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Maximum likelihood estimation of diffusions by continuous time Markov chain

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  • Kirkby, J.L.
  • Nguyen, Dang H.
  • Nguyen, Duy
  • Nguyen, Nhu N.

Abstract

A novel method is presented for estimating the parameters of a parametric diffusion process. The approach is based on a closed-form Maximum Likelihood estimator for an approximating Continuous Time Markov Chain (CTMC) of the diffusion process. Unlike typical time discretization approaches, such as pseudo-likelihood approximations with Shoji-Ozaki or Kessler's method, the CTMC approximation introduces no time-discretization error during parameter estimation, and is thus well-suited for typical econometric situations with infrequently sampled data. Due to the structure of the CTMC, closed-form approximations are obtained for the sample likelihood which hold for general univariate diffusions. Comparisons of the state-discretization approach with approximate MLE (time-discretization) and Exact MLE (when applicable) demonstrate favorable performance of the CTMC estimator. Simulated examples are provided in addition to real data experiments with FX rates and constant maturity interest rates.

Suggested Citation

  • Kirkby, J.L. & Nguyen, Dang H. & Nguyen, Duy & Nguyen, Nhu N., 2022. "Maximum likelihood estimation of diffusions by continuous time Markov chain," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    • Handle: RePEc:eee:csdana:v:168:y:2022:i:c:s0167947321002425
    DOI: 10.1016/j.csda.2021.107408
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