Inference for Non-Stationary Heavy Tailed Time Series

2022/12/21 by Fumiya Akashi, Konstantinos Fokianos, Akashi, Fumiya +3
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Forecasting Techniques and Applications #Monetary Policy and Economic Impact #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2212.11253

openalex publication_date 2022/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Statistical inference for continuous-time locally stationary processes\n using stationary approximations
• Inference in heavy-tailed non-stationary multivariate time series
• Gaussian Approximation For Non-stationary Time Series with Optimal Rate and Explicit Construction
• Auto-Regressive Approximations to Non-stationary Time Series, with Inference and Applications
• Inference on the tail process with application to financial time series modelling