Research project: Interval Forecasts for Realised Volatility at High Frequencies

In the last twenty years, the literature on financial econometrics has evolved considerably in the modelling and forecasting of volatility of financial returns. The availability of information at ultra-high frequencies such as one-minute prices has allowed the academia and industry to construct a new generation of models and estimators that approximate the underlying volatility process using realized measures of volatility. These new realized measures are, under very general conditions, consistent estimators of the integrated volatility process observed at lower frequencies such as hourly or daily.

Forecasting the volatility process using these realized measures is at the centre of this literature. Importantly, the properties of these realized measures are different that at lower frequencies, requiring of methodologies that accommodate long-range dependence and different sets of covariates. Although the recent literature has made enormous progress in developing models based on high-frequency returns that capture these nonstandard features of the data there is still a lack of understanding of the variables that have predictive power of the realized volatility measures, beyond its past history.

The aim of this project is to contribute to this literature in three dimensions. First, we propose a model that incorporates lagged values of the volatility of the volatility process as predictors of the realized variance. These predictors, obtained from high-frequency returns as functions of the realized quarticity, show empirically a strong forecasting performance. Our proposed model is in the same spirit of ARCH-in-mean processes originally proposed for modelling financial returns at low frequencies. The second contribution is to exploit the dependencies uncovered in the volatility of volatility process (realized quarticity) to construct prediction intervals about our model forecasts. By doing so, we attach uncertainty measures to our model predictions that also account for the presence of measurement errors induced by the use of realized measures rather than by the actual underlying volatility process. This project also explores the performance of machine learning techniques for volatility forecasting in high frequencies. In particular, we propose nonlinear versions of our benchmark prediction model and construct prediction intervals that are fitted using state-of-the-art deep neural network models.