We consider the problem of inference for non-stationary time series with heavy-tailed error distribution. Under a time-varying linear process framework we show that there exists a suitable local approximation by a stationary process with heavy-tails. This enable us to introduce a local approximation-based estimator which estimates consistently time-varying parameters of the model at hand. To develop a robust method, we also suggest a self-weighing scheme which is shown to recover the asymptotic normality of the estimator regardless of whether the finite variance of the underlying process exists. Empirical evidence favoring this approach is provided.

翻译：本文研究具有重尾误差分布的非平稳时间序列的推断问题。在时变线性过程框架下，我们证明存在一个适当的局部平稳重尾过程近似。基于此，我们引入一种局部近似的估计量，能够一致地估计模型的时变参数。为构建稳健方法，我们还提出一种自加权方案，该方案能在无论基础过程是否存在有限方差的情况下，恢复估计量的渐近正态性。本文提供了支持该方法的实证证据。