Simple Robust Tests for the Specification of High-Frequency Predictors of a Low-Frequency Series

I propose two simple variable addition test statistics for three tests of the specification of high-frequency predictors in a model to forecast a series observed at a lower frequency. The first is similar to existing test statistics and I show that it is robust to biased forecasts, integrated and cointegrated predictors, and deterministic trends, while it is feasible and consistent even if estimation is not feasible under the alternative. It is not robust to biased forecasts with integrated predictors under the null of a fully aggregated predictor, and size distortion may be severe in this case. The second test statistic proposed is an easily implemented modification of the first that sacrifices some power in small samples but is also robust to this case.