pymle: A Python Package for Maximum Likelihood Estimation and Simulation of Stochastic Differential Equations

Abstract

This paper introduces the object-oriented Python package pymle, which provides core functionality for maximum likelihood estimation and simulation of univariate stochastic differential equations. The package supports maximum likelihood estimation using Euler, Elerian, Ozaki, Shoji-Ozaki, Hermite polynomial, and Kessler density approximations, as well as a recently proposed continuous-time Markov chain approximation scheme. Exact maximum likelihood estimation is also provided when available. The framework supports estimation and simulation for 21 stochastic differential equations models at the time of writing, and its object oriented design facilitates easy extensions to new models and approximation methods.