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Long Memory Through Marginalization of Large Systems and Hidden Cross-Section Dependence

Author

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  • Guillaume Chevillon

    (ESSEC Business School, CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - CNRS - Centre National de la Recherche Scientifique)

  • Alain Hecq

    (Department of Quantitative Economics [Maastricht] - Maastricht University [Maastricht])

  • Sébastien Laurent

    (AMU IAE - Institut d'Administration des Entreprises (IAE) - Aix-en-Provence - AMU - Aix Marseille Université)

Abstract

This paper shows that large dimensional vector autoregressive (VAR) models of fi nite order can generate long memory in the marginalized univariate series. We derive high-level assumptions under which the fi nal equation representation of a VAR(1) leads to univariate fractional white noises and verify the validity of these assumptions for two speci fic models. We consider the implications of our findings for the variances of asset returns where the so-called golden-rule of realized variances states that they tend always to exhibit fractional integration of a degree close to 0:4.

Suggested Citation

  • Guillaume Chevillon & Alain Hecq & Sébastien Laurent, 2015. "Long Memory Through Marginalization of Large Systems and Hidden Cross-Section Dependence," Working Papers hal-01158524, HAL.
    • Handle: RePEc:hal:wpaper:hal-01158524
    Note: View the original document on HAL open archive server: https://essec.hal.science/hal-01158524
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    References listed on IDEAS

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    Cited by:

    1. Hecq Alain & Laurent Sébastien & Palm Franz C., 2016. "On the Univariate Representation of BEKK Models with Common Factors," Journal of Time Series Econometrics, De Gruyter, vol. 8(2), pages 91-113, July.
    2. Chevillon, Guillaume & Mavroeidis, Sophocles, 2017. "Learning can generate long memory," Journal of Econometrics, Elsevier, vol. 198(1), pages 1-9.

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    More about this item

    Keywords

    Long memory; Vector Autoregressive Model; Marginalization; Final Equation Representation; Volatility;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • 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
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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