37,602 research outputs found
Long-memory process and aggregation of AR(1) stochastic processes: A new characterization
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
Asymptotic results for random coefficient bifurcating autoregressive processes
The purpose of this paper is to study the asymptotic behavior of the weighted
least square estimators of the unknown parameters of random coefficient
bifurcating autoregressive processes. Under suitable assumptions on the
immigration and the inheritance, we establish the almost sure convergence of
our estimators, as well as a quadratic strong law and central limit theorems.
Our study mostly relies on limit theorems for vector-valued martingales.Comment: arXiv admin note: substantial text overlap with arXiv:1202.0470; and
text overlap with 0807.0528 by other author
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