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(31514,27071,29462,26105,22397,23843,21705,18089,20764,25316,17704,15548,28029,29383,36438,32034,22679,24319,18004,17537,20366,22782,19169,13807,29743,25591,29096,26482,22405,27044,17970,18730,19684,19785,18479,10698,31956,29506,34506,27165,26736,23691,18157,17328,18205,20995,17382,9367,31124,26551,30651,25859,25100,25778,20418,18688,20424,24776,19814,12738,31566,30111,30019,31934,25826,26835)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '0'
> par6 = '0'
> par5 = '12'
> par4 = '1'
> par3 = '0'
> par2 = '1'
> par1 = '50'
> #'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 25327047:  log likelihood = -39.77,  aic = 81.54
> (forecast <- predict(arima.out,fx))
$pred
Time Series:
Start = 17 
End = 66 
Frequency = 1 
 [1] 22397 23843 21705 18089 20764 25316 17704 15548 28029 29383 36438 32034
[13] 22397 23843 21705 18089 20764 25316 17704 15548 28029 29383 36438 32034
[25] 22397 23843 21705 18089 20764 25316 17704 15548 28029 29383 36438 32034
[37] 22397 23843 21705 18089 20764 25316 17704 15548 28029 29383 36438 32034
[49] 22397 23843

$se
Time Series:
Start = 17 
End = 66 
Frequency = 1 
 [1]  5032.598  5032.598  5032.598  5032.598  5032.598  5032.598  5032.598
 [8]  5032.598  5032.598  5032.598  5032.598  5032.598  7117.169  7117.169
[15]  7117.169  7117.169  7117.169  7117.169  7117.169  7117.169  7117.169
[22]  7117.169  7117.169  7117.169  8716.716  8716.716  8716.716  8716.716
[29]  8716.716  8716.716  8716.716  8716.716  8716.716  8716.716  8716.716
[36]  8716.716 10065.197 10065.197 10065.197 10065.197 10065.197 10065.197
[43] 10065.197 10065.197 10065.197 10065.197 10065.197 10065.197 11253.232
[50] 11253.232

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 17 
End = 66 
Frequency = 1 
 [1] 12533.1072 13979.1072 11841.1072  8225.1072 10900.1072 15452.1072
 [7]  7840.1072  5684.1072 18165.1072 19519.1072 26574.1072 22170.1072
[13]  8447.3490  9893.3490  7755.3490  4139.3490  6814.3490 11366.3490
[19]  3754.3490  1598.3490 14079.3490 15433.3490 22488.3490 18084.3490
[25]  5312.2365  6758.2365  4620.2365  1004.2365  3679.2365  8231.2365
[31]   619.2365 -1536.7635 10944.2365 12298.2365 19353.2365 14949.2365
[37]  2669.2143  4115.2143  1977.2143 -1638.7857  1036.2143  5588.2143
[43] -2023.7857 -4179.7857  8301.2143  9655.2143 16710.2143 12306.2143
[49]   340.6651  1786.6651
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 17 
End = 66 
Frequency = 1 
 [1] 32260.89 33706.89 31568.89 27952.89 30627.89 35179.89 27567.89 25411.89
 [9] 37892.89 39246.89 46301.89 41897.89 36346.65 37792.65 35654.65 32038.65
[17] 34713.65 39265.65 31653.65 29497.65 41978.65 43332.65 50387.65 45983.65
[25] 39481.76 40927.76 38789.76 35173.76 37848.76 42400.76 34788.76 32632.76
[33] 45113.76 46467.76 53522.76 49118.76 42124.79 43570.79 41432.79 37816.79
[41] 40491.79 45043.79 37431.79 35275.79 47756.79 49110.79 56165.79 51761.79
[49] 44453.33 45899.33
> 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$pred))
 [1] 31514 27071 29462 26105 22397 23843 21705 18089 20764 25316 17704 15548
[13] 28029 29383 36438 32034 22397 23843 21705 18089 20764 25316 17704 15548
[25] 28029 29383 36438 32034 22397 23843 21705 18089 20764 25316 17704 15548
[37] 28029 29383 36438 32034 22397 23843 21705 18089 20764 25316 17704 15548
[49] 28029 29383 36438 32034 22397 23843 21705 18089 20764 25316 17704 15548
[61] 28029 29383 36438 32034 22397 23843
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 17 
End = 66 
Frequency = 1 
 [1] 0.2246997 0.2110724 0.2318636 0.2782132 0.2423713 0.1987912 0.2842634
 [8] 0.3236814 0.1795497 0.1712759 0.1381140 0.1571018 0.3177733 0.2985014
[15] 0.3279046 0.3934529 0.3427648 0.2811332 0.4020091 0.4577546 0.2539216
[22] 0.2422206 0.1953227 0.2221755 0.3891912 0.3655881 0.4015995 0.4818794
[29] 0.4197995 0.3443165 0.4923586 0.5606326 0.3109892 0.2966585 0.2392205
[36] 0.2721083 0.4493993 0.4221447 0.4637271 0.5564264 0.4847427 0.3975824
[43] 0.5685267 0.6473628 0.3590994 0.3425517 0.2762280 0.3142036 0.5024437
[50] 0.4719722
> postscript(file="/var/www/html/rcomp/tmp/1do481229334603.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2gxm21229334603.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]
Warning message:
In NextMethod("[<-") :
  number of items to replace is not a multiple of replacement length
> 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/34xlx1229334603.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/44dpv1229334603.tab") 
> 
> system("convert tmp/1do481229334603.ps tmp/1do481229334603.png")
> system("convert tmp/2gxm21229334603.ps tmp/2gxm21229334603.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.884   0.365   0.967