A Data-Dependent Approach to Modeling Volatility in Financial Time Series

In the last twenty years, following the introduction of the ARCH and GARCH models, there has been wide-ranging research that extends the models to capture various nuances of financial data. One key area of research generalizes the models to capture the asymmetry related to the so called leverage effect. Although many different asymmetric GARCH type models have been developed, it still remains a challenge to capture the local nature of the leverage effect along with the corresponding interplay between the sign and magnitude of returns. In this paper we propose a new data-dependent approach to modeling financial time series volatility. This method allows self-detection of the presence of leverage effect. The proposed model also automatically adjusts the time-dependent random coefficients in an efficient manner. The examples show the flexibility and general superiority of the proposed model compared to some of the well-known asymmetric GARCH models.