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(2.4,2.4,2.5,2.6,2.4,2.6,2.4,2.3,2.4,2.4,2.4,2.4,2.4,2.4,2.4,2.4,2.5,2.1,2.1,2,2,2,1.9,1.9,2,1.8,1.6,1.3,1.4,1.4,1.5,1.7,1.6,1.5,1.6,1.5,1.1,1.1,1.1,1.4,1.3,1.4,1.3,1.1,1,0.9,0.8,0.8,0.8,0.8,1,1.1,1,0.9,1.1,1.2,1.2,1.4,1.5,1.7,1.9,1.9,1.9,1.7,1.7,2.1,2,2,2.5,2.4,2.5,2.5,2,1.9,2.2,2.7,3.1,2.8,2.6,2.3,2.2,2.2,2,2,2.6,2.5,2.5,2.3,2,1.9,2,2.1,2.1,2.3,2.3,2.3,2.1,2.4,2.5,2.1,1.8,1.9,1.9,2.1,2.2,2,2.2,2,1.9,1.6,1.7,2,2.5,2.4,2.3,2.3,2.1,2.4,2.2,2.4,1.9,2.1,2.1,2.1,2,2.1,2.2,2.2,2.6,2.5,2.3,2.2,2.4,2.3,2.2,2.5,2.5,2.5,2.4,2.3,1.7,1.6,1.9,1.9,1.8,1.8,1.9,1.9,1.9,1.9,1.8,1.7,2.1,2.6,3.1,3.1,3.2,3.3,3.6,3.3,3.7,4,4,3.8,3.6,3.2,2.1,1.6,1.1,1.2,0.6,0.6,0,-0.1,-0.6,-0.2,-0.3,-0.1,0.5,0.9)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '2'
> par7 = '1'
> par6 = '2'
> par5 = '12'
> par4 = '0'
> par3 = '0'
> par2 = '1'
> par1 = '11'
> #'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     ma1     sar1     sar2
      0.0483  0.9496  1.0000  -0.6372  -0.3478
s.e.  0.0294  0.0295  0.0203   0.0833   0.0818

sigma^2 estimated as 0.03574:  log likelihood = 35.11,  aic = -58.22
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 170 
End = 180 
Frequency = 1 
 [1] 1.0231290 0.8018908 0.9807897 0.7297822 0.5271668 0.5650704 0.7165635
 [8] 0.7073295 0.7782396 1.3070946 1.6162226

$se
Time Series:
Start = 170 
End = 180 
Frequency = 1 
 [1] 0.1895530 0.2739096 0.3331029 0.3869572 0.4308745 0.4734236 0.5099210
 [8] 0.5460861 0.5779794 0.6098999 0.6385748

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 170 
End = 180 
Frequency = 1 
 [1]  0.65160520  0.26502790  0.32790815 -0.02865388 -0.31734713 -0.36283975
 [7] -0.28288157 -0.36299937 -0.35459999  0.11169077  0.36461599
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 170 
End = 180 
Frequency = 1 
 [1] 1.394653 1.338754 1.633671 1.488218 1.371681 1.492981 1.716009 1.777658
 [9] 1.911079 2.502499 2.867829
> 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$pred))
  [1] 2.4000000 2.4000000 2.5000000 2.6000000 2.4000000 2.6000000 2.4000000
  [8] 2.3000000 2.4000000 2.4000000 2.4000000 2.4000000 2.4000000 2.4000000
 [15] 2.4000000 2.4000000 2.5000000 2.1000000 2.1000000 2.0000000 2.0000000
 [22] 2.0000000 1.9000000 1.9000000 2.0000000 1.8000000 1.6000000 1.3000000
 [29] 1.4000000 1.4000000 1.5000000 1.7000000 1.6000000 1.5000000 1.6000000
 [36] 1.5000000 1.1000000 1.1000000 1.1000000 1.4000000 1.3000000 1.4000000
 [43] 1.3000000 1.1000000 1.0000000 0.9000000 0.8000000 0.8000000 0.8000000
 [50] 0.8000000 1.0000000 1.1000000 1.0000000 0.9000000 1.1000000 1.2000000
 [57] 1.2000000 1.4000000 1.5000000 1.7000000 1.9000000 1.9000000 1.9000000
 [64] 1.7000000 1.7000000 2.1000000 2.0000000 2.0000000 2.5000000 2.4000000
 [71] 2.5000000 2.5000000 2.0000000 1.9000000 2.2000000 2.7000000 3.1000000
 [78] 2.8000000 2.6000000 2.3000000 2.2000000 2.2000000 2.0000000 2.0000000
 [85] 2.6000000 2.5000000 2.5000000 2.3000000 2.0000000 1.9000000 2.0000000
 [92] 2.1000000 2.1000000 2.3000000 2.3000000 2.3000000 2.1000000 2.4000000
 [99] 2.5000000 2.1000000 1.8000000 1.9000000 1.9000000 2.1000000 2.2000000
[106] 2.0000000 2.2000000 2.0000000 1.9000000 1.6000000 1.7000000 2.0000000
[113] 2.5000000 2.4000000 2.3000000 2.3000000 2.1000000 2.4000000 2.2000000
[120] 2.4000000 1.9000000 2.1000000 2.1000000 2.1000000 2.0000000 2.1000000
[127] 2.2000000 2.2000000 2.6000000 2.5000000 2.3000000 2.2000000 2.4000000
[134] 2.3000000 2.2000000 2.5000000 2.5000000 2.5000000 2.4000000 2.3000000
[141] 1.7000000 1.6000000 1.9000000 1.9000000 1.8000000 1.8000000 1.9000000
[148] 1.9000000 1.9000000 1.9000000 1.8000000 1.7000000 2.1000000 2.6000000
[155] 3.1000000 3.1000000 3.2000000 3.3000000 3.6000000 3.3000000 3.7000000
[162] 4.0000000 4.0000000 3.8000000 3.6000000 3.2000000 2.1000000 1.6000000
[169] 1.1000000 1.0231290 0.8018908 0.9807897 0.7297822 0.5271668 0.5650704
[176] 0.7165635 0.7073295 0.7782396 1.3070946 1.6162226
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 170 
End = 180 
Frequency = 1 
 [1] 0.1852679 0.3415797 0.3396272 0.5302365 0.8173399 0.8378134 0.7116200
 [8] 0.7720393 0.7426754 0.4666073 0.3951033
> postscript(file="/var/wessaorg/rcomp/tmp/1rnce1323214005.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/239td1323214005.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/36k5a1323214005.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/43z2q1323214005.tab") 
> 
> try(system("convert tmp/1rnce1323214005.ps tmp/1rnce1323214005.png",intern=TRUE))
character(0)
> try(system("convert tmp/239td1323214005.ps tmp/239td1323214005.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  2.533   0.286   2.833