Exact PDF for MA process

The exact PDF of an MA process is given by (10.6) with ${\bf R}_N$ formed from $r_t$ (10.37). An advantage of having a finite ACF (10.37), is that ${\bf R}_N$ will be a banded matrix with band width $2Q+1$. We can make computing the exact PDF more efficient by supplying the parameter $Q+1$ in the function toepsolve (See section 10.2.2) which specifies the ACF length:

   [y,ldetR] = toepsolve(r,x,Q+1);
   lpx = -N/2*log(2*pi) -.5*ldetR -.5*x'*y;

For a more efficient approach, the filtering approach for the for ARMA PDF (Section 10.2.3) may be used unaltered.