Exact PDF for MA process

The exact PDF of an MA process is given by (9.6) with $ {\bf R}_N$ formed from $ r_t$ (9.37). An advantage of having a finite ACF (9.37), 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 9.2.2) 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 9.2.3) may be used unaltered.

Baggenstoss 2017-05-19