Estimation Of Cointegrating Vectors With Time Series Measured At Different Periodicity

We discuss the effects of temporal aggregation on the estimation of cointegrating vectors and on testing linear restrictions on this vector. We adopt a discrete time approach and demonstrate, in contrast with the findings of Chambers (2003, Econometric Theory 19, 49–77), who adopts a continuous time approach, that in some situations, when the regressand must be aggregated, systematic sampling is preferable to average sampling for estimation purposes. Like Chambers, we show that the best aggregation scheme for regressors, in terms of asymptotic estimation efficiency, is always average sampling. We also show that different types of aggregation have no influence on the relative size of tests of linear restrictions on the cointegration vector.We thank Soren Johansen, Niels Haldrup, Raquel Waters, the associate editor, and two anonymous referees for their helpful comments. Of course, any remaining error is the responsibility of the authors. The first author gratefully acknowledges the financial support of a Marie Curie Fellowship of the European Community Programme “Improving the Human Research Potential and the Socio-Economic Knowledge Base” under contract HPMF-CT-2002-01662 and the Danish Research Council. The second author gratefully acknowledges the financial support of the Spanish Ministry of Science and Technology SEC2002-01512.