R version 2.13.0 (2011-04-13)
Copyright (C) 2011 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: i486-pc-linux-gnu (32-bit)

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> x <- c(23187,14727,43080,32519,39657,33614,28671,34243,27336,22916,24537,26128,22602,15744,41086,39690,43129,37863,35953,29133,24693,22205,21725,27192,21790,13253,37702,30364,32609,30212,29965,28352,25814,22414,20506,28806,22228,13971,36845,35338,35022,34777,26887,23970,22780,17351,21382,24561,17409,11514,31514,27071,29462,26105,22397,23843,21705,18089,20764,25316,17704,15548,28029,29383,36438,32034,22679,24319,18004,17537,20366,22782,19169,13807,29743,25591,29096,26482,22405,27044,17970,18730,19684,19785,18479,10698,31956,29506,34506,27165,26736,23691,18157,17328,18205,20995,17382,9367,31124,26551,30651,25859,25100,25778,20418,18688,20424,24776,19814,12738,31566,30111,30019,31934,25826,26835,20205,17789,20520,22518,15572,11509,25447,24090,27786,26195,20516,22759,19028,16971,20036,22485,18730,14538,27561,25985,34670,32066,27186,29586,21359,21553,19573,24256,22380)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '0'
> par7 = '1'
> par6 = '0'
> par5 = '12'
> par4 = '1'
> par3 = '1'
> par2 = '0.0'
> 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:
          ma1     sma1
      -0.7151  -1.0000
s.e.   0.0776   0.1457

sigma^2 estimated as 0.007691:  log likelihood = 95.42,  aic = -184.85
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 122 
End = 145 
Frequency = 1 
 [1]  9.354338 10.315737 10.204234 10.311150 10.204130 10.064123 10.070294
 [8]  9.858133  9.745558  9.824019  9.975006  9.741110  9.327110 10.288509
[15] 10.177006 10.283922 10.176902 10.036895 10.043066  9.830904  9.718330
[22]  9.796791  9.947778  9.713882

$se
Time Series:
Start = 122 
End = 145 
Frequency = 1 
 [1] 0.09209942 0.09575603 0.09927806 0.10267935 0.10597152 0.10916446
 [7] 0.11226662 0.11528534 0.11822701 0.12109724 0.12390099 0.12671988
[13] 0.13136440 0.13441881 0.13740533 0.14032831 0.14319163 0.14599881
[19] 0.14875302 0.15145715 0.15411385 0.15672552 0.15929437 0.16198744

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 122 
End = 145 
Frequency = 1 
 [1]  9.173824 10.128055 10.009649 10.109899  9.996426  9.850160  9.850252
 [8]  9.632173  9.513833  9.586668  9.732160  9.492739  9.069636 10.025048
[15]  9.907691 10.008879  9.896246  9.750737  9.751510  9.534048  9.416267
[22]  9.489609  9.635561  9.396386
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 122 
End = 145 
Frequency = 1 
 [1]  9.534853 10.503419 10.398819 10.512402 10.411834 10.278085 10.290337
 [8] 10.084092  9.977283 10.061369 10.217852  9.989481  9.584584 10.551970
[15] 10.446320 10.558966 10.457557 10.323052 10.334622 10.127760 10.020393
[22] 10.103973 10.259995 10.031377
> 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$pred))
  [1] 23187.00 14727.00 43080.00 32519.00 39657.00 33614.00 28671.00 34243.00
  [9] 27336.00 22916.00 24537.00 26128.00 22602.00 15744.00 41086.00 39690.00
 [17] 43129.00 37863.00 35953.00 29133.00 24693.00 22205.00 21725.00 27192.00
 [25] 21790.00 13253.00 37702.00 30364.00 32609.00 30212.00 29965.00 28352.00
 [33] 25814.00 22414.00 20506.00 28806.00 22228.00 13971.00 36845.00 35338.00
 [41] 35022.00 34777.00 26887.00 23970.00 22780.00 17351.00 21382.00 24561.00
 [49] 17409.00 11514.00 31514.00 27071.00 29462.00 26105.00 22397.00 23843.00
 [57] 21705.00 18089.00 20764.00 25316.00 17704.00 15548.00 28029.00 29383.00
 [65] 36438.00 32034.00 22679.00 24319.00 18004.00 17537.00 20366.00 22782.00
 [73] 19169.00 13807.00 29743.00 25591.00 29096.00 26482.00 22405.00 27044.00
 [81] 17970.00 18730.00 19684.00 19785.00 18479.00 10698.00 31956.00 29506.00
 [89] 34506.00 27165.00 26736.00 23691.00 18157.00 17328.00 18205.00 20995.00
 [97] 17382.00  9367.00 31124.00 26551.00 30651.00 25859.00 25100.00 25778.00
[105] 20418.00 18688.00 20424.00 24776.00 19814.00 12738.00 31566.00 30111.00
[113] 30019.00 31934.00 25826.00 26835.00 20205.00 17789.00 20520.00 22518.00
[121] 15572.00 11548.82 30204.22 27017.34 30066.00 27014.52 23485.13 23630.52
[129] 19113.16 17078.21 18472.14 21482.76 17002.40 11238.61 29392.91 26291.63
[137] 29258.41 26288.89 22854.30 22995.78 18599.77 16619.47 17975.96 20905.71
[145] 16545.70
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 122 
End = 145 
Frequency = 1 
 [1] 0.1009357 0.1053314 0.1095953 0.1137410 0.1177801 0.1217225 0.1255764
 [8] 0.1293493 0.1330474 0.1366763 0.1402409 0.1438446 0.1498258 0.1537890
[15] 0.1576871 0.1615244 0.1653049 0.1690318 0.1727084 0.1763375 0.1799218
[22] 0.1834635 0.1869649 0.1906545
> postscript(file="/var/wessaorg/rcomp/tmp/18qei1323186238.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/wessaorg/rcomp/tmp/20cr11323186238.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/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/wessaorg/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/wessaorg/rcomp/tmp/3lls91323186238.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/wessaorg/rcomp/tmp/4lerk1323186238.tab") 
> 
> try(system("convert tmp/18qei1323186238.ps tmp/18qei1323186238.png",intern=TRUE))
character(0)
> try(system("convert tmp/20cr11323186238.ps tmp/20cr11323186238.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  0.941   0.149   1.093