Testing for Long-Range Dependence in Financial Time Series

Abstract

Various trading strategies have been proposed that use estimates of the Hurst
coefficient, which is an indicator of long-range dependence, for the calculation
of buy and sell signals. This paper introduces frequency-domain tests for longrange dependence which do, in contrast to conventional procedures, not assume
that the number of used periodogram ordinates grow with the length of the time
series. These tests are applied to series of gold price returns and stock index
returns in a rolling analysis. The results suggest that there is no long-range
dependence, indicating that trading strategies based on fractal dynamics have
no sound statistical basis.