Limit theorems for bifurcating integer-valued autoregressive processes

Bernard Bercu () and Vassili Blandin ()

Statistical Inference for Stochastic Processes, 2015, vol. 18, issue 1, 33-67

Abstract: We study the asymptotic behavior of the weighted least squares estimators of the unknown parameters of bifurcating integer-valued autoregressive processes. Under suitable assumptions on the immigration, we establish the almost sure convergence of our estimators, together with a quadratic strong law and central limit theorems. All our investigation relies on asymptotic results for vector-valued martingales. Copyright Springer Science+Business Media Dordrecht 2015

Keywords: Bifurcating autoregressive process; Integer-valued process; Weighted least squares; Martingale; Almost sure convergence; Central limit theorem; Primary 60F15; Secondary 60F05; 60G42 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s11203-014-9105-6

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