Traditional models of financial asset yields are based on a number of simplifying assumptions. Among these are the primary assumptions that changes in asset yields are independent, and that the distribution of these yields is approximately normal. The development of financial asset pricing models has also incorporated these assumptions. A general feature of the pricing models is that the relationship between the model variables is fundamentally linear. Recent empirical research has however identified the possibility for these relations to be non-linear. The empirical research focused primarily on methodological issues relating to the application of the classical rescaled adjusted range. Some of the major issues investigated were: the use of overlapping versus contiguous subseries lengths in the calculation of the statistic's Hurst exponent; the asymptotic distribution of the Hurst exponent for Gaussian time-series and long-term dependent fBm's; matters pertaining to the estimation of the expected rescaled adjusted range. Empirical research in this thesis also considered alternate applications of rescaled range analysis, other than modelling non-linear long-term dependence. Issues relating to the use of the technique for estimating long-term dependent ARFIMA processes, and some implications of long-term dependence for financial time-series have both been investigated. Overall, the general shape of the asymptotic distribution of the Hurst exponent has been shown to be invariant to the level of dependence in the underlying series. While the rescaled adjusted range is a biased indicator of the level of long-term dependence in simulated time-series, it was found that the bias could be efficiently modelled. For real time-series containing structured short-term dependence, the bias was shown to be inconsistent with the simulated results. / Doctor of Philosophy (PhD)