Estimating long-range dependence: finite sample properties and confidence intervals

Abstract

A major issue in financial economics is the behavior of asset returns over long horizons. Various estimators of long-range dependence have been proposed. Even though some have known asymptotic properties, it is important to test their accuracy by using simulated series of different lengths. We test R/ S analysis, Detrended Fluctuation Analysis and periodogram regression methods on samples drawn from Gaussian white noise. The DFA statistics turns out to be the unanimous winner. Unfortunately, no asymptotic distribution theory has been derived for this statistics so far. We were able, however, to construct empirical (i.e. approximate) confidence intervals for all three methods. The obtained values differ largely from heuristic values proposed by some authors for the R/ S statistics and are very close to asymptotic values for the periodogram regression method.