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

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.

Figures (7)

• Figure 1: Overview of estimated conditional mean, quantiles, volatility and risk, plotted against times.
• Figure 2: Estimated conditional mean of log-return for LHM (left panels) and MMA (right panels) against the three types of geopolitical risk indices. The red lines are used for smoothing purposes.
• Figure 3: Estimated generalized variance of log-return for the two assets (LHM and MMA) against the three types of geopolitical risk indices. The blue lines are used for smoothing purposes.
• Figure 4: Estimates quantiles at $\tau=0.05, 0.50, 0.95$ for LHM (left panels) and MMA (right panels) against the three types of geopolitical risk indices.
• Figure B.1: Geopolitical Risk Indices (GPRD, GPRD-A, GPRD-T) against Time

Theorems & Definitions (13)

• Theorem 1
• Theorem 2
• Corollary 1
• Theorem 3
• Corollary 2
• Theorem 4
• proof : Proof of \ref{['thm:theorem1']} $(i)$
• proof : Proof of \ref{['thm:theorem1']} $(ii)$
• proof : Proof of \ref{['thm:theorem2']}
• Theorem 5