Dynamic Modeling via Autoregressive Conditional GB2 for Cross-Sectional Maxima of Financial Time Series Data

This article introduces the “autoregressive conditional generalized beta distribution of the second kind” (AcGB2) to model the dynamic cross-sectional maxima of multivariate financial times series. The temporal dependence of the resulting univariate maxima time series is characterized by the parameter dynamics of the standard GB2 distribution, which offer versatility in approximating various distributions, including heavy-tailed distributions, through parameter adjustments. Consequently, the newly proposed AcGB2 modeling enhances flexibility in fitting real data, especially in scenarios where extreme value theory conditions are not met, as demonstrated through simulations. Real data analysis is conducted on three datasets: two with medium-sized cross-sectional dimensions (30 or fewer) and one with high dimension (100 or higher). These datasets are based on the daily negative simple-returns of 30 stocks in the Dow Jones Industrial Average, stocks in S&P 100, and stocks from 22 primary dealers, respectively. The article establishes stationary and ergodic solutions for this new time series model under mild parameter conditions and derives the consistency, asymptotic normality, and uniqueness of the statistical conditional maximum likelihood estimators.