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Finite Lag Estimation of Non-Markovian Processes

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  • A Ronald Gallant
  • Halbert L White

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.

Suggested Citation

  • A Ronald Gallant & Halbert L White, 2024. "Finite Lag Estimation of Non-Markovian Processes," Journal of Financial Econometrics, Oxford University Press, vol. 22(5), pages 1656-1671.
    • Handle: RePEc:oup:jfinec:v:22:y:2024:i:5:p:1656-1671.
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    File URL: http://hdl.handle.net/10.1093/jjfinec/nbae011
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    More about this item

    Keywords

    efficient method of moments; finite lag approximation; maximum likelihood; non-Markovian; quasi maximum likelihood;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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