Using a generalized cross-spectral approach, we propose a model-free omnibus statistical procedure to check whether the direction of changes in an economic variable is predictable using the history of its past changes. A class of separate inference procedures are also given to gauge possible...

Under the squared error loss, the optimal forecast is the conditional mean, and the one-step forecast error is a martingale difference (MD). The one-step forecast error forms the conditional moment condition obtained from the loss derivative with respect to the forecast. Similarly, under a...