Entropy and predictability of stock market returns

We examine the predictability of stock market returns by employing a new metric entropy measure of dependence with several desirable properties. We compare our results with a number of traditional measures. The metric entropy is capable of detecting nonlinear dependence within the returns series, and is also capable of detecting nonlinear “affinity” between the returns and their predictions obtained from various models thereby serving as a measure of out-of-sample goodness-of-fit or model adequacy. Several models are investigated, including the linear and neural-network models as well as nonparametric and recursive unconditional mean models. We find significant evidence of small nonlinear unconditional serial dependence within the returns series, but fragile evidence of superior conditional predictability (profit opportunity) when using market-switching versus buy-and-hold strategies.