On non-negative definiteness of estimated moving average autocovariance sequences
Randolph L. Moses, D. Liu · 2003
The authors consider the following problem: given a normalized (finite-duration) covariance sequence which is not nonnegative definite (NND), find the closest NND sequence to it. Here, closeness is measured by the Euclidean distance in coefficient space. They provide a solution to this problem by considering a set of constrained minimization problems. The solution to the constrained minimization problem does not in general give NND solutions. Properties of NND solutions are established and used to find the minimizing NND sequence.>