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Aggregation of Seasonal Long-Memory Processes

Author

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  • del Barrio Castro, Tomás
  • Rachinger, Heiko

Abstract

To understand the impact of temporal aggregation on the properties of a seasonal long-memory process, the effects of skip and cumulation sampling on both stationary and nonstationary processes with poles at several potential frequencies are analyzed. By allowing for several poles in the disaggregated process, their interaction in the aggregated series is investigated. Further, by definning the process according to the truncated Type II definition, the proposed approach encompasses both stationary and nonstationary processes without requiring prior knowledge of the case. The frequencies in the aggregated series to which the poles in the disaggregated series are mapped can be directly deduced. Specifically, unlike cumulation sampling, skip sampling can impact on non-seasonal memory properties. Moreover, with cumulation sampling, seasonal long-memory can vanish in some cases. Using simulations, the mapping of the frequencies implied by temporal aggregation is illustrated and the estimation of the memory at the different frequencies is analyzed

Suggested Citation

  • del Barrio Castro, Tomás & Rachinger, Heiko, 2020. "Aggregation of Seasonal Long-Memory Processes," MPRA Paper 102890, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:102890
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    File URL: https://mpra.ub.uni-muenchen.de/102890/1/MPRA_paper_102813.pdf
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    References listed on IDEAS

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    1. Tomás del Barrio Castro & Paulo M. M. Rodrigues & A. M. Robert Taylor, 2019. "Temporal Aggregation of Seasonally Near‐Integrated Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 40(6), pages 872-886, November.
    2. Andrea Silvestrini & David Veredas, 2008. "Temporal Aggregation Of Univariate And Multivariate Time Series Models: A Survey," Journal of Economic Surveys, Wiley Blackwell, vol. 22(3), pages 458-497, July.
    3. Gregoir, Stéphane, 1999. "Multivariate Time Series With Various Hidden Unit Roots, Part Ii," Econometric Theory, Cambridge University Press, vol. 15(4), pages 469-518, August.
    4. Henghsiu Tsai & K. S. Chan, 2005. "Temporal Aggregation of Stationary And Nonstationary Discrete‐Time Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(4), pages 613-624, July.
    5. Chung, Ching-Fan, 1996. "Estimating a generalized long memory process," Journal of Econometrics, Elsevier, vol. 73(1), pages 237-259, July.
    6. Sun, Jingwei & Shi, Wendong, 2014. "Aggregation of the generalized fractional processes," Economics Letters, Elsevier, vol. 124(2), pages 258-262.
    7. Javier Hidalgo & Philippe Soulier, 2004. "Estimation of the location and exponent of the spectral singularity of a long memory process," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(1), pages 55-81, January.
    8. repec:hal:journl:peer-00815563 is not listed on IDEAS
    9. Arteche, Josu & Orbe, Jesus, 2017. "A strategy for optimal bandwidth selection in Local Whittle estimation," Econometrics and Statistics, Elsevier, vol. 4(C), pages 3-17.
    10. Gregoir, Stephane, 2006. "Efficient tests for the presence of a pair of complex conjugate unit roots in real time series," Journal of Econometrics, Elsevier, vol. 130(1), pages 45-100, January.
    11. Hassler, Uwe, 2011. "Estimation of fractional integration under temporal aggregation," Journal of Econometrics, Elsevier, vol. 162(2), pages 240-247, June.
    12. Arteche, Josu, 2020. "Exact Local Whittle Estimation In Long Memory Time Series With Multiple Poles," Econometric Theory, Cambridge University Press, vol. 36(6), pages 1064-1098, December.
    13. Henry L. Gray & Nien‐Fan Zhang & Wayne A. Woodward, 1989. "On Generalized Fractional Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 10(3), pages 233-257, May.
    14. Gregoir, Stéphane, 2010. "Fully Modified Estimation Of Seasonally Cointegrated Processes," Econometric Theory, Cambridge University Press, vol. 26(5), pages 1491-1528, October.
    15. Uwe Hassler, 2013. "Effect of temporal aggregation on multiple time series in the frequency domain," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(5), pages 562-573, September.
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    Cited by:

    1. del Barrio Castro, Tomás & Osborn, Denise R., 2023. "Periodic Integration and Seasonal Unit Roots," MPRA Paper 117935, University Library of Munich, Germany, revised 2023.

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    More about this item

    Keywords

    Aggregation; cumulation sampling; skip sampling; seasonal long memory.;
    All these keywords.

    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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