A simulation-based comparison of pseudo-marginal MCMC methods for the stochastic volatility model

Abstract

Stochastic volatility (SV) models offer a flexible framework to capture the time-varying nature of the volatility process, but their complex structure, which stems from the intractability of the likelihood function, makes parameter inference challenging. The dissertation provides a detailed, simulation-based comparison of several advanced Bayesian estimation methods designed to overcome this challenge, focusing on the family of pseudo-marginal Markov chain Monte Carlo (MCMC) algorithms. The core of this research is a simulation study that evaluates the performance of four main algorithms: the pseudo-marginal algorithm with importance sampler (PM-IS), its correlated version (CPM-IS), the Particle Marginal Metropolis-Hastings (PMMH) algorithm, and its correlated version (CPMMH). Two different proposal covariance structures are used for each algorithm variation - a simple diagonal covariance and an adaptive covariance. The algorithms are tested on simulated datasets of two sample sizes (𝑇 = 200 and 𝑇 = 700). The evaluation is conducted in a two-phase process. First, the reliable posterior convergence of all algorithm variants is evaluated by conducting convergence diagnostics. Second, the methods that pass these first-step checks are compared on their computational efficiency and statistical accuracy. The convergence diagnostics reveal that the choice of both the likelihood estimator and the proposal mechanism is essential for reliable inference. Only the PMMH variants that utilized an adaptive proposal covariance mechanism consistently passed all diagnostic checks, demonstrating the necessity of a proposal that can learn the structure of the correlations between parameters. The findings lead to a clear and practical recommendation: for robust and efficient estimation of SV models of relatively small sample sizes (𝑇 ≤ 700), the non-correlated Particle Marginal Metropolis-Hastings (PMMH) algorithm with an adaptive proposal mechanism is the most effective choice.