Estimating growth at risk with skewed stochastic volatility models

Abstract

This paper proposes a Skewed Stochastic Volatility (SSV) model to model time varying, asymmetric forecast distributions to estimate Growth at Risk as introduced in Adrian, Boyarchenko, and Giannone’s (2019) seminal paper ”Vulnerable Growth”. In contrary to their semi-parametric approach, the SSV model enables researchers to capture the evolution of the densities parametrically to conduct statistical tests and compare different models. The SSV-model forms a non-linear, non-gaussian state space model that can be estimated using Particle Filtering and MCMC algorithms. To remedy drawbacks of standard Bootstrap Particle Filters, I modify the Tempered Particle Filter of Herbst and Schorfheide’s (2019) to account for stochastic volatility and asymmetric measurement densities. Estimating the model based on US data yields conditional forecast densities that closely resemble the findings by Adrian et al. (2019). Exploiting the advantages of the proposed model, I find that the estimated parameter values for the effect of financial conditions on the variance and skewness of the conditional distributions are statistically significant and in line with the intuition of the results found in the existing literature.