Uncovering regimes in out of sample forecast errors from predictive regressions

We introduce a set of test statistics for assessing the presence of regimes in out of sample forecast errors produced by recursively estimated linear predictive regressions that can accommodate multiple highly persistent predictors. Our tests statistics are designed to be robust to the chosen starting window size and are shown to be both consistent and locally powerful. Their limiting none distributionsare also free of nuisance parameters and hence robust to the degree of persistence of the predictors.Our methods are subsequently applied to the predictability of the value premium whose dynamics are shown to be characterised by state dependence.Gonzalo gratefully acknowledges financial support from the Spanish Ministerio de Economia y Competitividad (grants ECO2016-78652, PID2019-104960GB-I00, and Maria de Maeztu MDM 2014- 0431), and MadEco-CM (grant S205/HUM-3444). Pitarakis thanks the British Academy for financial support through grant SRG170220