On parameter estimation for critical affine processes

TL;DR

This paper establishes conditions for the weak convergence of scaled affine processes and analyzes the asymptotic behavior of parameter estimators in a two-dimensional critical affine diffusion.

Contribution

It provides new sufficient conditions for weak convergence of affine processes and studies the asymptotics of least squares estimators in critical affine diffusions.

Findings

Established weak convergence conditions for scaled affine processes.

Analyzed asymptotic behavior of least squares estimators in a 2D critical affine diffusion.

Specialized results to one-dimensional continuous state branching processes with immigration.

Abstract

First we provide a simple set of sufficient conditions for the weak convergence of scaled affine processes with state space $R_+ \times R^d$. We specialize our result to one-dimensional continuous state branching processes with immigration. As an application, we study the asymptotic behavior of least squares estimators of some parameters of a two-dimensional critical affine diffusion process.