JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2025, Vol. 60 ›› Issue (3): 77-87.doi: 10.6040/j.issn.1671-9352.0.2023.439

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Least squares estimator of the first-order and mildly explosive autoregression with mixing errors

DUAN Ticheng1, XU Chengkai1, LU Zijie1, JIA Peiyan2, XIE Suya1, YANG Wenzhi1*   

  1. 1. School of Big Data and Statistics, Anhui University, Hefei 230601, Anhui, China;
    2. Wendian College, Anhui University, Hefei 230601, Anhui, China
  • Published:2025-03-10

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Abstract: The least squares(LS)estimator is studied for the first-order and mildly explosive autoregression with φ-mixing errors. Under some weak conditions of E(u1)=0, E(|u1|4)<∞ and φ(n)=O(n-8), the limit distribution of standard Cauchy distribution is obtained for the LS estimator. Some simulations are given, which agree with the theory results. As an application, the first-order mildly explosive model and autoregressive coefficient interval estimation are used to study the growth process of share price for the NVIDIA corporation common stock from 2013 to 2023.

Key words: mildly explosive autoregression, least squares estimator, Cauchy distribution, mixing sequence

CLC Number: 

  • O212.1
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