Autoregressive (AR) models with finite variance errors have been well studied. This paper is concerned with AR models with heavy-tailed errors, which is useful in various scientific research areas. Statistical estimation for AR models with infinite variance errors is very different from those for AR models with finite variance errors. In this paper, we consider a weighted quantile regression for AR models to deal with infinite variance errors. We further propose an induced smoothing method to deal with computational challenges in weighted quantile regression. We show that the difference between weighted quantile regression estimate and its smoothed version is negligible. We further propose a test for linear hypothesis on the regression coefficients. We conduct Monte Carlo simulation study to assess the finite sample performance of the proposed procedures. We illustrate the proposed methodology by an empirical analysis of a real-life data set.

中文翻译：

---

具有无限方差误差的 AR 模型的加权分位数回归

已经很好地研究了具有有限方差误差的自回归 (AR) 模型。本文关注具有重尾错误的 AR 模型，这在各个科学研究领域都很有用。具有无限方差误差的 AR 模型的统计估计与具有有限方差误差的 AR 模型的统计估计非常不同。在本文中，我们考虑了 AR 模型的加权分位数回归来处理无限方差错误。我们进一步提出了一种诱导平滑方法来应对加权分位数回归中的计算挑战。我们表明加权分位数回归估计与其平滑版本之间的差异可以忽略不计。我们进一步提出了对回归系数的线性假设的检验。我们进行蒙特卡罗模拟研究，以评估所提出程序的有限样本性能。我们通过对现实生活数据集的实证分析来说明所提出的方法。