TOWARD A UNIFORM ASYMPTOTIC THEORY FOR MILDLY EXPLOSIVE AUTOREGRESSION
为温和爆炸自回归模型提供统一渐近理论，证明柯西极限理论在多种误差过程中保持不变，包括长记忆、短记忆和反持久创新，并探讨了漂移变化模型的扩展。
Abstract This article provides a general asymptotic theory for mildly explosive autoregression. We confirm that Cauchy limit theory remains invariant across a broad range of error processes, including general linear processes with martingale difference innovations, stationary causal processes, and nonlinear autoregressive time series, such as threshold autoregressive and bilinear models. Our results unify the Cauchy limit theory for long memory, short memory, and anti-persistent innovations within a single framework. Notably, we demonstrate that in the presence of anti-persistent innovations, the Cauchy limit theory may be violated when the regression coefficient approaches the local-to-unity range. Additionally, we explore extensions to models with varying drift, which is of significant interest in its own right.