Estimation and Inference for Stochastic Volatility Models with Heavy-Tailed Distributions

Gabriel Rodriguez Rondon, Jean-Marie Dufour and Md. Nazmul Ahsan

Staff Working Papers from Bank of Canada

Abstract: Statistical inference--both estimation and testing--for stochastic volatility (SV) models is known to be challenging and computationally demanding. We propose simple and efficient estimators for SV models with conditionally heavy-tailed error distributions, particularly the Student’s t and Generalized Exponential Distributions (GED). The estimators rely on a small set of moment conditions derived from ARMA-type representations of SV models, with an option to apply “winsorization” to improve stability and finite-sample performance. Except for the degrees-of-freedom parameter, closed-form expressions are available for all other parameters, extending Ahsan and Dufour (2019, 2021), thus eliminating the need for numerical optimization or initial values. We derive the estimators’ asymptotic distribution and show that, due to their analytical tractability, they support reliable, and even exact, simulation-based inference via Monte Carlo or bootstrap methods. We assess their performance through extensive simulations and demonstrate their practical relevance in financial return data, which strongly reject the normality assumption in favor of heavy-tailed models.

Keywords: Financial markets and funds management; International markets and currencies; Models and tools; Econometric; statistical and computational methods; Economic models (search for similar items in EconPapers)
JEL-codes: C15 C22 C53 C58 (search for similar items in EconPapers)
Pages: 50 pages
Date: 2026-03
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