{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/estimation-of-the-lead-lag-parameter-from-non","title":"Estimation of the lead-lag parameter from non-synchronous data","arxiv_id":"1303.4871","date":"2013-03-20","proceeding":null,"authors":["M. Hoffmann","M. Rosenbaum","N. Yoshida"],"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.","url_abs":"http://arxiv.org/abs/1303.4871v1","url_pdf":"http://arxiv.org/pdf/1303.4871v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"estimation-of-the-lead-lag-parameter-from-non","repo_url":"https://github.com/philipperemy/lead-lag","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}