Systematic sampling, temporal aggregation, seasonal adjustment, and cointegration theory and evidence

We consider in this paper the theoretical possibility that a unit root at the zero frequency can arise because of temporal aggregation of series which, in fact, possess a unit root possibly at some seasonal frequency. Thus, the long-run component of a time series can be misinterpreted. Similarly, a finding of cointegration at the zero frequency could arise between a series which has a unit root at the zero frequency and another with a unit root at another frequency. Empirical evidence using an international macroeconomic data set is presented which suggests that the above theoretical results have some practical validity.