The exact PDF of an MA process is given by (9.6) with
formed from (9.37).
An advantage of having a finite ACF (9.37), is that will be a banded matrix
with band width . We can make computing the exact PDF more efficient
by supplying the parameter in the function toepsolve
(See section 9.2.2) which specifies the ACF length:
Exact PDF for MA process
[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.