Change detection in the Cox-Ingersoll-Ross model

TL;DR

This paper introduces a change detection method for the Cox-Ingersoll-Ross model, enabling the identification of parameter shifts crucial for financial applications, using estimators based on Brownian bridge asymptotics.

Contribution

It develops one- and two-sided tests for drift parameters in the Cox-Ingersoll-Ross model with proven asymptotic properties and change-point estimation.

Findings

Asymptotic distribution under no change is a Brownian bridge.

Test procedures are asymptotically consistent.

Change-point estimator has proven asymptotic properties.

Abstract

We propose a change detection method for the famous Cox--Ingersoll--Ross model. This model is widely used in financial mathematics and therefore detecting a change in its parameters is of crucial importance. We develop one- and two-sided testing procedures for both drift parameters of the process. The test process is based on estimators that are motivated by the discrete time least-squares estimators, and its asymptotic distribution under the no-change hypothesis is that of a Brownian bridge. We prove the asymptotic weak consistence of the test, and derive the asymptotic properties of the change-point estimator under the alternative hypothesis of change at one point in time.