Estimation of regime-switching diffusions via Fourier transforms

In this article, an algorithm for maximum-likelihood estimation of regime-switching diffusions is proposed. The proposed approach uses a Fourier transform to numerically solve the system of Fokker–Planck or forward Kolmogorow equations for the temporal evolution of the state densities. Monte Carlo simulations confirm the theoretically expected consistency of this approach for moderate sample sizes and its practical feasibility for certain regime-switching diffusions used in economics and biology with moderate numbers of states and parameters. An application to animal movement data serves as an illustration of the proposed algorithm.