Robust test for dispersion parameter change in discretely observed diffusion processes

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.

Estimation for change point of discretely observed ergodic diffusion processes

“…For non-ergodic diffusion processes, see De Gregorio and Iacus (2008) and Iacus and Yoshida (2012). For ergodic diffusion processes, we can refer to Song and Lee (2009), Lee (2011), Negri and Nishiyama (2017), Song (2020), and Tonaki et al (2020). De Gregorio and Iacus (2008) considered the detection of the parameter change in diffusion parameter and the estimation of the change point, and Iacus and Yoshida (2012) studied the estimating problem of the change point in diffusion parameter.…”

“…De Gregorio and Iacus (2008) considered the detection of the parameter change in diffusion parameter and the estimation of the change point, and Iacus and Yoshida (2012) studied the estimating problem of the change point in diffusion parameter. In contrast, Song and Lee (2009), Lee (2011) and Song (2020) considered the detection of the parameter change in diffusion parameter, and Negri and Nishiyama (2017) and Tonaki et al (2020) considered the detection of the parameter change in diffusion and drift parameters. Specifically, Negri and Nishiyama (2017) proposed simultaneous test for changes in diffusion and drift parameters, and Tonaki et al (2020) proposed adaptive tests for those changes.…”

Sequential change point test in the presence of outliers: the density power divergence based approach

“…Strictly speaking, when atypical observations are included in a data set being suspected of having parameter changes, whether the testing results are due to genuine changes or not cannot be readily determined. Such concern has been addressed, for example, in the recent studies by Song and Kang (2021) and Song (2020), where they reported that naive parameter change tests can be severely distorted by outliers.…”

Change point inference in ergodic diffusion processes based on high frequency data

“…In this paper, we consider the change point problem for ergodic diffusion processes. The change point problem for diffusion processes based on discrete observations has been studied by many researchers, for non-ergodic, see De Gregorio and Iacus (2008), Iacus and Yoshida (2012) and for ergodic, see Song and Lee (2009), Lee (2011), Negri and Nishiyama (2017), Song (2020), Tonaki et al (2020Tonaki et al ( ,2021 and reference therein. De Gregorio and Iacus (2008) considered the test for changes in the diffusion parameter and the change point estimation in non-ergodic case, and Iacus and Yoshida (2012) generalized the estimation method.…”

“…De Gregorio and Iacus (2008) considered the test for changes in the diffusion parameter and the change point estimation in non-ergodic case, and Iacus and Yoshida (2012) generalized the estimation method. Song and Lee (2009), Lee (2011), andSong (2020) considered the test for changes in the diffusion parameter in ergodic case. Furthermore, Negri and Nishiyama (2017) and Tonaki et al (2020) proposed simultaneous test and adaptive tests for changes in the diffusion and drift parameters, respectively, and Tonaki et al (2021) treated change point estimation for the case where there is a change in the diffusion parameter and for the case where there is no change in the diffusion parameter but there is a change in the drift parameter.…”