181.278 6481.469
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 68 
End = 95 
Frequency = 1 
 [1] 0.02929546 0.03682859 0.04768242 0.05093515 0.05777710 0.05463402
 [7] 0.05973139 0.06809434 0.07656884 0.08119597 0.07587170 0.07662563
[13] 0.09211946 0.10295621 0.11602641 0.11758857 0.12737534 0.11412101
[19] 0.12115820 0.13518619 0.15013958 0.15688972 0.14295828 0.14201019
[25] 0.16598634 0.18164819 0.20028815 0.19944785
> postscript(file="/var/www/html/rcomp/tmp/1smx81260540551.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/278j31260540551.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/3ty0g1260540551.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/4crcc1260540551.tab") 
> 
> system("convert tmp/1smx81260540551.ps tmp/1smx81260540551.png")
> system("convert tmp/278j31260540551.ps tmp/278j31260540551.png")
> 
> 
> proc.time()
   user  system elapsed 
  2.354   0.345   3.701