Robustness of Estimators of Long-Range Dependence and Self-Similarity under non-Gaussianity

TL;DR

This paper examines how estimators of long-range dependence and self-similarity perform under non-Gaussian conditions, highlighting biases and implications for natural systems analysis.

Contribution

It critically assesses the bias of popular estimators in non-Gaussian, trend-influenced systems and discusses models capturing combined long-range dependence and non-Gaussianity.

Findings

Popular estimators can be biased by trends and noise

Long-range dependence and non-Gaussianity coexist in natural systems

Implications for risk assessment and trend attribution

Abstract

Long-range dependence and non-Gaussianity are ubiquitous in many natural systems like ecosystems, biological systems and climate. However, it is not always appreciated that both phenomena may occur together in natural systems and that self-similarity in a system can be a superposition of both phenomena. These features, which are common in complex systems, impact the attribution of trends and the occurrence and clustering of extremes. The risk assessment of systems with these properties will lead to different outcomes (e.g. return periods) than the more common assumption of independence of extremes. Two paradigmatic models are discussed which can simultaneously account for long-range dependence and non-Gaussianity: Autoregressive Fractional Integrated Moving Average (ARFIMA) and Linear Fractional Stable Motion (LFSM). Statistical properties of estimators for long-range dependence and self-similarity are critically assessed. It is found that the most popular estimators can be biased in the presence of important features of many natural systems like trends and multiplicative noise. Also the long-range dependence and non-Gaussianity of two typical natural time series are discussed.