Approximate Bayesian Estimation of Stochastic Volatility in Mean Models using Hidden Markov Models: Empirical Evidence from Stock Latin American Markets

Carlos A. Abanto-Valle, Gabriel Rodríguez, Luis M. Castro Cepero and Hernán B. Garrafa-Aragón
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Carlos A. Abanto-Valle: Department of Statistics, Federal University of Rio de Janeiro
Luis M. Castro Cepero: Department of Statistics, Pontificia Universidad Católica de Chile
Hernán B. Garrafa-Aragón: Escuela de Ingeniería Estadística de la Universidad Nacional de Ingeniería

No 2021-502, Documentos de Trabajo / Working Papers from Departamento de Economía - Pontificia Universidad Católica del Perú

Abstract: The stochastic volatility in mean (SVM) model proposed by Koopman and Uspensky (2002) is revisited. This paper has two goals. The first is to offer a methodology that requires less computational time in simulations and estimates compared with others proposed in the literature as in Abanto-Valle et al. (2021) and others. To achieve the first goal, we propose to approximate the likelihood function of the SVM model applying Hidden Markov Models (HMM) machinery to make possible Bayesian inference in real-time. We sample from the posterior distribution of parameters with a multivariate Normal distribution with mean and variance given by the posterior mode and the inverse of the Hessian matrix evaluated at this posterior mode using importance sampling (IS). The frequentist properties of estimators is anlyzed conducting a simulation study. The second goal is to provide empirical evidence estimating the SVM model using daily data for five Latin American stock markets. The results indicate that volatility negatively impacts returns, suggesting that the volatility feedback effect is stronger than the effect related to the expected volatility. This result is exact and opposite to the finding of Koopman and Uspensky (2002). We compare our methodology with the Hamiltonian Monte Carlo (HMC) and Riemannian HMC methods based on Abanto-Valle et al. (2021). JEL Classification-JE: C11, C15, C22, C51, C52, C58, G12.

Keywords: Stock Latin American Markets; Stochastic Volatility in Mean; Feed-Back Effect; Hamiltonian Monte Carlo; Hidden Markov Models; Riemannian Manifold Hamiltonian Monte Carlo; Non Linear State Space Models. (search for similar items in EconPapers)
Pages: 28
Date: 2021
New Economics Papers: this item is included in nep-cmp, nep-ecm, nep-ets and nep-ore
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