Recursive Predictability Tests for Real-Time Data

We propose a sequential test for predictive ability. The test is designed for recursive regressions in which the researcher is interested in recursively assessing whether some economic variables have predictive or explanatory content for another variable. It is common in the forecasting literature to assess predictive ability by using "one-shot" tests at each estimation period. We show that this practice: (i) leads to size distortions; (ii) selects overfitted models and provides spurious evidence of in-sample predictive ability; (iii) may lower the accuracy of the model selected by the test. The usefulness of the proposed test is shown in well-know empirical applications to the real-time predictive content of money for output, and the selection between linear and non-linear models.