Robust test for dispersion parameter change in discretely observed diffusion processes

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 possesses 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.