A0494
Title: Lead-lag analysis of high-frequency financial data based on point processes
Authors: Yuta Koike - University of Tokyo (Japan) [presenting]
Takaki Hayashi - Keio University (Japan)
Takaaki Shiotani - Graduate School of Mathematical Sciences, The University of Tokyo (Japan)
Abstract: A new theoretical framework is developed to analyze lead-lag relationships between the order arrivals of two assets. A seminal work proposed model-free measurements of cross-market trading activity based on cross-counts of order arrivals and demonstrated that they can sharply identify their lead-lag relationships, but their mathematical meanings remained unclear. To resolve this issue, the problem of estimating lead-lag relationships in order is formulated as a problem of estimating the shape of the so-called cross-pair correlation function (CPCF) of a bivariate stationary point process, which has been extensively studied in the literature of biostatistics. Then, the lead-lag time parameter is defined as its maximizer. Within this framework, the peak in the prior study's cross-market activity measure can be interpreted as an estimator for the lead-lag time parameter. Furthermore, an alternative lead-lag time estimator is proposed based on kernel density estimation, and it is shown that it has desirable theoretical properties along with superior numerical performance.
