MA Modeling

where are assumed to be

>> e=randn(N,1); >> x=filter(b,1,e * sqrt(sig2));which is directly equivalent to (9.36) except for the initial startup. To alleviate startup effects, it is necessary to discard the first samples of

>> e=randn(N+Q,1); >> x=filter(b,1,e * sqrt(sig2)); >> x=x(Q+1:Q+N);In contrast to ARMA, MA has a finite ACF. An MA process has the autocorrelation function

Note that is zero when . In MATLAB,

>> b2=conv(b(:),flipud(b(:))); >> % Theoretical ACF of MA process >> r = sig2 * [b2(1+Q:end); zeros(N-Q-1,1)];The circular MA process is a special case of the circular ARMA process with PDF (9.7) and