Estimating the Lags of Lag Processes

Abstract

Recent studies of nonlinear prediction and of nonlinear filtering of stochastic processes in addition to studies of higher-order spectra have pointed out the usefulness of lag processes. Now suppose we are given observations on a filter operating on a lag process with an unknown lag. In this article we propose a way of estimating this (delay) lag. The method involves the definition of a quantity, S ₂(λ; u), termed lagged coherence, which is a function of the lag u and which is maximized for a proper choice of u.