Extending the Scope of Inference About Predictive Ability to Machine Learning Methods

Abstract

Though out-of-sample forecast evaluation is routinely recommended with modern machine learning methods and there exists a well-established classic inference theory for predictive ability, see West (1996, Asymptotic Inference About Predictive Ability, Econometrica, 64. 1067-1084), such theory is not directly applicable to modern machine learners such as the Lasso in the high dimensional setting. We investigate under which conditions such extensions are possible. Two key properties for standard out-of-sample asymptotic inference with machine learning are: (i) a zero mean condition for the score of the loss function; and (ii) a fast rate of convergence for the machine learner. Monte Carlo simulations confirm our theoretical results. We illustrate the applicability of our results with a new out-of-sample test for the Martingale Difference Hypothesis (MDH). We argue that for the MDH problem, a "dense" approach is more suitable than a "sparsity" based approach. We obtain the asymptotic null distribution of our test and apply it to evaluate the MDH of some major daily exchange rates.

Registration
You can sign up for this seminar by sending an email to eb-secr@ese.eur.nl. The lunch will be provided (vegetarian option included).