A unified approach to self-normalized block sampling

TL;DR

This paper introduces a unified self-normalized block sampling method for inference on the mean of stationary time series, effectively handling various dependence structures and tail behaviors without prior parameter estimation.

Contribution

It develops an asymptotic theory for self-normalized block sampling that unifies inference across different time series models without needing auxiliary parameter estimation.

Findings

Method performs well in finite samples as shown by simulations.

The approach is applicable to diverse dependence and tail conditions.

R implementation of the method is provided.

Abstract

The inference procedure for the mean of a stationary time series is usually quite different under various model assumptions because the partial sum process behaves differently depending on whether the time series is short or long-range dependent, or whether it has a light or heavy-tailed marginal distribution. In the current paper, we develop an asymptotic theory for the self-normalized block sampling, and prove that the corresponding block sampling method can provide a unified inference approach for the aforementioned different situations in the sense that it does not require the {\em a priori} estimation of auxiliary parameters. Monte Carlo simulations are presented to illustrate its finite-sample performance. The R function implementing the method is available from the authors.