An estimation of distribution algorithm for the computation of innovation estimators of diffusion processes

TL;DR

This paper explores the use of a continuous Univariate Marginal Distribution Algorithm (UMDAc) to improve the estimation of parameters in complex diffusion processes, addressing limitations of local optimization methods.

Contribution

It introduces a novel application of UMDAc for computing Innovation Estimators, enhancing their effectiveness in complex nonlinear stochastic diffusion models.

Findings

UMDAc improves the accuracy of Innovation Estimators.

Global optimization reduces dependence on initial parameter guesses.

Numerical experiments confirm effectiveness in complex models.

Abstract

Estimation of Distribution Algorithms (EDAs) and Innovation Method are recognized methods for solving global optimization problems and for the estimation of parameters in diffusion processes, respectively. Well known is also that the quality of the Innovation Estimator strongly depends on an adequate selection of the initial value for the parameters when a local optimization algorithm is used in its computation. Alternatively, in this paper, we study the feasibility of a specific EDA - a continuous version of the Univariate Marginal Distribution Algorithm (UMDAc) - for the computation of the Innovation Estimators. Numerical experiments are performed for two different models with a high level of complexity. The numerical simulations show that the considered global optimization algorithms substantially improves the effectiveness of the Innovation Estimators for different types of diffusion processes with complex nonlinear and stochastic dynamics.