Shrinkage-based tests of predictability

In this paper we derive a test of predictability by exploring the possibility that forecasts from a given model, adjusted by a shrinkage factor, will display lower mean squared prediction errors than forecasts from a simple random walk. This generalizes most previous tests which compare forecast errors of a benchmark model with errors of a proposed alternative model, not allowing for shrinkage. We show that our test is a particular extension of a recently developed test of the martingale difference hypothesis. Using simulations we explore the behavior of our test in small and moderate samples. Numerical results indicate that the test has good size and power properties. Finally, we illustrate the use of our test in an empirical application within the exchange rate literature.