A note on central limit theorems for quadratic variation in case of endogenous observation times

TL;DR

This paper investigates a central limit theorem for quadratic variation in the context of endogenous observation times, focusing on exit times from a regular grid, with detailed analysis for semimartingales with deterministic traits.

Contribution

It provides new insights into the behavior of quadratic variation under endogenous sampling schemes, especially for processes with deterministic characteristics and finite activity jumps.

Findings

Central limit theorem established for quadratic variation with exit time observations

Detailed analysis for semimartingales with deterministic characteristics

Discussion of technical challenges in more general settings

Abstract

This paper is concerned with a central limit theorem for quadratic variation when observations come as exit times from a regular grid. We discuss the special case of a semimartingale with deterministic characteristics and finite activity jumps in detail and illustrate technical issues in more general situations.