Limit theory for an AR(1) model with intercept and a possible infinite variance

被引：0

作者：

Liu, Qing ^{[1
,2
,3
]}

Xia, Chiyu ^{[1
,2
]}

Liu, Xiaohui ^{[1
,2
]}

机构：

[1] Jiangxi Univ Finance & Econ, Sch Stat & Data Sci, Nanchang 330013, Jiangxi, Peoples R China

[2] Jiangxi Univ Finance & Econ, Key Lab Data Sci Finance & Econ, Nanchang 330013, Jiangxi, Peoples R China

[3] Jiangxi Univ Finance & Econ, Res Ctr Appl Stat, Nanchang 330013, Jiangxi, Peoples R China

来源：

INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS | 2025年 / 56卷 / 02期

基金：

中国博士后科学基金;

关键词：

Limit distribution; Autoregressive model; Infinite variance; TIME-SERIES; UNIT-ROOT; INFERENCE; INTERVAL;

D O I：

10.1007/s13226-023-00506-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we derive the limit distribution of the least squares estimator for an AR(1) model with a non-zero intercept and a possible infinite variance. It turns out that the estimator has a quite different limit for the cases of |p| < 1, |p| > 1, and p = 1 + c/n(a) for some constant c is an element of Rand alpha is an element of (0, 1], and whether or not the variance of the model errors is infinite also has a great impact on both the convergence rate and the limit distribution of the estimator.

引用

页码：615 / 630

页数：16

共 21 条

[1] ON ASYMPTOTIC DISTRIBUTIONS OF ESTIMATES OF PARAMETERS OF STOCHASTIC DIFFERENCE-EQUATIONS [J].