Estimators of long range dependence : a survey of finite samples and robustness

Abstract

In traditional financial theory the returns of prices are assumed to be independent of each other, they are said to have short memory. However, it has been shown that returns in many cases are correlated and these instance are said to possess long memory or long range depen- dence. This phenomenon is also found in other research disciplines such as biology, economics, physics, linguistics and hydrology. Long memory can not be established on beforehand but has to be estimated. The goal of this thesis is to evaluate seven estimators of long range dependence by generating time series with varying known long memory parameters and then measure the performance of the estimators under such environments. The estimators are also evaluated when estimating a long memory time series distorted by heavy tailed noise for varying levels of corruption. The noise has similar features to what is observed in financial data. To the author’s knowledge this study of estimation algorithms has the broadest coverage of long memory parameters and noise in terms of numbers of replications which make the results statistically valid. The general observation is that a heavy persistent or heavy anti-persistent series leads to less accurate estimates although some estimators are unaffected by this. There are also differences among the point estimators in how they perform under different sample sizes. When adding noise to the time series the estimation is affected little by persistent series but is affected heavily by the anti-persistent series.