Temporal aggregation of seasonally near-integrated processes

Tomás del Barrio Castro, Paulo M.M. Rodrigues, A. M. Robert Taylor

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


We investigate the implications that temporally aggregating, either by average sampling or systematic (skip) sampling, a seasonal process has on the integration properties of the resulting series at both the zero and seasonal frequencies. Our results extend the existing literature in three ways. First, they demonstrate the implications of temporal aggregation for a general seasonally integrated process with S seasons. Second, rather than only considering the aggregation of seasonal processes with exact unit roots at some or all of the zero and seasonal frequencies, we consider the case where these roots are local-to-unity such that the original series is near-integrated at some or all of the zero and seasonal frequencies. These results show, among other things, that systematic sampling, although not average sampling, can impact on the non-seasonal unit root properties of the data; for example, even where an exact zero frequency unit root holds in the original data it need not necessarily hold in the systematically sampled data. Moreover, the systematically sampled data could be near-integrated at the zero frequency even where the original data is not. Third, the implications of aggregation on the deterministic kernel of the series are explored.-142.

Original languageEnglish
Pages (from-to)872-886
JournalJournal Of Time Series Analysis
Issue number6
Early online date1 Jan 2019
Publication statusPublished - Nov 2019


  • Aggregation
  • Average sampling
  • Demodulation
  • Seasonal (near-) unit roots
  • Systematic sampling


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