Convergence of the CUSUM estimation for a mean shift in linear processes with random coefficients

Yi Wu, Wei Wang and Xuejun Wang ()
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Yi Wu: Chizhou University
Wei Wang: Chizhou University
Xuejun Wang: Anhui University

Computational Statistics, 2024, vol. 39, issue 7, No 13, 3753-3778

Abstract: Abstract Let $$\{X_{i},1\le i\le n\}$$ { X i , 1 ≤ i ≤ n } be a sequence of linear process based on dependent random variables with random coefficients, which has a mean shift at an unknown location. The cumulative sum (CUSUM, for short) estimator of the change point is studied. The strong convergence, $$L_{r}$$ L r convergence, complete convergence and the rate of strong convergence are established for the CUSUM estimator under some mild conditions. These results improve and extend the corresponding ones in the literature. Simulation studies and two real data examples are also provided to support the theoretical results.

Keywords: Linear process; Random coefficients; Convergence; Cumulative sum estimator; Change point (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00180-024-01465-6

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