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

Robust test for dispersion parameter change in discretely observed diffusion processes