R version 2.12.0 (2010-10-15)
Copyright (C) 2010 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: i486-pc-linux-gnu (32-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> x <- c(5.2
+ ,7.9
+ ,8.7
+ ,8.9
+ ,15.3
+ ,15.4
+ ,18.1
+ ,19.7
+ ,13
+ ,12.6
+ ,6.2
+ ,3.5
+ ,3.4
+ ,0
+ ,9.5
+ ,8.9
+ ,10.4
+ ,13.2
+ ,18.9
+ ,19
+ ,16.3
+ ,10.6
+ ,5.8
+ ,3.6
+ ,2.6
+ ,5
+ ,7.3
+ ,9.2
+ ,15.7
+ ,16.8
+ ,18.4
+ ,18.1
+ ,14.6
+ ,7.8
+ ,7.6
+ ,3.8
+ ,5.6
+ ,2.2
+ ,6.8
+ ,11.8
+ ,14.9
+ ,16.7
+ ,16.7
+ ,15.9
+ ,13.6
+ ,9.2
+ ,2.8
+ ,2.5
+ ,4.8
+ ,2.8
+ ,7.8
+ ,9
+ ,12.9
+ ,16.4
+ ,21.8
+ ,17.8
+ ,13.5
+ ,10
+ ,10.4
+ ,5.5
+ ,4
+ ,6.8
+ ,5.7
+ ,9.1
+ ,13.6
+ ,15
+ ,20.9
+ ,20.4
+ ,14
+ ,13.7
+ ,7.1
+ ,0.8
+ ,2.1
+ ,1.3
+ ,3.9
+ ,10.7
+ ,11.1
+ ,16.4
+ ,17.1
+ ,17.3
+ ,12.9
+ ,10.9
+ ,5.3
+ ,0.7
+ ,-0.2
+ ,6.5
+ ,8.6
+ ,8.5
+ ,13.3
+ ,16.2
+ ,17.5
+ ,21.2
+ ,14.8
+ ,10.3
+ ,7.3
+ ,5.1
+ ,4.4
+ ,6.2
+ ,7.7
+ ,9.3
+ ,15.6
+ ,16.3
+ ,16.6
+ ,17.4
+ ,15.3
+ ,9.7
+ ,3.7
+ ,4.6
+ ,5.4
+ ,3.1
+ ,7.9
+ ,10.1
+ ,15
+ ,15.6
+ ,19.7
+ ,18.1
+ ,17.7
+ ,10.7
+ ,6.2
+ ,4.2
+ ,4
+ ,5.9
+ ,7.1
+ ,10.5
+ ,15.1
+ ,16.8
+ ,15.3
+ ,18.4
+ ,16.1
+ ,11.3
+ ,7.9
+ ,5.6
+ ,3.4
+ ,4.8
+ ,6.5
+ ,8.5
+ ,15.1
+ ,15.7
+ ,18.7
+ ,19.2
+ ,12.9
+ ,14.4
+ ,6.2
+ ,3.3
+ ,4.6
+ ,7.2
+ ,7.8
+ ,9.9
+ ,13.6
+ ,17.1
+ ,17.8
+ ,18.6
+ ,14.7
+ ,10.5
+ ,8.6
+ ,4.4
+ ,2.3
+ ,2.8
+ ,8.8
+ ,10.7
+ ,13.9
+ ,19.3
+ ,19.5
+ ,20.4
+ ,15.3
+ ,7.9
+ ,8.3
+ ,4.5
+ ,3.2
+ ,5
+ ,6.6
+ ,11.1
+ ,12.8
+ ,16.3
+ ,17.4
+ ,18.9
+ ,15.8
+ ,11.7
+ ,6.4
+ ,2.9
+ ,4.7
+ ,2.4
+ ,7.2
+ ,10.7
+ ,13.4
+ ,18.5
+ ,18.3
+ ,16.8
+ ,16.6
+ ,14.1
+ ,6.1
+ ,3.5
+ ,1.7
+ ,2.3
+ ,4.5
+ ,9.3
+ ,14.2
+ ,17.3
+ ,23
+ ,16.3
+ ,18.4
+ ,14.2
+ ,9.1
+ ,5.9
+ ,7.2
+ ,6.8
+ ,8
+ ,14.3
+ ,14.6
+ ,17.5
+ ,17.2
+ ,17.2
+ ,14.1
+ ,10.5
+ ,6.8
+ ,4.1
+ ,6.5
+ ,6.1
+ ,6.3
+ ,9.3
+ ,16.4
+ ,16.1
+ ,18
+ ,17.6
+ ,14
+ ,10.5
+ ,6.9
+ ,2.8
+ ,0.7
+ ,3.6
+ ,6.7
+ ,12.5
+ ,14.4
+ ,16.5
+ ,18.7
+ ,19.4
+ ,15.8
+ ,11.3
+ ,9.7
+ ,2.9)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '0'
> par6 = '3'
> par5 = '12'
> par4 = '1'
> par3 = '0'
> par2 = '1'
> 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:
         ar1     ar2     ar3
      0.1244  0.0638  0.1625
s.e.  0.0690  0.0712  0.0711

sigma^2 estimated as 5.578:  log likelihood = -464.84,  aic = 937.68
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 217 
End = 240 
Frequency = 1 
 [1]  6.227890  6.190350  7.569547 14.049536 14.442278 17.394429 17.136090
 [8] 17.159676 14.073745 10.483773  6.789751  4.093422  6.223780  6.187753
[15]  7.567892 14.048496 14.441621 17.394012 17.135828 17.159510 14.073640
[22] 10.483706  6.789709  4.093395

$se
Time Series:
Start = 217 
End = 240 
Frequency = 1 
 [1] 2.361741 2.379948 2.387305 2.425003 2.427620 2.428677 2.430175 2.430406
 [9] 2.430499 2.430571 2.430588 2.430595 3.392064 3.404973 3.410203 3.436828
[17] 3.438696 3.439450 3.440515 3.440679 3.440746 3.440797 3.440809 3.440814

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 217 
End = 240 
Frequency = 1 
 [1]  1.59887712  1.52565122  2.89042851  9.29653078  9.68414289 12.63422220
 [7] 12.37294652 12.39607924  9.30996652  5.71985341  2.02579875 -0.67054415
[13] -0.42466627 -0.48599464  0.88389421  7.31231304  7.70177743 10.65268973
[19] 10.39241865 10.41577799  7.32977846  3.73974467  0.04572408 -2.65059953
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 217 
End = 240 
Frequency = 1 
 [1] 10.856902 10.855049 12.248665 18.802541 19.200413 22.154635 21.899234
 [8] 21.923272 18.837524 15.247692 11.553704  8.857388 12.872225 12.861501
[15] 14.251890 20.784679 21.181464 24.135334 23.879237 23.903241 20.817502
[22] 17.227668 13.533695 10.837390
> 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]  5.200000  7.900000  8.700000  8.900000 15.300000 15.400000 18.100000
  [8] 19.700000 13.000000 12.600000  6.200000  3.500000  3.400000  0.000000
 [15]  9.500000  8.900000 10.400000 13.200000 18.900000 19.000000 16.300000
 [22] 10.600000  5.800000  3.600000  2.600000  5.000000  7.300000  9.200000
 [29] 15.700000 16.800000 18.400000 18.100000 14.600000  7.800000  7.600000
 [36]  3.800000  5.600000  2.200000  6.800000 11.800000 14.900000 16.700000
 [43] 16.700000 15.900000 13.600000  9.200000  2.800000  2.500000  4.800000
 [50]  2.800000  7.800000  9.000000 12.900000 16.400000 21.800000 17.800000
 [57] 13.500000 10.000000 10.400000  5.500000  4.000000  6.800000  5.700000
 [64]  9.100000 13.600000 15.000000 20.900000 20.400000 14.000000 13.700000
 [71]  7.100000  0.800000  2.100000  1.300000  3.900000 10.700000 11.100000
 [78] 16.400000 17.100000 17.300000 12.900000 10.900000  5.300000  0.700000
 [85] -0.200000  6.500000  8.600000  8.500000 13.300000 16.200000 17.500000
 [92] 21.200000 14.800000 10.300000  7.300000  5.100000  4.400000  6.200000
 [99]  7.700000  9.300000 15.600000 16.300000 16.600000 17.400000 15.300000
[106]  9.700000  3.700000  4.600000  5.400000  3.100000  7.900000 10.100000
[113] 15.000000 15.600000 19.700000 18.100000 17.700000 10.700000  6.200000
[120]  4.200000  4.000000  5.900000  7.100000 10.500000 15.100000 16.800000
[127] 15.300000 18.400000 16.100000 11.300000  7.900000  5.600000  3.400000
[134]  4.800000  6.500000  8.500000 15.100000 15.700000 18.700000 19.200000
[141] 12.900000 14.400000  6.200000  3.300000  4.600000  7.200000  7.800000
[148]  9.900000 13.600000 17.100000 17.800000 18.600000 14.700000 10.500000
[155]  8.600000  4.400000  2.300000  2.800000  8.800000 10.700000 13.900000
[162] 19.300000 19.500000 20.400000 15.300000  7.900000  8.300000  4.500000
[169]  3.200000  5.000000  6.600000 11.100000 12.800000 16.300000 17.400000
[176] 18.900000 15.800000 11.700000  6.400000  2.900000  4.700000  2.400000
[183]  7.200000 10.700000 13.400000 18.500000 18.300000 16.800000 16.600000
[190] 14.100000  6.100000  3.500000  1.700000  2.300000  4.500000  9.300000
[197] 14.200000 17.300000 23.000000 16.300000 18.400000 14.200000  9.100000
[204]  5.900000  7.200000  6.800000  8.000000 14.300000 14.600000 17.500000
[211] 17.200000 17.200000 14.100000 10.500000  6.800000  4.100000  6.227890
[218]  6.190350  7.569547 14.049536 14.442278 17.394429 17.136090 17.159676
[225] 14.073745 10.483773  6.789751  4.093422  6.223780  6.187753  7.567892
[232] 14.048496 14.441621 17.394012 17.135828 17.159510 14.073640 10.483706
[239]  6.789709  4.093395
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 217 
End = 240 
Frequency = 1 
 [1] 0.3792201 0.3844610 0.3153829 0.1726037 0.1680912 0.1396238 0.1418162
 [8] 0.1416348 0.1726974 0.2318413 0.3579790 0.5937807 0.5450168 0.5502762
[15] 0.4506146 0.2446403 0.2381101 0.1977376 0.2007790 0.2005115 0.2444816
[22] 0.3282042 0.5067682 0.8405769
> postscript(file="/var/www/rcomp/tmp/1blr71293467651.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/rcomp/tmp/27dpg1293467651.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/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/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/rcomp/tmp/37nld1293467651.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/rcomp/tmp/4ao211293467651.tab") 
> 
> try(system("convert tmp/1blr71293467651.ps tmp/1blr71293467651.png",intern=TRUE))
character(0)
> try(system("convert tmp/27dpg1293467651.ps tmp/27dpg1293467651.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  0.910   0.410   1.303