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Long-memory process and aggregation of AR(1) stochastic processes: A new characterization

Author

Listed:
  • Bernard Candelpergher

    (LJAD - Laboratoire Jean Alexandre Dieudonné - UNS - Université Nice Sophia Antipolis (1965 - 2019) - CNRS - Centre National de la Recherche Scientifique - UniCA - Université Côte d'Azur)

  • Michel Miniconi

    (JAD - Laboratoire Jean Alexandre Dieudonné - UNS - Université Nice Sophia Antipolis (1965 - 2019) - CNRS - Centre National de la Recherche Scientifique)

  • Florian Pelgrin

    (HEC Lausanne - Faculté des Hautes Etudes Commerciales (HEC Lausanne))

Abstract
Contemporaneous aggregation of individual AR(1) random processes might lead to different properties of the limit aggregated time series, in particular, long memory (Granger, 1980). We provide a new characterization of the series of autoregressive coefficients, which is defined from the Wold representation of the limit of the aggregate stochastic process, in the presence of long-memory features. Especially the infinite autoregressive stochastic process defined by the almost sure representation of the aggregate process has a unit root in the presence of the long-memory property. Finally we discuss some examples using some well-known probability density functions of the autoregressive random parameter in the aggregation literature. JEL Classification Code: C2, C13.

Suggested Citation

  • Bernard Candelpergher & Michel Miniconi & Florian Pelgrin, 2015. "Long-memory process and aggregation of AR(1) stochastic processes: A new characterization," Working Papers hal-01166527, HAL.
    • Handle: RePEc:hal:wpaper:hal-01166527
    Note: View the original document on HAL open archive server: https://hal.univ-cotedazur.fr/hal-01166527v2
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    File URL: https://hal.univ-cotedazur.fr/hal-01166527v2/document
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Aggregation; Autoregressive process; Heterogeneity; Complex variable analysis;
    All these keywords.

    JEL classification:

    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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