Maximum entropy for periodically correlated processes from nonconsecutive autocovariance coefficients

We consider the maximum entropy extension of a partially specified autocovariance sequence of a periodically correlated process. The sequence may be specified on a non-contiguous set. We give a method which solves the problem completely - it gives the positive definite solution when it exists and reports that it does not exist otherwise. The method is numerically reliable even when the solution is 'almost' semidefinite. It also works when only positive semidefinite extension(s) exist. Copyright 2009 Blackwell Publishing Ltd