On conditional least squares estimation for affine diffusions based on continuous time observations

TL;DR

This paper investigates the asymptotic properties of conditional least squares estimators for the drift parameters of two-factor affine diffusions, considering subcritical, critical, and supercritical regimes, and characterizes their limiting distributions.

Contribution

It provides a comprehensive analysis of the asymptotic behavior of estimators for affine diffusions across different critical regimes, including non-standard cases.

Findings

Asymptotic normality in subcritical and supercritical cases

Non-standard asymptotic behavior in the critical case

Characterization of limiting distributions for drift estimators

Abstract

We study asymptotic properties of conditional least squares estimators for the drift parameters of two-factor affine diffusions based on continuous time observations. We distinguish three cases: subcritical, critical and supercritical. For all the drift parameters, in the subcritical and supercritical cases, asymptotic normality and asymptotic mixed normality is proved, while in the critical case, non-standard asymptotic behavior is described.