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Robust test for dispersion parameter change in discretely observed diffusion processes

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  • Song, Junmo

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 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.

Suggested Citation

  • Song, Junmo, 2020. "Robust test for dispersion parameter change in discretely observed diffusion processes," Computational Statistics & Data Analysis, Elsevier, vol. 142(C).
    • Handle: RePEc:eee:csdana:v:142:y:2020:i:c:s0167947319301872
    DOI: 10.1016/j.csda.2019.106832
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    Cited by:

    1. Yozo Tonaki & Yusuke Kaino & Masayuki Uchida, 2023. "Estimation for change point of discretely observed ergodic diffusion processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(1), pages 142-183, March.
    2. Byungsoo Kim & Junmo Song & Changryong Baek, 2021. "Robust test for structural instability in dynamic factor models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(4), pages 821-853, August.
    3. Tonaki, Yozo & Uchida, Masayuki, 2023. "Change point inference in ergodic diffusion processes based on high frequency data," Stochastic Processes and their Applications, Elsevier, vol. 158(C), pages 1-39.
    4. Yozo Tonaki & Yusuke Kaino & Masayuki Uchida, 2022. "Adaptive tests for parameter changes in ergodic diffusion processes from discrete observations," Statistical Inference for Stochastic Processes, Springer, vol. 25(2), pages 397-430, July.

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