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(6802.96,7132.68,7073.29,7264.5,7105.33,7218.71,7225.72,7354.25,7745.46,8070.26,8366.33,8667.51,8854.34,9218.1,9332.9,9358.31,9248.66,9401.2,9652.04,9957.38,10110.63,10169.26,10343.78,10750.21,11337.5,11786.96,12083.04,12007.74,11745.93,11051.51,11445.9,11924.88,12247.63,12690.91,12910.7,13202.12,13654.67,13862.82,13523.93,14211.17,14510.35,14289.23,14111.82,13086.59,13351.54,13747.69,12855.61,12926.93,12121.95,11731.65,11639.51,12163.78,12029.53,11234.18,9852.13,9709.04,9332.75,7108.6,6691.49,6143.05)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '1'
> par6 = '1'
> par5 = '1'
> par4 = '0'
> par3 = '1'
> par2 = '1'
> par1 = '20'
> #'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:
         ar1      ma1
      0.6741  -0.2509
s.e.  0.2755   0.3928

sigma^2 estimated as 80032:  log likelihood = -275.65,  aic = 557.29
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 41 
End = 60 
Frequency = 1 
 [1] 14475.23 14653.22 14773.20 14854.08 14908.60 14945.35 14970.12 14986.82
 [9] 14998.08 15005.66 15010.78 15014.23 15016.55 15018.12 15019.17 15019.89
[17] 15020.37 15020.69 15020.91 15021.05

$se
Time Series:
Start = 41 
End = 60 
Frequency = 1 
 [1]  282.8998  492.0705  689.7313  874.5670 1046.3198 1205.6984 1353.8368
 [8] 1491.9777 1621.3179 1742.9427 1857.8050 1966.7277 2070.4145 2169.4652
[15] 2264.3903 2355.6250 2443.5412 2528.4582 2610.6511 2690.3579

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 41 
End = 60 
Frequency = 1 
 [1] 13920.742 13688.762 13421.330 13139.930 12857.813 12582.181 12316.602
 [8] 12062.545 11820.294 11589.497 11369.482 11159.441 10958.539 10765.966
[15] 10580.969 10402.861 10231.025 10064.911  9904.031  9747.953
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 41 
End = 60 
Frequency = 1 
 [1] 15029.71 15617.68 16125.08 16568.23 16959.39 17308.52 17623.64 17911.10
 [9] 18175.86 18421.83 18652.08 18869.01 19074.56 19270.27 19457.38 19636.91
[17] 19809.71 19976.47 20137.78 20294.16
> 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$pred))
 [1]  6802.96  7132.68  7073.29  7264.50  7105.33  7218.71  7225.72  7354.25
 [9]  7745.46  8070.26  8366.33  8667.51  8854.34  9218.10  9332.90  9358.31
[17]  9248.66  9401.20  9652.04  9957.38 10110.63 10169.26 10343.78 10750.21
[25] 11337.50 11786.96 12083.04 12007.74 11745.93 11051.51 11445.90 11924.88
[33] 12247.63 12690.91 12910.70 13202.12 13654.67 13862.82 13523.93 14211.17
[41] 14475.23 14653.22 14773.20 14854.08 14908.60 14945.35 14970.12 14986.82
[49] 14998.08 15005.66 15010.78 15014.23 15016.55 15018.12 15019.17 15019.89
[57] 15020.37 15020.69 15020.91 15021.05
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 41 
End = 60 
Frequency = 1 
 [1] 0.01954372 0.03358105 0.04668800 0.05887722 0.07018230 0.08067381
 [7] 0.09043592 0.09955264 0.10810172 0.11615231 0.12376473 0.13099093
[13] 0.13787550 0.14445653 0.15076663 0.15683375 0.16268187 0.16833171
[19] 0.17380116 0.17910580
> postscript(file="/var/www/html/rcomp/tmp/1nxp71260797837.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2d3rt1260797837.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/35yfl1260797837.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/4krvt1260797837.tab") 
> 
> try(system("convert tmp/1nxp71260797837.ps tmp/1nxp71260797837.png",intern=TRUE))
character(0)
> try(system("convert tmp/2d3rt1260797837.ps tmp/2d3rt1260797837.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  0.586   0.304   0.715