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(18992,0,21552,1868501,7185612,10348382,6942386,4306121,2833176,1515513,1242981,699343,89497,128,10585,1070323,7167741,13193530,7885720,6785683,3106846,1706331,1286534,499079,24637,16,27309,873433,8435418,11290088,6840395,3803252,4388988,2680940,1174135,328388,22943,5657,28156,770831,8378147,13274946,7297840,2848227,2892179,1762224,1009375,188388,3393,0,13807,2619905,13297704,6240087,5108460,4553381,3148546,2433387,1748108,723454,58525,792,42585,1634386,10360570,6798599,4847748,4971202,343863,2200366,1549422,90144,63288,338,44863,1678135,9293357,9361258,6766402,4331272,3518962,2425786,1701795,552452,16104,0,90198,1731332,7954135,11561342,6834733,4255652,4243070,3415216,1841237,655456)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '1'
> par7 = '0'
> par6 = '0'
> par5 = '12'
> par4 = '1'
> par3 = '0'
> par2 = '1'
> 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 <- 6 #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      ar4      ar5      ar6    sar1     sma1
      -0.0421  -0.1716  0.0112  -0.0649  -0.0066  -0.0175  0.3101  -1.0000
s.e.   0.1176   0.1171  0.1175   0.1185   0.1150   0.1216  0.1272   0.3149

sigma^2 estimated as 1.392e+12:  log likelihood = -1117.37,  aic = 2252.75
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 85 
End = 96 
Frequency = 1 
 [1] -122086.30  -55534.81   18620.96 1563336.51 9135837.60 9837556.86
 [7] 6629649.70 4443941.58 3106776.50 2191823.40 1494314.53  488036.71

$se
Time Series:
Start = 85 
End = 96 
Frequency = 1 
 [1] 1252572 1253663 1271288 1271684 1272529 1272573 1272574 1272574 1272578
[10] 1272573 1272352 1272339

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 85 
End = 96 
Frequency = 1 
 [1] -2577127.6 -2512713.4 -2473104.4  -929164.1  6641681.4  7343313.4
 [7]  4135405.5  1949696.7   612523.4  -302419.9  -999495.7 -2005746.8
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 85 
End = 96 
Frequency = 1 
 [1]  2332955  2401644  2510346  4055837 11629994 12331800  9123894  6938187
 [9]  5601030  4686067  3988125  2981820
> 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$pred))
 [1]    18992.00        0.00    21552.00  1868501.00  7185612.00 10348382.00
 [7]  6942386.00  4306121.00  2833176.00  1515513.00  1242981.00   699343.00
[13]    89497.00      128.00    10585.00  1070323.00  7167741.00 13193530.00
[19]  7885720.00  6785683.00  3106846.00  1706331.00  1286534.00   499079.00
[25]    24637.00       16.00    27309.00   873433.00  8435418.00 11290088.00
[31]  6840395.00  3803252.00  4388988.00  2680940.00  1174135.00   328388.00
[37]    22943.00     5657.00    28156.00   770831.00  8378147.00 13274946.00
[43]  7297840.00  2848227.00  2892179.00  1762224.00  1009375.00   188388.00
[49]     3393.00        0.00    13807.00  2619905.00 13297704.00  6240087.00
[55]  5108460.00  4553381.00  3148546.00  2433387.00  1748108.00   723454.00
[61]    58525.00      792.00    42585.00  1634386.00 10360570.00  6798599.00
[67]  4847748.00  4971202.00   343863.00  2200366.00  1549422.00    90144.00
[73]    63288.00      338.00    44863.00  1678135.00  9293357.00  9361258.00
[79]  6766402.00  4331272.00  3518962.00  2425786.00  1701795.00   552452.00
[85]  -122086.30   -55534.81    18620.96  1563336.51  9135837.60  9837556.86
[91]  6629649.70  4443941.58  3106776.50  2191823.40  1494314.53   488036.71
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 85 
End = 96 
Frequency = 1 
 [1] -10.2597269 -22.5743569  68.2719080   0.8134422   0.1392898   0.1293587
 [7]   0.1919519   0.2863615   0.4096137   0.5806002   0.8514621   2.6070550
> postscript(file="/var/wessaorg/rcomp/tmp/16htr1324554117.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2lsji1324554117.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/3w8np1324554117.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/4hqiv1324554117.tab") 
> 
> try(system("convert tmp/16htr1324554117.ps tmp/16htr1324554117.png",intern=TRUE))
character(0)
> try(system("convert tmp/2lsji1324554117.ps tmp/2lsji1324554117.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  2.289   0.251   2.536