Maximum likelihood inference for asymmetric stochastic volatility models

In this paper, we propose a new method for estimating and forecasting asymmetric stochastic volatility models. The proposal is based on dynamic linear models with Markov switching written as state space models. Then, the likelihood is calculated through Kalman filter outputs and the estimates are obtained by the maximum likelihood method. Monte Carlo experiments are performed to assess the quality of estimation. In addition, a backtesting exercise with the real-life time series illustrates that the proposed method is a quick and accurate alternative for forecasting value-at-risk.