Temporal aggregation and the power of tests for a unit root

The asymptotic local power of unit root tests with the same data span is shown to be independent of sampling frequency. A measure of the power trade-off between sampling frequency and time span for distinct alternatives is derived using an approximate slopes approach. Only small span increases are generally required to maintain power when reducing sampling frequency. Monte Carlo results support the asymptotic analysis for finite samples. An application is made to a consumption function for the UK. Cointegration of consumption and wealth is rejected with quarterly data but convincingly accepted with a longer span of annual data.