Forecast Evaluation for Functional Data

ABSTRACT This paper proposes methods for comparing the accuracy of two competing sets of functional forecasts. This is increasingly relevant as many economic and financial forecasters are interested in predicting variables which are observed as functional data objects. However, to date there has been very little research on formal statistical tests to evaluate the relative accuracy of competing functional forecasts. We propose a suite of novel tests, building on the classic Diebold‐Mariano test, to provide formal statistical guidance on forecast accuracy in the case of functional data. We derive the asymptotic properties of the tests, including their self‐normalised versions, and demonstrate the validity of analytic or bootstrap‐based critical values. We investigate the finite sample performance of the tests using Monte Carlo simulations. We illustrate the use of our method by comparing forecasts of the U.S. yield curve based on forward rates with a random walk benchmark.