A nonparametric approach to understand multivariate quantile dynamics in financial time series

2026-03-17

AI Summary

This study addresses the dynamic modeling of conditional means, volatilities, and conditional geometric quantiles in multivariate financial time series by proposing a nonparametric regression framework that accommodates multidimensional responses and covariates. The approach captures temporal dynamics through functional dependence structures and integrates nonparametric kernel estimation with multivariate conditional geometric quantile techniques. Under temporal dependence, the paper establishes, for the first time, the consistency of the conditional geometric quantile estimator and demonstrates that the framework subsumes several classical parametric models as special cases. Theoretical analysis provides both strong and weak convergence results for the proposed estimators. Extensive simulations and empirical applications to stock returns of Maersk and Lockheed Martin confirm the method’s effectiveness and practical utility.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

Over the last decade, nonparametric methods have gained increasing attention for modeling complex data structures due to their flexibility and minimal structural assumptions. In this paper, we study a general multivariate nonparametric regression framework that encompasses a broad class of parametric models commonly used in financial econometrics. Both the response and the covariate processes are allowed to be multivariate with fixed finite dimensions, and the framework accommodates temporal dependence, thereby introducing additional modeling and theoretical hurdles. To address these challenges, we adopt a functional dependence structure which permits flexible dynamic behavior while maintaining tractable asymptotic analysis. Within this setting, we establish strong and weak convergence results for the estimators of the conditional mean and volatility functions. In addition, we investigate conditional geometric quantiles in the multivariate time series context and prove their consistency under mild regularity conditions. The finite sample performance is examined through comprehensive simulation studies, and the methodology is illustrated by modeling the stock returns of Maersk and Lockheed Martin as a nonparametric function of a geopolitical risk index.

Problem

• multivariate time series
• nonparametric regression
• conditional quantiles
• financial econometrics
• temporal dependence

Innovation

• nonparametric regression
• multivariate time series
• conditional geometric quantiles
• functional dependence
• volatility estimation