Statistical inference for stationary linear models with tapered data

TL;DR

This paper reviews recent advances in statistical inference for stationary linear models with tapered data, focusing on spectral analysis, robustness, and mathematical tools like tapered Toeplitz matrices, across Gaussian and Lévy-driven processes.

Contribution

It provides a comprehensive survey of spectral inference methods for tapered stationary processes and discusses new theoretical results on tapered Toeplitz operators and limit theorems.

Findings

Analysis of spectral properties of tapered data

Results on robustness of inferences under small trends

Development of mathematical tools for tapered Toeplitz matrices

Abstract

In this paper, we survey some recent results on statistical inference (parametric and nonparametric statistical estimation, hypotheses testing) about the spectrum of stationary models with tapered data, as well as, a question concerning robustness of inferences, carried out on a linear stationary process contaminated by a small trend. We also discuss some question concerning tapered Toeplitz matrices and operators, central limit theorems for tapered Toeplitz type quadratic functionals, and tapered Fej\'er-type kernels and singular integrals. These are the main tools for obtaining the corresponding results, and also are of interest in themselves. The processes considered will be discrete-time and continuous-time Gaussian, linear or L\'evy-driven linear processes with memory.