A Consistent Estimator for Skewness of Partial Sums of Dependent Data

TL;DR

This paper presents a new estimator for the skewness of partial sums in dependent data, enabling better understanding of the distributional properties of sample means in linear processes with short and long memory.

Contribution

It introduces a consistent skewness estimator for dependent data and provides a general framework for asymptotic moments, simplifying derivations of central limit theorems.

Findings

Skewness of sample mean converges to zero at the same rate as in i.i.d. data.

The estimator can be extended to higher moments like kurtosis.

Provides a tool to empirically assess CLT errors in dependent processes.

Abstract

We introduce an estimation method for the scaled skewness coefficient of the sample mean of short and long memory linear processes. This method can be extended to estimate higher moments such as curtosis coefficient of the sample mean. Also a general result on computing all asymptotic moments of partial sums is obtained, allowing in particular a much easier derivation of some existing central limit theorems for linear processes. The introduced skewness estimator provides a tool to empirically examine the error of the central limit theorem for long and short memory linear processes. We also show that, for both short and long memory linear processes, the skewness coefficient of the sample mean converges to zero at the same rate as in the i.i.d. case.