A Stochastic Model for Return Sign Predictability and How it Relates to Mean Nonlinearity

Abstract

This work examines the relationship between redictability of return sign and conditional moments. A nonlinear time series model, la

ter restricted to a first-order Taylor expansion in the innovations, is used for this purpose. As a result, it is shown why sign predictability depends only on odd-numbered order conditional moments (on the conditional mean in the restricted model), which makes testing for linearity or non linearity in the mean interesting before attempting directional forecasting. As an application, the presence of nonlinearity in the mean in the Colombian stock exchange index IGBC is examined applying the BDS test to the residuals of an ARMA-GARCH filter and the White Neural Network Test for Nonlinearity to the residuals of an AR filter. Both tests show that the IGBC exhibits nonlinearity in the mean.