Selection of Multivariate Stochastic Volatility Models via Bayesian Stochastic Search

Abstract

We propose a Bayesian stochastic search approach to selecting restrictions on multivariate regression models where the errors exhibit deterministic or stochastic conditional volatilities. We develop a Markov Chain Monte Carlo (MCMC) algorithm that generates posterior restrictions on the regression coefficients and Cholesky decompositions of the covariance matrix of the errors.Numerical simulations with artificially generated data show that the proposed method is effective in selecting the data-generating model restrictions and improving the forecasting performance of the model. Applying the method to daily foreign exchange rate data, we conduct stochastic search on a VAR model with stochastic conditional volatilities.

Bayesian Markov Switching Stochastic Correlation Models

“…The credibility intervals for the autoregressive coefficients A 10 and A 10 + A 11 (third and fourth block, left graph of Figure 11) show a strong evidence in favour of the absence of serial correlation in the daily exchange rate returns. These results support the restrictions imposed by Kim et al (1998) and are in line with those obtained by Loddo et al (2011), which analyse the same rates on a shorter time period (2001)(2002)(2003)(2004)(2005)) assuming a VAR model with one lag. We arrive at the same conclusion with a Markov-switching VAR model and extend their results, by documenting no substantial differences, in the returns autocorrelation, between the high-and lowvolatility regimes.…”

Sparse Bayesian time-varying covariance estimation in many dimensions

“…Nakajima and West (2013) and Nakajima and West (2017) who employ a latent thresholding process to enforce time-varying sparsity. Moreover, Zhao et al (2016) approach this issue via dependence networks, Loddo et al (2011) use stochastic search for model selection, and Basturk et al (2016) use time-varying combinations of dynamic models and equity momentum strategies. These methods are typically very flexible in terms of the dynamics they can capture but are applied to moderate dimensional data only.…”

Skew selection for factor stochastic volatility models

“…The paper is related to the literature on Bayesian sparsity modeling in the context of multivariate SV for reducing the number of parameters. Loddo et al (2011) propose a Bayesian stochastic search approach; Kastner (2018) develops a global-local shrinkage prior; and Nakajima and West (2013b) and Zhou et al (2014) incorporate time-varying sparsity with a latent thresholding process.…”