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

2015/06/23 by Bernard Candelpergher, Candelpergher, Bernard, Michel Miniconi +3
Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #Complex Variables (math.CV) #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Statistics Theory (math.ST) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1506.07446

openalex publication_date 2015/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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