Fractional Integration and Asymmetric Volatility in European, American and Asian Bull and Bear Markets: Application to High-frequency Stock Data

This paper is a follow‐up to another paper by the same authors. In that paper, fractional integration and symmetric volatility modelling were considered on monthly frequency data, while the present paper considers high‐frequency data on an asymmetric volatility model. The data were first identified within the respective bull and bear phases following earlier results in the previous paper. Then, fractional integration and the asymmetric volatility model of Glosten, Jaganathan and Runkle were applied on the stock returns. Long‐range dependence was detected in the squared stock returns at each market phase, and they were more persistent than those obtained in the monthly frequency data. The estimates of asymmetry of the Glosten, Jaganathan and Runkle model actually detected the different patterns of the bad news (bear phases) and the good news (bull phases). Copyright © 2015 John Wiley & Sons, Ltd.