The Markov Switching Asymmetric Multiplicative Error Model
The empirical evidence behind the dynamics of high frequency based measures of volatility is that they exhibit persistence and at times abrupt changes in the average level by subperiods. In the past ten years this pattern has a clear interpretation in reference to the dot com bubble, the quiet period of expansion of credit and then the harsh times after the burst of the subprime mortgage crisis. We conjecture that the inadequacy of many econometric volatility models (a very high level of estimated persistence, serially correlated residuals) can be solved with an adequate representation of such a pattern. We insert a Markovian dynamics in a Multiplicative Error Model to represent the conditional expectation of the realized volatility, allowing us to address the issues of a slow moving average level of volatility and of a different dynamics across regime. We apply the model to realized volatility of the S&P500 index and we gauge the usefulness of such an approach by a more interpretable persistence, better residual properties, and an increased goodness of fit.
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