C. L. E. Franzke, T. Graves, N. W. Watkins, R. B. Gramacy and C. Hughes Robustness of estimators of long-range dependence and self-similarity under non-Gaussianity
Keywords
Memory, Paradigmatic Models, Multiplicative Noise
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 usually occur together in natural systems and that the superposition of both phenomena constitute the self-similarity of a system. 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 are not robust. In particular, they can be biased in the presence of important features of many natural systems like annual cycles, trends and multiplicative noise. Also the longrange dependence and non-Gaussianity of two exemplary natural time series are discussed.