Maximum Likelihood Estimation of Diffusions by Continuous Time Markov Chain
Abstract
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- August 2021
- DOI:
- 10.48550/arXiv.2108.12649
- arXiv:
- arXiv:2108.12649
- Bibcode:
- 2021arXiv210812649K
- Keywords:
-
- Statistics - Methodology;
- Mathematics - Probability;
- Mathematics - Statistics Theory;
- 34D20;
- 60H10;
- 92D25;
- 93D05;
- 93D20