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(17885.8,16937.6,16184.9,18148.5,19053.2,20976.7,21272.7,22421.3,23294.5,24382.9,22426.1,20486.0,21382.5,17905.4,20531.3,21459.1,22317.6,23989.7,24632.0,26713.3,27570.6,29388.6,27775.1,24109.,25640.6,23038.9,22723.0,24241.5,25290.6,27071.0,28601.2,28424.5,29419.0,31555.4,29780.7,25656.6,26193.0,24095.9,22440.2,25951.7,27634.5,27930.6,31247.3,31823.7,33078.7,34032.4,28265.0,25079.5,24743.5,18845.5,21224.7,21920.6,22734.1,23972.8,25671.1,25798.1,27893.9,29557.8,27541.7,26470.1,25185.1,23363.8,24300.2,25905.7,29036.8,32866.5,33260.0,35288.5,34999.2,34820.2)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '2'
> par7 = '0'
> par6 = '2'
> par5 = '12'
> par4 = '1'
> par3 = '1'
> par2 = '1'
> par1 = '24'
> #'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      ar2     sar1     sar2
      -0.6257  -0.3430  -0.5238  -0.2997
s.e.   0.1784   0.1702   0.2466   0.3129

sigma^2 estimated as 907112:  log likelihood = -275.61,  aic = 561.22
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 47 
End = 70 
Frequency = 1 
 [1] 32625.77 29290.40 30005.39 27466.15 27393.16 29655.17 30967.03 32006.60
 [9] 34116.24 34978.65 36055.51 37532.32 35982.00 32370.59 33290.11 30831.40
[17] 30330.88 32650.07 33966.35 35061.30 37267.81 37754.74 38846.84 40404.07

$se
Time Series:
Start = 47 
End = 70 
Frequency = 1 
 [1]  952.4242 1016.9518 1093.7817 1237.1954 1317.3588 1399.0141 1486.5304
 [8] 1561.0192 1633.7224 1704.8919 1771.7498 1836.5548 2062.2524 2163.2224
[15] 2266.2512 2390.0570 2490.2341 2588.9441 2688.0362 2780.3928 2870.4317
[22] 2958.3653 3043.1617 3125.8166

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 47 
End = 70 
Frequency = 1 
 [1] 30759.02 27297.18 27861.58 25041.25 24811.14 26913.10 28053.44 28947.01
 [9] 30914.15 31637.06 32582.88 33932.68 31939.99 28130.68 28848.26 26146.89
[17] 25450.02 27575.74 28697.80 29611.73 31641.76 31956.34 32882.24 34277.47
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 47 
End = 70 
Frequency = 1 
 [1] 34492.52 31283.63 32149.21 29891.05 29975.19 32397.23 33880.63 35066.20
 [9] 37318.34 38320.24 39528.14 41131.97 40024.02 36610.51 37731.96 35515.91
[17] 35211.74 37724.40 39234.91 40510.87 42893.85 43553.13 44811.43 46530.67
> 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$pred))
 [1] 17885.80 16937.60 16184.90 18148.50 19053.20 20976.70 21272.70 22421.30
 [9] 23294.50 24382.90 22426.10 20486.00 21382.50 17905.40 20531.30 21459.10
[17] 22317.60 23989.70 24632.00 26713.30 27570.60 29388.60 27775.10 24109.00
[25] 25640.60 23038.90 22723.00 24241.50 25290.60 27071.00 28601.20 28424.50
[33] 29419.00 31555.40 29780.70 25656.60 26193.00 24095.90 22440.20 25951.70
[41] 27634.50 27930.60 31247.30 31823.70 33078.70 34032.40 32625.77 29290.40
[49] 30005.39 27466.15 27393.16 29655.17 30967.03 32006.60 34116.24 34978.65
[57] 36055.51 37532.32 35982.00 32370.59 33290.11 30831.40 30330.88 32650.07
[65] 33966.35 35061.30 37267.81 37754.74 38846.84 40404.07
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 47 
End = 70 
Frequency = 1 
 [1] 0.02919239 0.03471963 0.03645284 0.04504437 0.04809079 0.04717607
 [7] 0.04800364 0.04877179 0.04788694 0.04874093 0.04913950 0.04893262
[13] 0.05731344 0.06682677 0.06807581 0.07752022 0.08210228 0.07929368
[19] 0.07913820 0.07930090 0.07702175 0.07835746 0.07833744 0.07736390
> postscript(file="/var/www/html/rcomp/tmp/1wupo1293198650.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/html/rcomp/tmp/2a4nx1293198650.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/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/3rw1u1293198650.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/4vx0h1293198650.tab") 
> 
> try(system("convert tmp/1wupo1293198650.ps tmp/1wupo1293198650.png",intern=TRUE))
character(0)
> try(system("convert tmp/2a4nx1293198650.ps tmp/2a4nx1293198650.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.041   0.364   5.402