A threshold stochastic volatility model

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Abstract
This article introduces a new model to capture simultaneously the mean and variance asymmetries in time series. Threshold non‐linearity is incorporated into the mean and variance specifications of a stochastic volatility model. Bayesian methods are adopted for parameter estimation. Forecasts of volatility and Value‐at‐Risk can also be obtained by sampling from suitable predictive distributions. Simulations demonstrate that the apparent variance asymmetry documented in the literature can be due to the neglect of mean asymmetry. Strong evidence of the mean and variance asymmetries was detected in US and Hong Kong data. Asymmetry in the variance persistence was also discovered in the Hong Kong stock market. Copyright © 2002 John Wiley & Sons, Ltd.