Do We Need Ultra-High Frequency Data to Forecast Variances?

In this paper we study various MIDAS models in which the future daily variance is directly related to past observations of intraday predictors. Our goal is to determine if there exists an optimal sampling frequency in terms of volatility prediction. Via Monte Carlo simulations we show that in a world without microstructure noise, the best model is the one using the highest available frequency for the predictors. However, in the presence of microstructure noise, the use of ultra high-frequency predictors may be problematic, leading to poor volatility forecasts. In the application, we consider two highly liquid assets (i.e., Microsoft and S&P 500). We show that, when using raw intraday squared log-returns for the explanatory variable, there is a "high-frequency wall" or frequency limit above which MIDAS-RV forecasts deteriorate. We also show that an improvement can be obtained when using intraday squared log-returns sampled at a higher frequency, provided they are pre-filtered to account for the presence of jumps, intraday periodicity and/or microstructure noise. Finally, we compare the MIDAS model to other competing variance models including GARCH, GAS, HAR-RV and HAR-RV-J models. We find that the MIDAS model provides equivalent or even better variance forecasts than these models, when it is applied on filtered data.