Estimating and Predicting Multivariate Volatility Thresholds in Global Stock Markets

This paper proposes a double tree structured AR-GARCH model for the analysis of stock index return series, which extends previous approaches to incorporate (i) an arbitrary number of multivariate thresholds in conditional means and volatilities of stock index returns and (ii) a richer specification for the impact of foreign index returns news in the determination of each regime threshold. The approach is based on the idea of a binary tree where every terminal node parameterizes a (local) AR-GARCH model for a partition cell of a (multivariate) state space. Each cell can depend on the conditioning values of domestic and foreign news as well. Thus, our model encompasses as special cases several ones in the literature like for instance the GJR-AR-GARCH model, the double TAR-GARCH model or the VS-GARCH model. We propose a computationally feasible algorithm that can be applied to estimate the model in practice. We estimate and evaluate the out-of-sample performance of our model for eight among the major stock-indices worldwide while allowing for the conditional impact of both US market news and domestic news in determining the multiple conditional mean and conditional variance thresholds. We find strong evidence for the presence of more than two regimes in conditional means and variances of stock index returns. Conditioning information from the US market often affects the estimated thresholds in the estimated model and has strong out-of-sample predictive power, improving the forecasts relatively to some competing models in the literature. By constrast, information on past domestic volatilities does not generally affect the mean and the volatility of the estimated thresholds. Specifically, with the exception of the Italian market we find at least two volatility regimes, due to an asymmetric structure of volatility as a function of bad and good domestic news. Moreover, in the majority of the series under scrutiny we also identify one further regime determined by the different impact of domestic news in the joint presence of either bad or good US market news