Inference for Non-Stationary Heavy Tailed Time Series

TL;DR

This paper develops a robust local approximation-based estimator for non-stationary heavy-tailed time series, capable of consistent parameter estimation and asymptotic normality even with infinite variance, supported by empirical evidence.

Contribution

It introduces a novel local approximation method and a self-weighing scheme for inference in non-stationary heavy-tailed time series, handling infinite variance cases.

Findings

Estimator achieves consistent parameter estimation.

Method recovers asymptotic normality regardless of variance finiteness.

Empirical results support the robustness of the proposed approach.

Abstract

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.