Mildly Explosive Autoregression with Anti‐persistent Errors

Yiu Lim Lui, Weilin Xiao, Jun Yu   Published : August, 2020   JEL Code: C15, C22   URL to this Article: https://doi.org/10.1111/obes.12395

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.

Keywords

Anti-persistence; Unit root; Mildly explosive; Sequential limit theory; Bubble; Fractional integration