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.
Cite
@article{arxiv.1506.07446,
title = {Long-memory process and aggregation of AR(1) stochastic processes: A new characterization},
author = {Bernard Candelpergher and Michel Miniconi and Florian Pelgrin},
journal= {arXiv preprint arXiv:1506.07446},
year = {2015}
}