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

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.
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Contributor : Michel Miniconi <>
Submitted on : Friday, August 7, 2015 - 10:27:10 PM
Last modification on : Monday, October 12, 2020 - 2:28:05 PM
Long-term archiving on: : Wednesday, April 26, 2017 - 10:10:55 AM


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  • HAL Id : hal-01166527, version 2
  • ARXIV : 1506.07446



Bernard Candelpergher, Michel Miniconi, Florian Pelgrin. Long-memory process and aggregation of AR(1) stochastic processes: A new characterization. 2015. ⟨hal-01166527v2⟩



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