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

Author

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  • Qing Liu

    (Jiangxi University of Finance and Economics
    Jiangxi University of Finance and Economics
    Jiangxi University of Finance and Economics)

  • Chiyu Xia

    (Jiangxi University of Finance and Economics
    Jiangxi University of Finance and Economics)

  • Xiaohui Liu

    (Jiangxi University of Finance and Economics
    Jiangxi University of Finance and Economics)

Abstract

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 $$|\rho | 1$$ | ρ | > 1 , and $$\rho = 1 + \frac{c}{n^\alpha }$$ ρ = 1 + c n α for some constant $$c \in R$$ c ∈ R and $$\alpha \in (0, 1]$$ α ∈ ( 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.

Suggested Citation

  • Qing Liu & Chiyu Xia & Xiaohui Liu, 2025. "Limit theory for an AR(1) model with intercept and a possible infinite variance," Indian Journal of Pure and Applied Mathematics, Springer, vol. 56(2), pages 615-630, June.
    • Handle: RePEc:spr:indpam:v:56:y:2025:i:2:d:10.1007_s13226-023-00506-y
    DOI: 10.1007/s13226-023-00506-y
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    References listed on IDEAS

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