On the Estimation of Asymmetric Long Memory Stochastic Volatility Models

The asymmetric long memory stochastic volatility (A-LMSV) model has two attractive features for modeling financial returns: i) the autocorrelation function of the log-variance presents hyperbolic decay; and ii) the two random noises that define the model have nonzero correlation. In this work, we present a maximum likelihood method for estimating both the parameters and the unobserved components, together with a method for value-at-risk (VaR) forecasting. Our method takes advantage of a state-space representation of the model which is written as a dynamic linear model with Markov switching. Then, the likelihood can be readily calculated by the Kalman filter. The proposed method is assessed by Monte Carlo experiments, and illustrations of risk forecasting with real time series returns are provided.