Forecast encompassing tests and probability forecasts

Clements, M. P. ORCID: https://orcid.org/0000-0001-6329-1341 and Harvey, D. I. (2010) Forecast encompassing tests and probability forecasts. Journal of Applied Econometrics, 25 (6). pp. 1028-1062. ISSN 1099-1255 doi: 10.1002/jae.1097

Abstract/Summary

We consider tests of forecast encompassing for probability forecasts, for both quadratic and logarithmic scoring rules. We propose test statistics for the null of forecast encompassing, present the limiting distributions of the test statistics, and investigate the impact of estimating the forecasting models' parameters on these distributions. The small-sample performance is investigated, in terms of small numbers of forecasts and model estimation sample sizes. We show the usefulness of the tests for the evaluation of recession probability forecasts from logit models with different leading indicators as explanatory variables, and for evaluating survey-based probability forecasts.