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Temporal aggregation of seasonally near-integrated processes

Author

Listed:
  • del Barrio Castro, Tomás
  • Rodrigues, Paulo MM
  • Taylor, AM Robert
Abstract
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 sea- sonally 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 frequen- cies, 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.

Suggested Citation

  • del Barrio Castro, Tomás & Rodrigues, Paulo MM & Taylor, AM Robert, 2019. "Temporal aggregation of seasonally near-integrated processes," Essex Finance Centre Working Papers 23878, University of Essex, Essex Business School.
    • Handle: RePEc:esy:uefcwp:23878
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    File URL: https://repository.essex.ac.uk/23878/
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    References listed on IDEAS

    as
    1. Phillips, Peter C B, 1988. "Regression Theory for Near-Integrated Time Series," Econometrica, Econometric Society, vol. 56(5), pages 1021-1043, September.
    2. Burridge, Peter & Taylor, A. M. Robert, 2001. "On regression-based tests for seasonal unit roots in the presence of periodic heteroscedasticity," Journal of Econometrics, Elsevier, vol. 104(1), pages 91-117, August.
    3. Burridge, Peter & Taylor, A M Robert, 2001. "On the Properties of Regression-Based Tests for Seasonal Unit Roots in the Presence of Higher-Order Serial Correlation," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(3), pages 374-379, July.
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    Cited by:

    1. Tomás del Barrio Castro & Gianluca Cubadda & Denise R. Osborn, 2022. "On cointegration for processes integrated at different frequencies," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(3), pages 412-435, May.
    2. del Barrio Castro, Tomás & Rachinger, Heiko, 2021. "Aggregation of Seasonal Long-Memory Processes," Econometrics and Statistics, Elsevier, vol. 17(C), pages 95-106.
    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. Sheng-Hung Chen & Song-Zan Chiou-Wei & Zhen Zhu, 2022. "Stochastic seasonality in commodity prices: the case of US natural gas," Empirical Economics, Springer, vol. 62(5), pages 2263-2284, May.

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    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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