On the asymptotic distribution of the mean absolute deviation about the mean

TL;DR

This paper derives the asymptotic distribution of the sample mean absolute deviation for stationary, ergodic time series, accommodating serial dependence and infinite variance scenarios, providing a broad theoretical foundation.

Contribution

It introduces an asymptotic expansion for the mean absolute deviation about the mean applicable to diverse time series conditions, including dependence and infinite moments.

Findings

Asymptotic distribution derived for mean absolute deviation

Applicable to dependent and infinite variance time series

Provides theoretical basis for statistical inference

Abstract

The mean absolute deviation about the mean is an alternative to the standard deviation for measuring dispersion in a sample or in a population. For stationary, ergodic time series with a finite first moment, an asymptotic expansion for the sample mean absolute deviation is proposed. The expansion yields the asymptotic distribution of the sample mean absolute deviation under a wide range of settings, allowing for serial dependence or an infinite second moment.