Empirical likelihood method for detecting change points in network autoregressive models

Jingjing Yang; Weizhong Tian; Chengliang Tian; Sha Li; Wei Ning; Jingjing Yang; Weizhong Tian; Chengliang Tian; Sha Li; Wei Ning

doi:10.3934/math.20241206

AIMS Mathematics

2024, Volume 9, Issue 9: 24776-24795. doi: 10.3934/math.20241206

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Research article

Empirical likelihood method for detecting change points in network autoregressive models

1.
Department of Applied Mathematics, Xi'an University of Technology, Xi'an 710048, China
2.
College of Big Data and Internet, Shenzhen Technology University, Shenzhen 518118, China
3.
College of Computer Science and Technology, Qingdao University, Qingdao 266071, China
4.
School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China
5.
Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43403, USA

Received: 05 June 2024 Revised: 08 August 2024 Accepted: 14 August 2024 Published: 23 August 2024
MSC : 62C12, 62J05, 62G10

The network autoregressive model is a super high-dimensional time series model that can fully explain social relationships. This model can fully reflect the complex relationships in reality. Therefore, it plays a vital role in detecting the inflection point problem of this network autoregressive model for economics and finance. In this paper, we proposed the change-point problem of detecting network autoregressive models using empirical likelihood statistics based on the expected error term of the switching rule being 0, using the empirical likelihood method. Moreover, the asymptotic null distribution of the proposed empirical likelihood statistic was investigated. Simulation studies based on different settings were considered, and the results showed that the power of test statistics is significant. In the end, the Chinese stock market was investigated to demonstrate the significance of the proposed method.
- network autoregressive models,
- change point,
- empirical likelihood,
- Gumbel distribution,
- Chinese stock market
Citation: Jingjing Yang, Weizhong Tian, Chengliang Tian, Sha Li, Wei Ning. Empirical likelihood method for detecting change points in network autoregressive models[J]. AIMS Mathematics, 2024, 9(9): 24776-24795. doi: 10.3934/math.20241206

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Abstract

The network autoregressive model is a super high-dimensional time series model that can fully explain social relationships. This model can fully reflect the complex relationships in reality. Therefore, it plays a vital role in detecting the inflection point problem of this network autoregressive model for economics and finance. In this paper, we proposed the change-point problem of detecting network autoregressive models using empirical likelihood statistics based on the expected error term of the switching rule being 0, using the empirical likelihood method. Moreover, the asymptotic null distribution of the proposed empirical likelihood statistic was investigated. Simulation studies based on different settings were considered, and the results showed that the power of test statistics is significant. In the end, the Chinese stock market was investigated to demonstrate the significance of the proposed method.

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