On the weak invariance principle for non-adapted stationary random fields under projective criteria

In this paper, we study the central limit theorem (CLT) and its weak invariance principle (WIP) for sums of stationary random fields non-necessarily adapted, under different normalizations. To do so, we first state sufficient conditions for the validity of a suitable ortho-martingale approximation. Then, with the help of this approximation, we derive projective criteria under which the CLT as well as the WIP hold. These projective criteria are in the spirit of Hannan’s condition and are well adapted to linear random fields with ortho-martingale innovations and which exhibit long memory.

On the Estimation of Spectral Functionals of the Fourth Order for Stationary Random Fields

This paper is concerned with the estimation of integral functionals of the fourth order spectral densities for stationary random fields based on tapered data. The considered functionals are related, in particular, to the problem of parameter estimation in the spectral domain. The main focus is on the bias of the proposed estimators, conditions for their consistency are also discussed.