[Gretl-users] Initial values for simulating an AR(p) process

Dear all, I experimenting a bit with simulating dynamic ARDL models. I've got three questions: 1) In the script below, you see a simulation of an AR(p) model for two different initial values which are sent to filter(), y0 and y00. I think y00 should be the correct initial value but I would like to know your opinion. 2) Do you think there are any concerns about the ysim() function? 3) I was thinking of simulating a series of length k*T where k is some positive integer and T the length of the actual series. The first (k-1)*T values would be taken as the "burn-in phase". However, I am not sure how to program this cleverly as "Z" and thus "z" have some fixed length in the ysim() function. Much appreciated if somebody comes up with a nice idea ;-) Best, Artur <hansl> clear set echo off set messages off open denmark.gdt -q set seed 1234 function void ysim (series y, matrix ARcoef, list Z "lD~uhat", matrix Zbeta "Coefficients of all exogenous | 1 (for uhat)", scalar pq, scalar y0, series *Ysim) series z = lincomb(Z, Zbeta) series Ysim = filter(z,1,ARcoef,y0) smpl $t1 $t1+pq-1 Ysim = y # add first initial (historical) values smpl full end function series Y = LRY list lD = const #time scalar nD = nelem(lD) # AR(p) scalar p = 2 ols Y lD Y(-1 to -p) matrix ARbeta = $coeff[(1+nD):] matrix Zbeta = $coeff[1:nD] # Simulate the Y-series series uhat = resample($uhat) scalar y0 = Y[$t1] # initial value 1 scalar y00 = Y[$t1+p-1] # initial value 2 list Z = lD uhat Zbeta |= 1 # add unit coeff for uhat series Yb0 = 0 # simulated series 1 ysim(Y,ARbeta,Z,Zbeta,p,y0,&Yb0) series Yb00 = 0 # simulated series 2 ysim(Y,ARbeta,Z,Zbeta,p,y00,&Yb00) gnuplot Y Yb0 Yb00 --with-lines --time-series --output=display </hansl>