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On Heteroskedasticity and Regimes in Volatility Forecasting

In this paper we discuss some deep implications of the recent paper by Bollerslev et al. (2016) (BPQ). In BPQ the volatility dynamics modeled as a HAR is augmented by a term involving quarticity in order to correct measurement errors in realized variance. We show that the model is observationally equivalent to another where a quadratic term in realized variance accounts for a faster mean reversion when volatility is high. We argue that heteroskedasticity (volatility of volatility) and a time-varying mean seem to play a role of higher order of importance than measurement errors. In fact, the quarticity/quadratic terms disappear within an AMEM, and more so when a Markov Switching dynamics is considered. Some simulation results show that when the DGP is a (MS-)AMEM, such terms turn out spuriously significant in a HAR. Forecast performance of the (MS-)AMEM is superior to the augmented HARs.