# Robust test for dispersion parameter change in discretely observed diffusion processes

## TL;DR

This paper introduces a robust CUSUM test for detecting changes in dispersion parameters of discretely observed diffusion processes, effectively handling outliers and outperforming traditional methods in simulations and real data applications.

## Contribution

It proposes a novel trimmed-residual based CUSUM test that is robust to outliers and demonstrates its effectiveness through theoretical convergence and empirical evaluations.

## Key findings

- The test converges weakly to a Brownian bridge under the null hypothesis.
- Simulations show strong robustness against outliers.
- Application to KOSPI200 data identifies change points missed by naive tests.

## Abstract

This paper deals with the problem of testing for dispersion parameter change in discretely observed diffusion processes when the observations are contaminated by outliers. To lessen the impact of outliers, we first calculate residuals using a robust estimate and then propose a trimmed-residual based CUSUM test. The proposed test is shown to converge weakly to a function of the Brownian bridge under the null hypothesis of no parameter change. We conduct simulations to evaluate performances of the proposed test in the presence of outliers. Numerical results confirm that the proposed test posses a strong robust property against outliers. In real data analysis, we fit the Ornstein-Uhlenbeck process to KOSPI200 volatility index data and locate some change points that are not detected by a naive CUSUM test.