Estimators for Long Range Dependence: An Empirical Study

TL;DR

This paper empirically compares 12 estimators for long-range dependence parameters in time series, assessing their performance on simulated data and real-world data to identify the most accurate methods.

Contribution

It provides a comprehensive simulation-based comparison of multiple estimators for the Hurst and fractional integration parameters in long memory series.

Findings

Certain estimators outperform others in accuracy.

Performance varies with series length and parameter values.

Some estimators are more robust on real-world data.

Abstract

We present the results of a simulation study into the properties of 12 different estimators of the Hurst parameter, $H$, or the fractional integration parameter, $d$, in long memory time series. We compare and contrast their performance on simulated Fractional Gaussian Noises and fractionally integrated series with lengths between 100 and 10,000 data points and $H$ values between 0.55 and 0.90 or $d$ values between 0.05 and 0.40. We apply all 12 estimators to the Campito Mountain data and estimate the accuracy of their estimates using the Beran goodness of fit test for long memory time series. MCS code: 37M10