Ergodic behavior and estimation for periodically correlated processes

Abstract

A complex second-order stochastic process {X(t); t [set membership, variant] } is periodically correlated (PC) when its mean function m(t) and covariance R(s, t) are periodic with the period T. In the following note the relationship between the hierarchy of chaos and estimation for the stochastic process is investigated. The results are based on the Correspondence Principle for the PC processes.Periodically correlated process [phi]-mixing spectral density estimation