function loglike_MA1(theta,y) # the log-likelihood function for MA(1) # input: theta = [psi sigma2]; y = data psi = theta[1]; sigma2 = theta[2]; T = length(y); H = sparse(I,T,T) .+ psi*sparse(2:T,1:T-1,ones(T-1),T,T); HH = H*H'; l = -T/2*log(2*pi*sigma2) - .5/sigma2*y'*(HH\y); return l end