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

Bernard Candelpergher (), Michel Miniconi () and Florian Pelgrin ()
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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)

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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.

Keywords: Aggregation; Autoregressive process; Heterogeneity; Complex variable analysis (search for similar items in EconPapers)
Date: 2015-08-07
New Economics Papers: this item is included in nep-ets
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