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On Cointegration for Processes Integrated at Different Frequencies

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Abstract

This paper explores the possibility of cointegration existing between processes integrated at different frequencies. Using the demodulator operator, we show that such cointegration can exist and explore its form using both complex- and real-valued representations. A straightforward approach to test for the presence of cointegration between processes integrated at different frequencies is proposed, with a Monte Carol study and an application showing that the testing approach works well.

Suggested Citation

  • Tomás del Barrio Castro & Gianluca Cubadda & Denise R. Osborn, 2020. "On Cointegration for Processes Integrated at Different Frequencies," CEIS Research Paper 502, Tor Vergata University, CEIS, revised 11 Sep 2020.
    • Handle: RePEc:rtv:ceisrp:502
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    Cited by:

    1. del Barrio Castro, Tomás, 2021. "Testing for the cointegration rank between Periodically Integrated processes," MPRA Paper 106603, University Library of Munich, Germany, revised 2021.
    2. Bauer, Dietmar & del Barrio Castro, Tomás, 2025. "The Effect of Aggregation on Seasonal Cointegration in Mixed Frequency data," MPRA Paper 126066, University Library of Munich, Germany.
    3. del Barrio Castro, Tomás & Osborn, Denise R., 2023. "Periodic Integration and Seasonal Unit Roots," MPRA Paper 117935, University Library of Munich, Germany, revised 2023.
    4. Jing Tian & Jan P.A.M. Jacobs & Denise R. Osborn, 2024. "Multivariate Trend‐Cycle‐Seasonal Decompositions with Correlated Innovations," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 86(5), pages 1260-1289, October.
    5. Yushan Cheng & Yongchang Hui & Michael McAleer & Wing-Keung Wong, 2021. "Spurious Relationships for Nearly Non-Stationary Series," JRFM, MDPI, vol. 14(8), pages 1-24, August.

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    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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