Quasi-autocorrelation coefficient change test of heavy-tailed sequences based on M-estimation

Xiaofeng Zhang; Hao Jin; Yunfeng Yang; Xiaofeng Zhang; Hao Jin; Yunfeng Yang

doi:10.3934/math.2024955

AIMS Mathematics

2024, Volume 9, Issue 7: 19569-19596. doi: 10.3934/math.2024955

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Research article

Quasi-autocorrelation coefficient change test of heavy-tailed sequences based on M-estimation

1.
School of Sciences, Xi'an University of Science and Technology, Xi'an 710054, China
2.
School of Computer Science and Technology, Xi'an University of Science and Technology, Xi'an 710054, China

Received: 29 November 2023 Revised: 16 May 2024 Accepted: 30 May 2024 Published: 13 June 2024
MSC : 62E20, 62M10, 65C05

A new test to detect the change-point in the quasi-autocorrelation coefficient (QAC) structure of a simple linear model with heavy-tailed series was developed. It is more general than previous approaches to the change-point problem in that it allows for the process with innovations in the domain of the attraction of a stable law with index $ \kappa\; (0 < \kappa < 2) $. Since the existing methods for QAC change detection are not satisfactory, we converted QAC change to mean change through the moving window method, which greatly improved the efficiency. Thus, the aim of this paper was to construct a ratio-typed test based on M-estimation for the testing of mean change. Under regular conditions, the asymptotic distribution under the no change null hypothesis was functional of a Wiener process, not that of a Lévy stable process. The divergent rate under the alternative hypothesis was also given. The simulation results demonstrate that the performances of our proposed tests were outstanding. Finally, the theoretical results were applied to an analysis of daily USD/CNY exchange rates with respect to QAC change.
- autocorrelation coefficient change,
- moving window method,
- M-estimation,
- heavy-tailed,
- ratio-typed test
Citation: Xiaofeng Zhang, Hao Jin, Yunfeng Yang. Quasi-autocorrelation coefficient change test of heavy-tailed sequences based on M-estimation[J]. AIMS Mathematics, 2024, 9(7): 19569-19596. doi: 10.3934/math.2024955

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Abstract

A new test to detect the change-point in the quasi-autocorrelation coefficient (QAC) structure of a simple linear model with heavy-tailed series was developed. It is more general than previous approaches to the change-point problem in that it allows for the process with innovations in the domain of the attraction of a stable law with index $ \kappa\; (0 < \kappa < 2) $. Since the existing methods for QAC change detection are not satisfactory, we converted QAC change to mean change through the moving window method, which greatly improved the efficiency. Thus, the aim of this paper was to construct a ratio-typed test based on M-estimation for the testing of mean change. Under regular conditions, the asymptotic distribution under the no change null hypothesis was functional of a Wiener process, not that of a Lévy stable process. The divergent rate under the alternative hypothesis was also given. The simulation results demonstrate that the performances of our proposed tests were outstanding. Finally, the theoretical results were applied to an analysis of daily USD/CNY exchange rates with respect to QAC change.

References

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