Testing for Cointegration with Temporally Aggregated and Mixed-frequency Time Series

We examine the effects of mixed sampling frequencies and temporal aggregation on standard tests for cointegration. We find that the effects of aggregation on the size of the tests may be severe. Matching sampling schemes of all series generally reduces size, and the nominal size is obtained when all series are skip sampled in the same way. When matching all schemes is not feasible, but when some high-frequency data are available, we show how to use mixed-frequency models to improve the size distortion of the tests. We test stock prices and dividends for cointegration as an empirical demonstration.