A stochastic approach to modelling and forecasting dependent time-series

An important assumption underlying traditional theories of financial time-series behaviour is that consecutive changes in the price of an asset (ie. asset returns) are independent of each other. For analysts seeking to predict the future value of an asset, this implies that the best step-ahead forecast of a time-series is its current value plus or minus a random error. If asset returns are serially correlated rather than independent, knowledge of the sign and magnitude of the dependence should improve the accuracy of future return estimates. The significance of this study is that it develops an integrated approach to forecasting financial time-series by incorporating the principles underlying long-term dependence. The approach is unique in that both the magnitude and the sign of the dependence is considered. Compared to simple random forecasting, the integrated approach is proven superior when there is dependence in the underlying series.