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 long-range 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.