Estimation of the lead-lag parameter from non-synchronous data

Abstract

We propose a simple continuous time model for modeling the lead-lag effect between two financial assets. A two-dimensional process $(X_t,Y_t)$ reproduces a lead-lag effect if, for some time shift $\vartheta \in \mathbb{R}$, the process $(X_t,Y_{t+\vartheta })$ is a semi-martingale with respect to a certain filtration. The value of the time shift $\vartheta$ is the lead-lag parameter. Depending on the underlying filtration, the standard no-arbitrage case is obtained for $\vartheta =0$. We study the problem of estimating the unknown parameter $\vartheta \in \mathbb{R}$, given randomly sampled non-synchronous data from $(X_t)$ and $(Y_t)$. By applying a certain contrast optimization based on a modified version of the Hayashi-Yoshida covariation estimator, we obtain a consistent estimator of the lead-lag parameter, together with an explicit rate of convergence governed by the sparsity of the sampling design.

Published in at http://dx.doi.org/10.3150/11-BEJ407 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

References in corpus (2)

• Integrated volatility and round-off error
• Second-order asymptotic expansion for a non-synchronous covariation estimator

Cited by in corpus (11)

• Human mobility and COVID-19 initial dynamics
• Forecasting asylum-related migration flows with machine learning and data at scale
• Multi-Graph Convolutional Network for Relationship-Driven Stock Movement Prediction
• Selecting stock pairs for pairs trading while incorporating lead-lag relationship
• Quasi likelihood analysis of point processes for ultra high frequency data
• NAPLES;Mining the lead-lag Relationship from Non-synchronous and High-frequency Data
• Gaussian approximation of maxima of Wiener functionals and its application to high-frequency data
• Examining Lead-Lag Relationships In-Depth, With Focus On FX Market As Covid-19 Crises Unfolds
• Estimation of the lead-lag parameter between two stochastic processes driven by fractional Brownian motions
• On the asymptotic structure of Brownian motions with a small lead-lag effect
• Wavelet-based methods for high-frequency lead-lag analysis