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(11.04,11.02,11.03,11.17,11.19,11.15,11.13,11.06,11.01,11.03,10.99,10.94,11.00,11.06,11.06,11.05,11.04,11.15,11.20,11.16,11.30,11.23,11.25,11.25,11.12,11.14,11.17,11.25,11.27,11.34,11.39,11.44,11.46,11.49,11.51,11.48,11.49,11.52,11.56,11.58,11.58,11.58,11.60,11.62,11.62,11.64,11.67,11.66,11.72,11.82,11.90,12.04,12.08,12.15,12.19,12.22,12.23,12.25,12.26,12.27,12.34,12.38,12.42,12.43,12.48,12.50,12.50,12.49,12.46,12.45,12.45,12.38,12.42)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '1'
> par7 = '1'
> par6 = '3'
> par5 = '12'
> par4 = '0'
> par3 = '1'
> par2 = '1'
> par1 = '12'
> #'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:
          ar1     ar2     ar3     ma1     sar1
      -0.5928  0.3494  0.3809  0.9143  -0.1610
s.e.   0.1344  0.1398  0.1315  0.0865   0.1618

sigma^2 estimated as 0.002248:  log likelihood = 96.96,  aic = -181.93
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 62 
End = 73 
Frequency = 1 
 [1] 12.32791 12.34368 12.33590 12.33224 12.33539 12.32700 12.32942 12.32832
 [9] 12.32659 12.32704 12.32492 12.31524

$se
Time Series:
Start = 62 
End = 73 
Frequency = 1 
 [1] 0.04741582 0.07857787 0.10536062 0.13799098 0.16277055 0.18971540
 [7] 0.21311840 0.23547168 0.25679191 0.27630893 0.29531447 0.31297077

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 62 
End = 73 
Frequency = 1 
 [1] 12.23497 12.18967 12.12939 12.06178 12.01636 11.95516 11.91171 11.86680
 [9] 11.82328 11.78547 11.74611 11.70182
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 62 
End = 73 
Frequency = 1 
 [1] 12.42084 12.49769 12.54240 12.60271 12.65442 12.69884 12.74713 12.78985
 [9] 12.82990 12.86860 12.90374 12.92866
> 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$pred))
 [1] 11.04000 11.02000 11.03000 11.17000 11.19000 11.15000 11.13000 11.06000
 [9] 11.01000 11.03000 10.99000 10.94000 11.00000 11.06000 11.06000 11.05000
[17] 11.04000 11.15000 11.20000 11.16000 11.30000 11.23000 11.25000 11.25000
[25] 11.12000 11.14000 11.17000 11.25000 11.27000 11.34000 11.39000 11.44000
[33] 11.46000 11.49000 11.51000 11.48000 11.49000 11.52000 11.56000 11.58000
[41] 11.58000 11.58000 11.60000 11.62000 11.62000 11.64000 11.67000 11.66000
[49] 11.72000 11.82000 11.90000 12.04000 12.08000 12.15000 12.19000 12.22000
[57] 12.23000 12.25000 12.26000 12.27000 12.34000 12.32791 12.34368 12.33590
[65] 12.33224 12.33539 12.32700 12.32942 12.32832 12.32659 12.32704 12.32492
[73] 12.31524
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 62 
End = 73 
Frequency = 1 
 [1] 0.003846217 0.006365839 0.008540979 0.011189446 0.013195413 0.015390236
 [7] 0.017285351 0.019100062 0.020832355 0.022414868 0.023960756 0.025413293
> postscript(file="/var/www/html/freestat/rcomp/tmp/1gjw71292854706.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/www/html/freestat/rcomp/tmp/25lbj1292854706.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/www/html/freestat/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/html/freestat/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/freestat/rcomp/tmp/3zpxj1292854706.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/www/html/freestat/rcomp/tmp/4fmoj1292854706.tab") 
> 
> try(system("convert tmp/1gjw71292854706.ps tmp/1gjw71292854706.png",intern=TRUE))
character(0)
> try(system("convert tmp/25lbj1292854706.ps tmp/25lbj1292854706.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.168   0.456   1.269