Analyzing Rational Speculative Bubbles in S&P 500 Index Sectors Through Fractional Integration and Generalized Link-Based Additive Survival Models

This study aims to detect rational speculative bubbles in the sub-sectors of the S&P 500 index by integrating a non-parametric duration dependence test with fractional integration models. A flexible P-splines hazard function, robust to censoring, ensures precise estimation and Bayesian confidence intervals. Analyzing weekly and monthly data from October 1989 to June 2023, the findings provide empirical evidence of rational speculative bubbles in specific sub-sectors and the index as a whole. This is the first application of fractional integration with a non-parametric hazard function for this purpose. © 2025