A weighted least squares procedure to approximate least absolute deviation estimation in time series with specific reference to infinite variance unit root problems

TL;DR

This paper introduces a weighted least squares approach that approximates least absolute deviation estimation for large-sample, heavy-tailed time series, improving hypothesis testing especially with bootstrap methods.

Contribution

It presents a novel weighted regression method tailored for heavy-tailed innovations, enhancing estimation and hypothesis testing in large-sample, high-dimensional time series.

Findings

Effective approximation of least absolute deviation in large samples

Improved bootstrap hypothesis testing for unit roots

Successful application to autoregressive models including random walk

Abstract

A weighted regression procedure is proposed for regression type problems where the innovations are heavy-tailed. This method approximates the least absolute regression method in large samples, and the main advantage will be if the sample is large and for problems with many independent variables. In such problems bootstrap methods must often be utilized to test hypotheses and especially in such a case this procedure has an advantage over least absolute regression. The procedure will be illustrated on first-order autoregressive problems, including the random walk. A bootstrap procedure is used to test the unit root hypothesis and good results were found.