R version 2.8.0 (2008-10-20)
Copyright (C) 2008 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> x <- c(6340.5,7901.5,8191.1,7181.7,7594.4,7384.7,7876.7,8463.4,8317.2,7778.7,8532.8,7272.2,6680.1,8427.6,8752.8,7952.7,8694.3,7787,8474.2,9154.7,8557.2,7951.1,9156.7,7865.7,7337.4,9131.7,8814.6,8598.8,8439.6,7451.8,8016.2,9544.1,8270.7,8102.2,9369,7657.7,7816.6,9391.3,9445.4,9533.1,10068.7,8955.5,10423.9,11617.2,9391.1,10872,10230.4,9221,9428.6,10934.5,10986,11724.6,11180.9,11163.2,11240.9,12107.1,10762.3,11340.4,11266.8,9542.7,9227.7,10571.9,10774.4,10392.8,9920.2,9884.9,10174.5,11395.4,10760.2,10570.1,10536,9902.6,8889,10837.3,11624.1,10509,10984.9,10649.1,10855.7,11677.4,10760.2,10046.2,10772.8,9987.7,8638.7,11063.7,11855.7,10684.5,11337.4,10478,11123.9,12909.3,11339.9,10462.2,12733.5,10519.2,10414.9,12476.8,12384.6,12266.7,12919.9,11497.3,12142,13919.4,12656.8,12034.1,13199.7,10881.3,11301.2,13643.9,12517,13981.1,14275.7,13435,13565.7,16216.3,12970,14079.9,14235,12213.4,12581)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '0'
> 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: AUTHOR(S), (YEAR), YOUR SOFTWARE TITLE (vNUMBER) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_YOURPAGE.wasp/
> #Source of accompanying publication: Office for Research, Development, and Education
> #Technical description: Write here your technical program description (don't use hard returns!)
> 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")


sigma^2 estimated as 432995:  log likelihood = -759.19,  aic = 1520.37
> (forecast <- predict(arima.out,fx))
$pred
Time Series:
Start = 110 
End = 121 
Frequency = 1 
 [1] 13363.1 13270.9 13153.0 13806.2 12383.6 13028.3 14805.7 13543.1 12920.4
[10] 14086.0 11767.6 12187.5

$se
Time Series:
Start = 110 
End = 121 
Frequency = 1 
 [1]  658.0235  930.5858 1139.7302 1316.0470 1471.3853 1611.8219 1740.9666
 [8] 1861.1716 1974.0705 2080.8531 2182.4171 2279.4603

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 110 
End = 121 
Frequency = 1 
 [1] 12073.374 11446.952 10919.129 11226.748  9499.685  9869.129 11393.406
 [8]  9895.204  9051.222 10007.528  7490.062  7719.758
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 110 
End = 121 
Frequency = 1 
 [1] 14652.83 15094.85 15386.87 16385.65 15267.52 16187.47 18217.99 17191.00
 [9] 16789.58 18164.47 16045.14 16655.24
> 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$pred))
  [1]  6340.5  7901.5  8191.1  7181.7  7594.4  7384.7  7876.7  8463.4  8317.2
 [10]  7778.7  8532.8  7272.2  6680.1  8427.6  8752.8  7952.7  8694.3  7787.0
 [19]  8474.2  9154.7  8557.2  7951.1  9156.7  7865.7  7337.4  9131.7  8814.6
 [28]  8598.8  8439.6  7451.8  8016.2  9544.1  8270.7  8102.2  9369.0  7657.7
 [37]  7816.6  9391.3  9445.4  9533.1 10068.7  8955.5 10423.9 11617.2  9391.1
 [46] 10872.0 10230.4  9221.0  9428.6 10934.5 10986.0 11724.6 11180.9 11163.2
 [55] 11240.9 12107.1 10762.3 11340.4 11266.8  9542.7  9227.7 10571.9 10774.4
 [64] 10392.8  9920.2  9884.9 10174.5 11395.4 10760.2 10570.1 10536.0  9902.6
 [73]  8889.0 10837.3 11624.1 10509.0 10984.9 10649.1 10855.7 11677.4 10760.2
 [82] 10046.2 10772.8  9987.7  8638.7 11063.7 11855.7 10684.5 11337.4 10478.0
 [91] 11123.9 12909.3 11339.9 10462.2 12733.5 10519.2 10414.9 12476.8 12384.6
[100] 12266.7 12919.9 11497.3 12142.0 13919.4 12656.8 12034.1 13199.7 10881.3
[109] 11301.2 13363.1 13270.9 13153.0 13806.2 12383.6 13028.3 14805.7 13543.1
[118] 12920.4 14086.0 11767.6 12187.5
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 110 
End = 121 
Frequency = 1 
 [1] 0.04924183 0.07012228 0.08665173 0.09532290 0.11881725 0.12371697
 [7] 0.11758759 0.13742582 0.15278711 0.14772491 0.18545983 0.18703264
> postscript(file="/var/www/html/freestat/rcomp/tmp/1ec0z1229265486.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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.se <- array(0, dim=fx)
> perf.mse <- 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$pred[i]
+ perf.mape[i] = perf.mape[i] + abs(perf.pe[i])
+ perf.se[i] = (x[nx+i] - forecast$pred[i])^2
+ perf.mse[i] = perf.mse[i] + perf.se[i]
+ 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 = perf.mape / fx
> perf.mse = perf.mse / fx
> perf.rmse = sqrt(perf.mse)
> postscript(file="/var/www/html/freestat/rcomp/tmp/26dzo1229265487.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[1:12] <- 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/freestat/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/html/freestat/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/freestat/rcomp/tmp/3d4vb1229265487.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.mape[i],4))
+ a<-table.element(a,round(perf.se[i],4))
+ a<-table.element(a,round(perf.mse[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/freestat/rcomp/tmp/412r01229265487.tab") 
> 
> system("convert tmp/1ec0z1229265486.ps tmp/1ec0z1229265486.png")
> system("convert tmp/26dzo1229265487.ps tmp/26dzo1229265487.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.831   0.449   0.925