Realized volatility forecasting in the presence of time-varying noise

Observed high-frequency …nancial prices can be considered as comprising two components, a true price and a market microstructure noise perturbation. It is an empirical regularity, coherent with classical market microstructure theories of price determination, that the second moment of market microstructure noise is time-varying. We study the optimal, from a …nite-sample forecast MSE standpoint, frequency selection for realized variance in linear variance forecasting models with time-varying market microstructure noise. We show that the resulting sampling frequencies are generally considerably lower than those that would be optimally chosen when time-variation in the second moment of the noise is unaccounted for. These optimal, lower frequencies have the potential to translate into considerable out-of-sample MSE gains. When forecasting using high-frequency variance estimates, we recommend treating the relevant frequency as a parameter and evaluating it jointly with the parameters of the forecasting model. The proposed joint solution is robust to the features of the true price formation mechanism and generally applicable to a variety of forecasting models and high-frequency variance estimators, including those for which the typical choice variable is a smoothing parameter, rather a frequency. Keywords: Realized Variance, Time-Varying Market Microstructure Noise, Volatility Forecasting. We thank Torben Andersen, Nour Meddahi, two anonymous referees, the Co-Editor, Jonathan Wright, and seminar participants at the Imperial College Workshop on High-Frequency Data (London, February 22, 2007), the Conference on Volatility and High-Frequency Data (Chicago, April 21-22, 2007), and the 75th Cowles Foundation Anniversary Conference "Looking to the Future: A New Generation of Econometricians" (New Haven, June 11-12, 2007) for discussions. We are grateful to the William S. Fishman Faculty Research Fund at Chicago Booth, University of Chicago, and Carey Business School, Johns Hopkins University (Bandi), NYU Stern (Russell), and Chicago Booth, University of Chicago (Bandi, Russell, and Yang) for …nancial support. Correspondence can be sent to: [email protected], je¤[email protected], [email protected].