Efficient estimators enhance stochastic volatility models with heavy tails
A Bank of Canada staff working paper introduces simple and efficient estimators for stochastic volatility models with heavy-tailed error distributions. These estimators utilize moment conditions from ARMA-type representations, providing closed-form solutions and enabling reliable simulation-based inference.
Simplifying complex volatility inference
Statistical inference for stochastic volatility (SV) models is known to be challenging and computationally demanding.
This paper proposes simple and efficient estimators for SV models with conditionally heavy-tailed error distributions, specifically 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.
A key contribution is the extension of this framework to handle heavy-tailed error distributions by incorporating the degrees-of-freedom parameter.
Closed-form expressions are available for all parameters except the degrees-of-freedom, eliminating the need for numerical optimization or initial values.
This analytical tractability supports reliable and even exact simulation-based inference via Monte Carlo or bootstrap methods.
Robustness, speed, and real-world application
The proposed estimators incorporate winsorized versions to improve stability and finite-sample performance, effectively reducing sensitivity to outliers.
Their asymptotic distribution is formally derived, confirming root-T consistency and asymptotic normality.
Extensive Monte Carlo simulations validate the estimators' precision and robustness, even in challenging scenarios with small samples and heavy tails.
A key advantage is their computational speed, which is orders of magnitude faster than existing simulation-based methods.
Empirical application to daily returns of major U.S. stock indices demonstrates strong evidence of heavy tails and persistent volatility, consistently rejecting the normality assumption in favor of heavy-tailed models.