Exact Bayesian inference for Markov switching diffusions

TL;DR

This paper introduces an exact Bayesian inference method for regime switching diffusions, enabling precise parameter and latent process estimation without approximation errors, demonstrated through numerical examples.

Contribution

It presents the first exact Bayesian methodology for inference in discretely observed regime switching diffusions using MCMC and MCEM algorithms.

Findings

Algorithms target the correct posterior distribution of the continuous model.

Method is scalable and comparable in cost to discrete approximation methods.

Avoids shortcomings of approximate inference techniques.

Abstract

We develop the first exact Bayesian methodology for the problem of inference in discretely observed regime switching diffusions. Switching diffusion models extend ordinary diffusions by allowing for jumps in instantaneous drift and volatility. The jumps are driven by a latent, continuous time Markov switching process. We address the problem through an MCMC and an MCEM algorithm that target the exact posterior of diffusion parameters and the latent regime process. The algorithms are exact in the sense that they target the correct posterior distribution of the continuous model, so that the errors are due to Monte Carlo only. We illustrate the method on numerical examples, including an empirical analysis of the method's scalability in the length of the time series, and find that it is comparable in computational cost with discrete approximations while avoiding their shortcomings.