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PreprintCC BY 4.0HAL

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

  • Emmanuel Gobet
  • Louis Latournerie
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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.

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Cite

BibTeXRIS
BibTeX
@misc{gobet2026l2error,
  title = {{L2-error bounds for covariation estimation under asynchronous mixed time-space sampling}},
  author = {Emmanuel Gobet and Louis Latournerie},
  howpublished = {HAL},
  year = {2026},
  month = nov,
  url = {https://hal.science/hal-05849949v1},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - L2-error bounds for covariation estimation under asynchronous mixed time-space sampling
AU  - Emmanuel Gobet
AU  - Louis Latournerie
PY  - 2026
DA  - 2026/11/03
PB  - HAL
UR  - https://hal.science/hal-05849949v1
AB  - 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.
ER  -