Bias in the estimation of mean reversion in continuous-time Lévy processes

- This paper studies the bias issue in continuous-time Lévy processes.
- The approximate bias of the least squares estimator of κ is derived.
- Both known and unknown long-run mean cases are considered.
- We consider both fixed and random initial conditions in approximating bias.
- Simulations are conducted to examine the performance of the bias approximation and correction.

This paper develops the approximate bias of the ordinary least squares estimator of the mean reversion parameter in continuous-time Lévy processes. Several cases are considered, depending on whether the long-run mean is known or unknown and whether the initial condition is fixed or random. The approximate bias is used to construct a bias corrected estimator. The performance of the approximate bias and the bias corrected estimator is examined using simulated data.