Martingale estimating functions for stochastic processes: A review toward a unifying tool

Abstract

Large sample theory and various estimation methods for stochastic processes are reviewed in a unified framework via martingale estimating functions. Results on asymptotic op¬timality of the estimates are discussed for both ergodic and non-ergodic processes. To illustrate the main results, various parameter estimates for GARCH-type processes, bifur¬cating and explosive autoregressive processes, conditionally linear autoregressive processes, and branching Markov processes are presented.