L2-error bounds for covariation estimation under asynchronous mixed time-space sampling

Emmanuel Gobet () and Louis Latournerie
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Emmanuel Gobet: LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique - UPCité - Université Paris Cité, Kaiko [Paris]
Louis Latournerie: CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique, CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - Groupe ENSAE-ENSAI - Groupe des Écoles Nationales d'Économie et Statistique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - Groupe ENSAE-ENSAI - Groupe des Écoles Nationales d'Économie et Statistique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique

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Abstract: We study the estimation of the quadratic covariation of two continuous Itô martingales X and Y observed asynchronously under endogenous mixed time-space sampling schemes. For each process, observations are triggered either when the process variation reaches a fixed deviation threshold or when a prescribed maximum time interval, referred to as the heartbeat threshold, has elapsed. The resulting observation times of X and Y are therefore asynchronous and endogenous. In this setting, we derive an explicit convergence rate for the Hayashi-Yoshida estimator, expressed in terms of the deviation and heartbeat thresholds.

Keywords: Time-space sampling; High-frequency data; Quadratic covariation; Consistency; Decentralized Finance (search for similar items in EconPapers)
Date: 2026-11-03
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