2021/08/28 by J. L. Kirkby, Dang Khoa Nguyen, Kirkby, J. L. +5
Mathematics · #34D20 #60H10 #92D25 #93D05 #93D20 #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Probability (math.PR) #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2108.12649
openalex publication_date 2021/08/28 · openalex created_date 2022/09/10 · openalex updated_date 2026/07/28
In this paper we present a novel method for estimating the parameters of a parametric diffusion processes. Our 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 psuedo-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, we are able to obtain closed-form approximations 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 CMTC estimator. Simulated examples are provided in addition to real data experiments with FX rates and constant maturity interest rates.