Maximum likelihood estimation of order m for stationary stochastic processes

Abstract

SUMMARY Sometimes the likelihood cannot be computed even introducing approximations whose effect is asymptotically negligible. To overcome this problem for inference from a stochastic process, we approximate the log likelihood by a sum whose generic term is the density function of the corresponding sample element conditional on the m most recent observations, for some m ≥ 0. General results on the asymptotic properties of the associated estimates are given, and numerical comparisons with other estimators are carried out in special cases.