Mildly Explosive Autoregression with Strong Mixing Errors

In this paper, we consider the mildly explosive autoregression [Formula: see text] , [Formula: see text] , where [Formula: see text] , [Formula: see text] , [Formula: see text] , and [Formula: see text] are arithmetically [Formula: see text]-mixing errors. Under some weak conditions, such as [Formula: see text] , [Formula: see text] for some [Formula: see text] and mixing coefficients [Formula: see text] , the Cauchy limiting distribution is established for the least squares (LS) estimator [Formula: see text] of [Formula: see text] , which extends the cases of independent errors and geometrically [Formula: see text]-mixing errors. Some simulations for [Formula: see text] , such as the empirical probability of the confidence interval and the empirical density, are presented to illustrate the Cauchy limiting distribution, which have good finite sample performances. In addition, we use the Cauchy limiting distribution of the LS estimator [Formula: see text] to illustrate real data from the NASDAQ composite index from April 2011 to April 2021.