Inferência Bayesiana em modelos de volatilidade estocástica na média utilizando o método de Monte Carlo Hamiltoniano em variedade Riemanniana

Abstract

This paper considers the stochastic volatility in mean model, where the conditional distribution of the data belongs to the mixed-scale normal family for modeling financial time series. This model class is more robust in accommodating errors with heavier tails than the normal distribution, a characteristic often observed in financial data. Parameter estimation is conducted through a Bayesian algorithm employing Markov Chain methods, specifically the Hamiltonian Monte Carlo (HMC) method and its variant, the Riemannian Manifold Hamiltonian Monte Carlo (RMHMC) method. The algorithm is implemented using the Rcpp and RcppArmadillo libraries in the R language. Recently developed information criteria, namely the Watanabe Akaike Information Criterion (WAIC) and leave-one-out cross-validation (LOO-CV), along with the deviance information criterion (DIC), are calculated to compare the model fits. Simulation studies are conducted to illustrate and evaluate the performance of the proposed method. Finally, we apply the developed methodology to real return series, providing empirical evidence of its effectiveness.