R version 2.12.0 (2010-10-15)
Copyright (C) 2010 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: i486-pc-linux-gnu (32-bit)

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> x <- c(5732,6938,6660,6695,6484,7716,5927,4768,7081,6947,7723,7319,6285,6655,7331,6468,7653,7330,5907,5257,7029,8885,9477,6822,8595,8738,11380,9831,10560,10336,8872,7598,9713,10858,10430,7516,8344,8623,9238,10350,9415,9550,8301,6405,10251,10082,8683,7829,6712,7354,8402,8211,8377,9133,8301,5932,9080,9459,9647,8646,7503,10000,10441,6435,8102,9983,8662,6575,9088,9336,9089)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '2'
> par7 = '1'
> par6 = '0'
> par5 = '12'
> par4 = '1'
> par3 = '1'
> par2 = '1'
> par1 = '12'
> #'GNU S' R Code compiled by R2WASP v. 1.0.44 ()
> #Author: Prof. Dr. P. Wessa
> #To cite this work: Wessa P., (2009), ARIMA Forecasting (v1.0.5) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_arimaforecasting.wasp/
> #Source of accompanying publication: 
> #Technical description: 
> 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 <- as.numeric(par6) #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:
          ma1     sar1     sar2
      -0.4983  -0.4367  -0.6962
s.e.   0.1210   0.1453   0.1114

sigma^2 estimated as 521084:  log likelihood = -376.55,  aic = 761.09
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 60 
End = 71 
Frequency = 1 
 [1]  7985.741  8376.161  8764.933 11035.092  9560.490 10404.167 10638.997
 [8]  9475.182  7745.823  9993.489 11048.005 11218.930

$se
Time Series:
Start = 60 
End = 71 
Frequency = 1 
 [1]  721.8613  807.6121  885.0936  956.3180 1022.5936 1084.8277 1143.6803
 [8] 1199.6491 1253.1207 1304.4021 1353.7424 1401.3465

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 60 
End = 71 
Frequency = 1 
 [1] 6570.892 6793.241 7030.149 9160.708 7556.207 8277.905 8397.384 7123.870
 [9] 5289.707 7436.861 8394.670 8472.291
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 60 
End = 71 
Frequency = 1 
 [1]  9400.589  9959.080 10499.716 12909.475 11564.774 12530.430 12880.611
 [8] 11826.494 10201.940 12550.117 13701.340 13965.569
> 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$pred))
 [1]  5732.000  6938.000  6660.000  6695.000  6484.000  7716.000  5927.000
 [8]  4768.000  7081.000  6947.000  7723.000  7319.000  6285.000  6655.000
[15]  7331.000  6468.000  7653.000  7330.000  5907.000  5257.000  7029.000
[22]  8885.000  9477.000  6822.000  8595.000  8738.000 11380.000  9831.000
[29] 10560.000 10336.000  8872.000  7598.000  9713.000 10858.000 10430.000
[36]  7516.000  8344.000  8623.000  9238.000 10350.000  9415.000  9550.000
[43]  8301.000  6405.000 10251.000 10082.000  8683.000  7829.000  6712.000
[50]  7354.000  8402.000  8211.000  8377.000  9133.000  8301.000  5932.000
[57]  9080.000  9459.000  9647.000  7985.741  8376.161  8764.933 11035.092
[64]  9560.490 10404.167 10638.997  9475.182  7745.823  9993.489 11048.005
[71] 11218.930
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 60 
End = 71 
Frequency = 1 
 [1] 0.09039379 0.09641793 0.10098122 0.08666154 0.10696037 0.10426857
 [7] 0.10749888 0.12660961 0.16178018 0.13052520 0.12253274 0.12490910
> postscript(file="/var/www/rcomp/tmp/1vq1z1293185070.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/www/rcomp/tmp/2rzy81293185070.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/www/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/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/rcomp/tmp/3g0dk1293185070.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/rcomp/tmp/4j1cq1293185070.tab") 
> 
> try(system("convert tmp/1vq1z1293185070.ps tmp/1vq1z1293185070.png",intern=TRUE))
character(0)
> try(system("convert tmp/2rzy81293185070.ps tmp/2rzy81293185070.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  0.940   0.520   1.403