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

Qing Liu, Chiyu Xia and Xiaohui Liu ()
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Qing Liu: Jiangxi University of Finance and Economics
Chiyu Xia: Jiangxi University of Finance and Economics
Xiaohui Liu: Jiangxi University of Finance and Economics

Indian Journal of Pure and Applied Mathematics, 2025, vol. 56, issue 2, 615-630

Abstract: 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.

Keywords: Limit distribution; Autoregressive model; Infinite variance (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13226-023-00506-y

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