Statistical methods with applications to pairs trading and equipment lifetime modeling

Abstract

This dissertation develops innovative statistical methods with applications to financial markets and risk-based management, presenting two main contributions: first, we introduce a family of distribution-based approaches to pairs trading that enhance the traditional cointegration strategy; second, we address the critical question of estimating the time-to-failure of industrial equipment when no failure data is available. In our first contribution, the family of pairs trading methods uses the distribution of the hedge ratio as a confirmatory layer for trading signals. Under the parametric method, we use a Bayesian hierarchical model that derives the full conditional distribution of the hedge ratio, whereas a Non-Overlapping Block Bootstrap is adopted as the non-parametric strategy. Both methods demonstrate significant outperformance across U.S. and Brazilian markets through 2025 with improved returns, reduced volatility, and enhanced risk-adjusted metrics. In the second part, we develop a methodology under the hierarchical Bayesian model framework with simulated likelihood to compensate for the lack of failure data. The model relies on carefully constructed prior distributions that can incorporate manufacturer-specified and expert information. We used the case of the National Bio and Agro-Defense Facility (NBAF) to validate our approach.