Change point detection for a skew normal distribution based on the Q-function

Yang Du; Weihu Cheng; Yang Du; Weihu Cheng

doi:10.3934/math.20241392

AIMS Mathematics

2024, Volume 9, Issue 10: 28698-28721. doi: 10.3934/math.20241392

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Research article

Change point detection for a skew normal distribution based on the Q-function

Yang Du ^1,2,
Weihu Cheng ^{1
,
,}

1.
School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing 100124, China
2.
Department of Applied Mathematics, Harbin University of Science and Technology, Harbin 150080, China

Received: 16 July 2024 Revised: 17 September 2024 Accepted: 26 September 2024 Published: 10 October 2024
MSC : 62F03, 62P20

In this paper, we enhanced change point detection in skew normal distribution models by integrating the EM algorithm's Q-function with the modified information criterion (MIC). The new QMIC framework improves sensitivity and accuracy in detecting changes, outperforming the modified information criterion (MIC) and the traditional Bayesian information criterion (BIC). Due to the complexity of deriving analytic asymptotic distributions, bootstrap simulations were used to determine critical values at various significance levels. Extensive simulations demonstrate that QMIC offers superior detection capabilities. We applied the QMIC method to two stock market datasets, successfully identifying multiple change points, and highlighting its effectiveness for real-world financial data analysis.
- skew normal distribution,
- change point detection,
- expectation maximization,
- Q-function,
- binary segmentation method
Citation: Yang Du, Weihu Cheng. Change point detection for a skew normal distribution based on the Q-function[J]. AIMS Mathematics, 2024, 9(10): 28698-28721. doi: 10.3934/math.20241392

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Abstract

In this paper, we enhanced change point detection in skew normal distribution models by integrating the EM algorithm's Q-function with the modified information criterion (MIC). The new QMIC framework improves sensitivity and accuracy in detecting changes, outperforming the modified information criterion (MIC) and the traditional Bayesian information criterion (BIC). Due to the complexity of deriving analytic asymptotic distributions, bootstrap simulations were used to determine critical values at various significance levels. Extensive simulations demonstrate that QMIC offers superior detection capabilities. We applied the QMIC method to two stock market datasets, successfully identifying multiple change points, and highlighting its effectiveness for real-world financial data analysis.

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