Finite Lag Estimation of Non-Markovian Processes

A Ronald Gallant and Halbert White

Journal of Financial Econometrics, 2024, vol. 22, issue 5, 1656-1671

Abstract: We consider the quasi-maximum likelihood estimator (qmle) obtained by replacing each transition density in the correct likelihood for a non-Markovian, stationary process by a transition density with a fixed number of lags. This estimator is of interest because it is asymptotically equivalent to the efficient method of moments estimator as typically implemented in dynamic macro and finance applications. We show that the standard regularity conditions of quasi-maximum likelihood imply that a score vector defined over the infinite past exists. We verify that the existence of a score on the infinite past implies that the asymptotic variance of the finite lag qmle tends to the asymptotic variance of the maximum likelihood estimator as the number of lags tends to infinity.

Keywords: efficient method of moments; finite lag approximation; maximum likelihood; non-Markovian; quasi maximum likelihood (search for similar items in EconPapers)
JEL-codes: C14 C15 C32 C58 (search for similar items in EconPapers)
Date: 2024
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