Realized Higher Moments and Realized Distributional Forecasts – ReaDi

• Applicant: Professor Dr. Ostap Okhrin
• Subject Area: Statistics and Econometrics
• Term: since 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 497262150

There was tremendous progress in estimation and prediction of daily returns variance based on high-frequency data in the last years. On the other hand-side, little attention was paid to predicting higher moments on the same data basis, even if this would open a way of predicting the complete density based on some expansion. We aim at bringing it forward by setting the following goals: 1. Develop estimators of the higher realized moments of daily returns based on the high-frequency data. As for HF data, termed in the literature realized skewness and realized kurtosis are not estimators of the daily skewness nor kurtosis, but rather estimators of the integrated third or fourth power of intraday returns or averaged jump component, and are shown to be informative basically for the cross-section of next week’s stock returns or in predicting RV at mid and long-term horizons. We will develop efficient estimators for the daily skewness and kurtosis (estimators of the integrated processes' high-order expectations). We already a) derived all the theoretical moments for the processes like Heston, Bates, CIR, and now will propose model-driven estimators; b) developed a simulation approach that can generate data from these models, which match with the theoretical higher moments. We will use these approaches as a laboratory to test the developed higher moment estimators. 2. Estimate the conditional distribution of the daily returns and forecast it. Based on moment estimation, we will derive an ex-post approximation of the conditional distribution of returns based on intra-day information using various distributional expansions as Edgeworth/Cornish-Fisher or Gram- Charlier. Although the assumption of normality of daily returns is not supported by empirical evidence, it has been heavily advocated in the financial econometrics literature. 3. Develop a model to predict future ex-post density approximations. Using the modified CAViaR model in which the quantile regression takes realized skewness and kurtosis into account, we aim at a simultaneous estimation of ES and VaR.

• DFG Programme: Research Grants
• International Connection: Italy, Switzerland
• Cooperation Partners: Professor Michael Rockinger, Ph.D.; Professor Dr. Giuseppe Storti
• Co-Investigator: Professorin Dr. Roxana Halbleib