The multiple lag process and its estimation

We derive estimators for the multiple lag process, a generalization of the lag process, via spectral representations of stationary processes by complex random spectral measures. We present estimators of transfer functions for the multiple lag model with a given vector of lags and derive a multiple-lag (quadratic) coherence which can be maximized to choose the best vector of lags in the minimum mean squared error sense from a given set of lag vectors. We also demonstrate the estimation scheme by a simulation example and point out possible applications for the multiple-lag model in speech processing.