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(13363,12530,11420,10948,10173,10602,16094,19631,17140,14345,12632,12894,11808,10673,9939,9890,9283,10131,15864,19283,16203,13919,11937,11795,11268,10522,9929,9725,9372,10068,16230,19115,18351,16265,14103,14115,13327,12618,12129,11775,11493,12470,20792,22337,21325,18581,16475,16581,15745,14453,13712,13766,13336,15346,24446,26178,24628,21282,18850,18822,18060,17536,16417,15842,15188,16905,25430,27962,26607,23364,20827,20506,19181,18016,17354,16256,15770,17538,26899,28915,25247,22856,19980,19856,16994,16839,15618,15883,15513,17106,25272,26731,22891,19583,16939,16757,15435,14786,13680,13208,12707,14277,22436,23229,18241,16145,13994,14780,13100,12329,12463,11532,10784,13106,19491,20418,16094,14491,13067)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '2'
> par7 = '1'
> par6 = '1'
> par5 = '12'
> par4 = '1'
> par3 = '1'
> par2 = '0.3'
> 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     ma1     sar1     sar2
      -0.7521  0.6131  -0.2807  -0.0212
s.e.   0.1879  0.2173   0.1089   0.1263

sigma^2 estimated as 0.03664:  log likelihood = 21.53,  aic = -33.07
> (forecast <- predict(arima.out,fx))
$pred
Time Series:
Start = 108 
End = 119 
Frequency = 1 
 [1] 17.49946 16.91850 16.74498 16.32736 16.21992 16.03439 16.62652 19.12010
 [9] 19.37686 18.07858 17.33482 16.54987

$se
Time Series:
Start = 108 
End = 119 
Frequency = 1 
 [1] 0.1914053 0.2525795 0.3129722 0.3560496 0.3994517 0.4351342 0.4705023
 [8] 0.5016999 0.5322665 0.5603137 0.5876365 0.6133014

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 108 
End = 119 
Frequency = 1 
 [1] 17.12431 16.42344 16.13155 15.62950 15.43700 15.18152 15.70434 18.13677
 [9] 18.33362 16.98037 16.18305 15.34779
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 108 
End = 119 
Frequency = 1 
 [1] 17.87461 17.41355 17.35841 17.02522 17.00285 16.88725 17.54871 20.10343
 [9] 20.42011 19.17680 18.48659 17.75194
> 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$pred))
  [1] 13363.00 12530.00 11420.00 10948.00 10173.00 10602.00 16094.00 19631.00
  [9] 17140.00 14345.00 12632.00 12894.00 11808.00 10673.00  9939.00  9890.00
 [17]  9283.00 10131.00 15864.00 19283.00 16203.00 13919.00 11937.00 11795.00
 [25] 11268.00 10522.00  9929.00  9725.00  9372.00 10068.00 16230.00 19115.00
 [33] 18351.00 16265.00 14103.00 14115.00 13327.00 12618.00 12129.00 11775.00
 [41] 11493.00 12470.00 20792.00 22337.00 21325.00 18581.00 16475.00 16581.00
 [49] 15745.00 14453.00 13712.00 13766.00 13336.00 15346.00 24446.00 26178.00
 [57] 24628.00 21282.00 18850.00 18822.00 18060.00 17536.00 16417.00 15842.00
 [65] 15188.00 16905.00 25430.00 27962.00 26607.00 23364.00 20827.00 20506.00
 [73] 19181.00 18016.00 17354.00 16256.00 15770.00 17538.00 26899.00 28915.00
 [81] 25247.00 22856.00 19980.00 19856.00 16994.00 16839.00 15618.00 15883.00
 [89] 15513.00 17106.00 25272.00 26731.00 22891.00 19583.00 16939.00 16757.00
 [97] 15435.00 14786.00 13680.00 13208.00 12707.00 14277.00 22436.00 23229.00
[105] 18241.00 16145.00 13994.00 13912.83 12431.95 12012.00 11042.14 10801.80
[113] 10395.40 11731.09 18691.05 19540.92 15507.72 13481.28 11551.76
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 108 
End = 119 
Frequency = 1 
 [1] 0.03737986 0.05148498 0.06500788 0.07638355 0.08681319 0.09620519
 [7] 0.10058263 0.09283307 0.09745354 0.11083119 0.12201654 0.13433332
> postscript(file="/var/www/html/rcomp/tmp/1469i1229772879.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/256x71229772879.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/3nahy1229772879.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/46rnw1229772879.tab") 
> 
> system("convert tmp/1469i1229772879.ps tmp/1469i1229772879.png")
> system("convert tmp/256x71229772879.ps tmp/256x71229772879.png")
> 
> 
> proc.time()
   user  system elapsed 
  1.539   0.341   2.105