I propose two variable addition test statistics aimed at the specification of a high-frequency predictor of a series observed at a lower frequency. Under the null, the high-frequency predictor is aggregated to the low frequency versus mixed-frequency alternatives. The first test statistic is similar to those in the extant literature, but I show its robustness to conditionally biased forecast error and cointegrated and deterministically trending covariates. It is feasible and consistent even if estimation is not feasible under the alternative.
We show how temporal aggregation affects the size and power of the DOLS residual-based KPSS test of the null of cointegration. Size is effectively controlled by setting the minimum number of leads equal to one -- as opposed to zero -- when selecting the lag/lead order of the DOLS regression, but at a cost to power in finite samples. If high-frequency data for one or more series are available, we show how to effectively utilize the high-frequency data to increase power while controlling size.