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.
Description
Masteroppgave i økonomi og administrasjon - Universitetet i Agder 2012