Maximum entropy for periodically correlated processes from nonconsecutive autocovariance coefficients

Georgy Boshnakov (1) , Sophie Lambert-Lacroix (2)

1 PSG - Probability and Statistics Group
2 SMS - Statistique et Modélisation Stochatisque

We consider the maximum entropy extention 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 extention(s) exist.

Mots clés: Maximum entropy method; partial autocorrelation; periodically correlated processes

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Georgy Boshnakov, Sophie Lambert-Lacroix. Maximum entropy for periodically correlated processes from nonconsecutive autocovariance coefficients. Journal of Time Series Analysis, 2009, 30 (5), pp.467-486. ⟨10.1111/j.1467-9892.2009.00619.x⟩. ⟨hal-00354373⟩