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(15.59,13.17,11.20,13.30,10.78,11.60,15.18,15.87,12.58,11.43,10.30,11.17,11.26,11.20,9.99,11.17,10.29,10.47,14.36,16.06,14.47,13.24,13.03,14.43,13.98,13.62,12.20,12.24,12.07,12.30,16.12,18.38,14.59,12.96,14.14,13.92,14.24,14.10,12.91,13.69,14.11,13.99,17.93,21.37,16.25,14.53,15.36,14.95,15.95,15.25,12.67,13.86,14.65,12.41,17.46,18.95,15.33,15.31,14.84,14.75,15.83,14.83,13.00,13.92,13.94,12.54,18.12,17.83,14.41,15.18,12.99,13.06,12.81,12.95,10.48,13.23,11.80,11.69,15.33,14.89,12.92,11.27,10.68,11.55)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '0'
> par6 = '3'
> par5 = '12'
> par4 = '1'
> par3 = '1'
> par2 = '1'
> par1 = '20'
> #'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
      -0.2983  -0.0235  0.3516
s.e.   0.1388   0.1467  0.1376

sigma^2 estimated as 0.8206:  log likelihood = -67.59,  aic = 143.18
> (forecast <- predict(arima.out,fx))
$pred
Time Series:
Start = 65 
End = 84 
Frequency = 1 
 [1] 14.66745 12.71021 17.58191 19.10350 15.57769 15.46616 15.03236 14.96683
 [9] 16.00649 15.03068 13.20302 14.10757 14.86808 12.90813 17.77490 19.30262
[17] 15.77414 15.66152 15.23027 15.16307

$se
Time Series:
Start = 65 
End = 84 
Frequency = 1 
 [1] 0.9058466 1.1065993 1.3067286 1.6467572 1.8369911 2.0385562 2.2599169
 [8] 2.4253372 2.5979272 2.7663187 2.9121590 3.0599463 3.5727584 3.8982690
[15] 4.2266934 4.6490995 4.9654734 5.2886320 5.6224789 5.9075199

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 65 
End = 84 
Frequency = 1 
 [1] 12.891991 10.541275 15.020725 15.875860 11.977191 11.470587 10.602925
 [8] 10.213170 10.914556  9.608699  7.495187  8.110075  7.865474  5.267520
[15]  9.490582 10.190383  6.041814  5.295805  4.210210  3.584328
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 65 
End = 84 
Frequency = 1 
 [1] 16.44291 14.87914 20.14310 22.33115 19.17820 19.46173 19.46180 19.72049
 [9] 21.09843 20.45267 18.91085 20.10506 21.87069 20.54873 26.05922 28.41485
[17] 25.50647 26.02724 26.25033 26.74181
> 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$pred))
 [1] 15.59000 13.17000 11.20000 13.30000 10.78000 11.60000 15.18000 15.87000
 [9] 12.58000 11.43000 10.30000 11.17000 11.26000 11.20000  9.99000 11.17000
[17] 10.29000 10.47000 14.36000 16.06000 14.47000 13.24000 13.03000 14.43000
[25] 13.98000 13.62000 12.20000 12.24000 12.07000 12.30000 16.12000 18.38000
[33] 14.59000 12.96000 14.14000 13.92000 14.24000 14.10000 12.91000 13.69000
[41] 14.11000 13.99000 17.93000 21.37000 16.25000 14.53000 15.36000 14.95000
[49] 15.95000 15.25000 12.67000 13.86000 14.65000 12.41000 17.46000 18.95000
[57] 15.33000 15.31000 14.84000 14.75000 15.83000 14.83000 13.00000 13.92000
[65] 14.66745 12.71021 17.58191 19.10350 15.57769 15.46616 15.03236 14.96683
[73] 16.00649 15.03068 13.20302 14.10757 14.86808 12.90813 17.77490 19.30262
[81] 15.77414 15.66152 15.23027 15.16307
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 65 
End = 84 
Frequency = 1 
 [1] 0.06175897 0.08706381 0.07432232 0.08620184 0.11792446 0.13180754
 [7] 0.15033678 0.16204748 0.16230458 0.18404477 0.22056767 0.21690102
[13] 0.24029723 0.30200113 0.23778998 0.24085332 0.31478564 0.33768310
[19] 0.36916480 0.38959927
> postscript(file="/var/www/html/rcomp/tmp/1lzop1229555202.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2svz31229555202.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/3ei191229555203.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/4qnot1229555203.tab") 
> 
> system("convert tmp/1lzop1229555202.ps tmp/1lzop1229555202.png")
> system("convert tmp/2svz31229555202.ps tmp/2svz31229555202.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.623   0.315   0.792