Forecasting daily volatility with intraday data

Abstract

The aim of this paper is to assess to what extent intraday data can explain and predict end-of-the-day volatility. Using a realized volatility measure as proposed by Andersen, T., T. Bollerslev, F. Diebold, and P. Labys. 2001. The distribution of realized exchange rate volatility. Journal of the American Statistical Association 96: 42–55, we hypothesize that volatility generated at the start of the day is an important predictor of daily volatility either on its own accord or in conjunction with information about the seasonal pattern characterizing intraday volatility. We address the question of how much information needs to arrive to the market before a good predictor can be formed. Using data from a specialist market (NYSE), a dealer market (Nasdaq) and a continuous auction market (Paris Bourse), we investigate how different trading structures may affect intraday volatility formation. As a preview to our results, we find that the explanatory power of first-hour volatility for daily volatility is as high as 68%, whereas the average volatility generated during this first hour is <30%. Comparison to a standard GARCH model shows that the forecasts based on the intraday data are generally highly informative both on their own accord and in combination with the GARCH forecasts.

Keywords:

• intraday return volatility
• volatility forecasting
• realized volatility
• quadratic variation

Notes

To test for the robustness of our results, we have also conducted our analyses at a one- and two-minute sampling frequency. The results of these robustness checks are in line with those reported here and are therefore not shown. However, they are available upon request.

• It has to be noted that RV _t and RV are overlapping and therefore the R ² of this regression will be inflated (we thank a referee for pointing this out). A regression that controls for this would be of the form

  However, since we want to assess the forecasting performance of our start-of-the-day volatility measure across different intraday segments, we adhere to regressions of the form of Equation (3), so that results across regressions can be compared. To acknowledge this fact, we compute variance ratios and compare these to the R ². We should also emphasize that our primary interest is to evaluate the ability of start-of-day volatility to predict daily volatility and in this sense the use of regressions like (3’) may compromise performance assessments unduly. For example, in the extreme case, where all/most of daily volatility was generated at the start of the day, Equation (3’) will indicate very poor performance when in fact our forecasts will be highly accurate.

The two normalizing constants are defined as N ₁=(N+1)/2 and .

All shapes are normalized to 1.