Chapter 10

Realized Volatility and Covariance


This chapter introduces the concept of realized variance (RV) and covariance. In particular, Section 10.1 defines RV and explains how it can be estimated. It also discusses the problem of microstructure noise that tends to plague high-frequency data, and proposes a number of solutions to the issue that have been proposed in the literature. Section 10.2 explains how RV can be forecasted using the heterogeneous autoregressive model and range-based variance measures. Finally, Section 10.3 introduces the concept of realized covariance and shows how the range-based approach can be extended to covariance prediction.


High-frequency data; microstructure noise; quadratic variation; integrated ...

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