Parameter Estimation in Two-type Continuous-state Branching Processes with Immigration

TL;DR

This paper investigates parameter estimation methods for two-type continuous-state branching processes with immigration, proving ergodicity and establishing the statistical properties of estimators based on low frequency data.

Contribution

It introduces consistent and asymptotically normal estimators for the process parameters, extending the statistical theory for multi-type CBI-processes.

Findings

Proved ergodicity of the processes

Established strong consistency of estimators

Derived central limit theorems for estimators

Abstract

We study the estimation of two-type continuous-state branching processes with immigration (CBI-processes). The ergodicity of the processes is proved. We also establish the strong consistency and central limit theorems of the conditional least squares estimators and the weighted conditional least squares estimators of the drift and diffusion coefficients based on low frequency observations.