Market timing and predictive complexity

We propose a new method for selecting the local estimation window in forecasting and trading financial returns. The method is built around a particular definition of predictive complexity and we apply it in the simplest of predictors, the sample mean. We derive the exact conditions for the process of optimally selecting the local estimation window among a theoretically found grid of potential values of it. We use different loss functions, statistical and financial, which are first considered individually and then pooled under two selection concepts, stochastic dominance and minimum description length, and find exact expressions as to how the associated complexities and their combinations can be derived and applied. Our results are based on a set of probabilistic assumptions for the time series under study, and, based on those, we offer an inferential procedure for testing the presence of excess trading returns. Our empirical illustration on a set of diverse exchange-traded funds, across different asset classes, suggests that the method works very well in practice and that it can generate both statistical and financial performance enhancements. Extensions to different predictors and different underlying assumptions are discussed.