On Mon, 19 Oct 2009, Francisco Sosa wrote: > >> Thank you very much Allin, but I still have another question, do > >> you apply a small sample correction or something else? Because I > >> tried to double check this formula and is not the same, in my > >> sample I only have 7 years, let me show some of my numbers... > > > >If you want a definitive answer to this, please send me the > >dataset and script that you are using, so I can see exactly where > >your numbers are coming from. > > I have attached some files to this e-mail, please let me know if you can't > see them. In the .ppt file I explain how I do the calculations.
OK, I see: your model has an AR(1) specification for the dependent variable as well as an AR(1) for the error term via Prais-Winsten. So then the formula I gave does not apply. Here is how to replicate the forecast standard errors given by gretl. <script> open Global_Sales_Beer.gdt genr y = Global_Sales ar1 y 0 y(-1) --pwe S2 = $sigma^2 beta = $coeff[2] rho = $rho psi = rho + beta addobs 1 smpl 2007 2009 fcast series fcerr = $fcerr scalar sum_psi_sq = 1 scalar k = 1 loop i=2007..2009 -q scalar err = sqrt(sum_psi_sq * S2) printf "check: %g - %g = %g\n", fcerr[i], err, fcerr[i] - err sum_psi_sq += (psi^k)^2 k++ endloop </script> See Box and Jenkins, Time Series Analysis: Forecasting and Control, 1976, p. 508, "Program 4", for the general algorithm. Allin Cottrell
