Volatility Forecasting and Microstructure Noise

Abstract

It is common practice to use the sum of frequently sampled squared returns to estimate volatility, yielding so called realized volatility. Unfortunately, returns are contaminated by market microstructure noise. Several noise-corrected realized volatility measures have been proposed. We assess to what extend correction for microstructure noise improves forecasting future volatility using the MIxed DAta Sampling (MIDAS) framework. We start by studying the population properties of predictions using various realized volatility measures. We do this in a general regression setting and with both i.i.d. as well as depend microstructure noise. Next we study optimal sampling issues theoretically, when the objective is forecasting and microstructure noise contaminates realized volatility. For the volatility measures constructed using five-minute returns, microstructure corrections tend to reduce predictability. The subsampling and averaging class of estimators (Zhang, Mykland, and Ait-Sahalia 2005) predicts volatility the best at this frequency. In particular, a new power variation estimator constructed by averaging over subsamples has the best performance. This result reinforces earlier findings of (Ghysels, Santa-Clara, and Valkanov 2006) and Forsberg and Ghysels (2004). Finally, the volatility dynamics are more complicated for one-minute returns and the results are not that clear-cut. Moreover, when we study optimal sampling empirically, we find its implementation hampered by the requirement to estimate fourth order moments.