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The CUSUM statistics of change-point models based on dependent sequences
Saisai Ding1, Hongyan Fang1, Xiang Dong2
1School of Mathematical Sciences, Anhui University, Hefei, People's Republic of China.
Journal of Applied Statistics
|June 27, 2022
Summary
This study introduces mean change-point models using associated sequences. The Cumulative Sum (CUSUM) statistic
Area of Science:
- Statistics
- Time Series Analysis
- Financial Mathematics
Background:
- Change-point detection is crucial for analyzing sequential data.
- Existing methods may have limitations under certain data conditions.
- Mean change-point models are essential for identifying shifts in data distributions.
Purpose of the Study:
- To develop and analyze mean change-point models for associated sequences.
- To establish the theoretical properties of the CUSUM statistic for change detection.
- To apply these models to real-world financial data analysis.
Main Methods:
- Derivation of the limit distribution for the CUSUM statistic under weak conditions.
- Investigation of the consistency of sample covariances and change-point estimators.
- Monte Carlo simulations using Normal and Lognormal data to evaluate performance.
Main Results:
- A limit distribution for the CUSUM statistic was obtained, enabling change-point detection.
- The consistency of key statistics was theoretically established.
- Simulations demonstrated the effectiveness of the proposed methods in terms of empirical size, power, and convergence.
Conclusions:
- The developed mean change-point models provide a robust framework for detecting shifts in associated sequences.
- The CUSUM statistic is a reliable tool for identifying mean changes.
- The application to financial series highlights the practical utility of the methodology.
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