Implementing Residual-Based KPSS Tests for Cointegration with Data Subject to Temporal Aggregation and Mixed Sampling Frequencies
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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.