Computer-intensive rate estimation, diverging statistics and scanning

TL;DR

This paper introduces a general, tuning-parameter-free rate estimation method using diverging/converging statistics, enhanced by a scanning technique to improve accuracy in heavy tail and long memory analysis.

Contribution

It presents a novel rate estimation approach based on simple least squares without tuning parameters, and introduces a scanning method to extract and combine subsample estimators for better accuracy.

Findings

Accurate rate estimators in general settings

Effective application to heavy tail index estimation

Improved long memory parameter estimation

Abstract

A general rate estimation method is proposed that is based on studying the in-sample evolution of appropriately chosen diverging/converging statistics. The proposed rate estimators are based on simple least squares arguments, and are shown to be accurate in a very general setting without requiring the choice of a tuning parameter. The notion of scanning is introduced with the purpose of extracting useful subsamples of the data series; the proposed rate estimation method is applied to different scans, and the resulting estimators are then combined to improve accuracy. Applications to heavy tail index estimation as well as to the problem of estimating the long memory parameter are discussed; a small simulation study complements our theoretical results.