Versatile HAR model for realized volatility: A least square model averaging perspective

Abstract

A rapidly growing body of literature has documented improvements in forecasting financial return volatility measurement using various heterogeneous autoregression (HAR) type models. Most HAR-type models use a fixed lag index of (1,5,22) to mirror the daily, weekly, and monthly components of the volatility process, but they ignore model specification uncertainty. In this paper, we propose applying the least squares model averaging approach to HAR-type models with signed realized semivariance to account for model uncertainty and to allow for a more flexible lag structure. We denote this approach as MARS and prove that the MARS estimator is asymptotically optimal in the sense of achieving the lowest possible mean squared forecast error. Selected by the data-driven model averaging method, the lag combination in the MARS method changes with various data series and different forecast horizons. Employing high frequency data from the NASDAQ 100 index and its 104 constituents, our empirical results demonstrate that acknowledging model uncertainty under the HAR framework and solving with the model averaging method can significantly improve the accuracy of financial return volatility forecasting.