Wavelet-based methods for high-frequency lead-lag analysis

TL;DR

This paper introduces a wavelet-based framework for analyzing lead-lag relationships between financial assets across multiple time scales, integrating continuous-time models with discrete wavelet methods.

Contribution

It develops a novel multi-scale analysis framework that combines continuous-time modeling with wavelet methods for lead-lag analysis, including a new statistical methodology and asymptotic theory.

Findings

Effective multi-scale lead-lag analysis demonstrated through numerical experiments

Framework accommodates stochastic volatilities and irregular sampling

Provides asymptotic theory for scale-by-scale analysis

Abstract

We propose a novel framework to investigate lead-lag relationships between two financial assets. Our framework bridges a gap between continuous-time modeling based on Brownian motion and the existing wavelet methods for lead-lag analysis based on discrete-time models and enables us to analyze the multi-scale structure of lead-lag effects. We also present a statistical methodology for the scale-by-scale analysis of lead-lag effects in the proposed framework and develop an asymptotic theory applicable to a situation including stochastic volatilities and irregular sampling. Finally, we report several numerical experiments to demonstrate how our framework works in practice.