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(2058.00,2160.00,2260.00,2498.00,2695.00,2799.00,2947.00,2930.00,2318.00,2540.00,2570.00,2669.00,2450.00,2842.00,3440.00,2678.00,2981.00,2260.00,2844.00,2546.00,2456.00,2295.00,2379.00,2479.00,2057.00,2280.00,2351.00,2276.00,2548.00,2311.00,2201.00,2725.00,2408.00,2139.00,1898.00,2537.00,2069.00,2063.00,2526.00,2440.00,2191.00,2797.00,2074.00,2628.00,2287.00,2146.00,2430.00,2141.00,1827.00,2082.00,1788.00,1743.00,2245.00,1963.00,1828.00,2527.00,2114.00,2424.00)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '0'
> par6 = '3'
> par5 = '12'
> par4 = '0'
> par3 = '0'
> par2 = '-1.7'
> 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")

Coefficients:
         ar1     ar2     ar3
      0.2822  0.3751  0.3360
s.e.  0.1412  0.1333  0.1409

sigma^2 estimated as 1.188e-13:  log likelihood = 617.16,  aic = -1226.33
> (forecast <- predict(arima.out,fx))
$pred
Time Series:
Start = 47 
End = 58 
Frequency = 1 
 [1] 1.858350e-06 1.991758e-06 1.987655e-06 1.932217e-06 1.959856e-06
 [6] 1.945483e-06 1.933169e-06 1.933589e-06 1.924260e-06 1.917648e-06
[11] 1.912425e-06 1.905337e-06

$se
Time Series:
Start = 47 
End = 58 
Frequency = 1 
 [1] 3.446393e-07 3.580957e-07 3.908806e-07 4.374810e-07 4.614797e-07
 [6] 4.910333e-07 5.191199e-07 5.431594e-07 5.675618e-07 5.904985e-07
[11] 6.121648e-07 6.332339e-07

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 47 
End = 58 
Frequency = 1 
 [1] 1.182857e-06 1.289890e-06 1.221529e-06 1.074754e-06 1.055355e-06
 [6] 9.830574e-07 9.156936e-07 8.689964e-07 8.118389e-07 7.602712e-07
[11] 7.125821e-07 6.641989e-07
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 47 
End = 58 
Frequency = 1 
 [1] 2.533843e-06 2.693626e-06 2.753781e-06 2.789680e-06 2.864356e-06
 [6] 2.907908e-06 2.950643e-06 2.998181e-06 3.036681e-06 3.075025e-06
[11] 3.112268e-06 3.146476e-06
> 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$pred))
 [1] 2058.000 2160.000 2260.000 2498.000 2695.000 2799.000 2947.000 2930.000
 [9] 2318.000 2540.000 2570.000 2669.000 2450.000 2842.000 3440.000 2678.000
[17] 2981.000 2260.000 2844.000 2546.000 2456.000 2295.000 2379.000 2479.000
[25] 2057.000 2280.000 2351.000 2276.000 2548.000 2311.000 2201.000 2725.000
[33] 2408.000 2139.000 1898.000 2537.000 2069.000 2063.000 2526.000 2440.000
[41] 2191.000 2797.000 2074.000 2628.000 2287.000 2146.000 2350.182 2256.266
[49] 2259.004 2296.908 2277.798 2287.682 2296.243 2295.949 2302.490 2307.157
[57] 2310.861 2315.914
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 47 
End = 58 
Frequency = 1 
 [1] 0.1553033 0.1485668 0.1691853 0.2102312 0.2241009 0.2520950 0.2816366
 [8] 0.3065009 0.3374349 0.3690150 0.4017008 0.4381353
> postscript(file="/var/www/html/rcomp/tmp/1bqbc1261678884.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/rcomp/tmp/24sx01261678884.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/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/3mzsm1261678884.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/rcomp/tmp/488o61261678884.tab") 
> 
> try(system("convert tmp/1bqbc1261678884.ps tmp/1bqbc1261678884.png",intern=TRUE))
character(0)
> try(system("convert tmp/24sx01261678884.ps tmp/24sx01261678884.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  0.596   0.315   0.847