An asymptotic distribution is derived for the least squares (LS) estimate of a first‐order autoregression with a mildly explosive root and anti‐persistent errors. While the sample moments depend on the Hurst parameter asymptotically, the Cauchy limiting distribution theory remains valid for the LS estimates in the model without intercept and a model with an asymptotically negligible intercept. Monte Carlo studies are designed to check the precision of the Cauchy distribution in finite samples. An empirical study based on the monthly NASDAQ index highlights the usefulness of the model and the new limiting distribution.

中文翻译：

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具有持久性错误的轻度爆炸自回归*

得出一阶自回归的最小二乘估计（LS）的渐近分布，该阶自回归具有轻度爆炸性根和反持久误差。尽管样本矩渐近取决于Hurst参数，但柯西极限分布理论对于没有截距的模型和具有渐近可忽略的截距的模型中的LS估计仍然有效。蒙特卡洛研究旨在检查有限样本中柯西分布的精度。基于每月纳斯达克指数的实证研究强调了该模型的有效性和新的极限分布。