Testing for Cointegration with Temporally Aggregated and Mixed‐Frequency Time Series

We examine the effects of mixed sampling frequencies and temporal aggregation on the size of commonly used tests for cointegration, and we find that these effects may be severe. Matching sampling schemes of all series generally reduces size distortion, and the nominal size is obtained asymptotically only when all series are skip sampled in the same way – for example, end‐of‐period sampling. We propose and analyse mixed‐frequency versions of the cointegration tests in order to control the size when some high‐frequency data are available. Otherwise, when no high‐frequency data are available, we discuss controlling size using bootstrapped critical values. We test stock prices and dividends for cointegration as an empirical demonstration.

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