Mildly Explosive Autoregression with Anti‐persistent Errors*
研究了当自回归系数略大于1且误差项具有反持久性时，最小二乘估计的渐近分布仍为柯西分布，并通过纳斯达克指数月度数据验证了模型实用性。
Abstract 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.