Trend estimation for time series with polynomial-tailed noise

TL;DR

This paper introduces a nonlinear wavelet estimator for nonparametric trend estimation in time series with polynomial-tailed noise, accommodating irregular sampling and providing a thresholding scheme for sparse signals.

Contribution

It develops a novel wavelet-based method tailored for trend estimation under polynomial-tailed noise and non-uniform sampling, extending existing techniques.

Findings

Effective trend estimation with polynomial-tailed noise

Adaptation to non-dyadic and irregular sampling

A new thresholding scheme for sparse signals

Abstract

For time series data observed at non-random and possibly non-equidistant time points, we estimate the trend function nonparametrically. Under the assumption of a bounded total variation of the function and low-order moment conditions on the errors we propose a nonlinear wavelet estimator which uses a Haar-type basis adapted to a possibly non-dyadic sample size. An appropriate thresholding scheme for sparse signals with an additive polynomial-tailed noise is first derived in an abstract framework and then applied to the problem of trend estimation.