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Preprints, Working Papers, ... Year : 2015

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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Dates and versions

hal-01166527 , version 1 (23-06-2015)
hal-01166527 , version 2 (07-08-2015)

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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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