Limit theorems for bifurcating integer-valued autoregressive processes

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.
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Bernard Bercu, Vassili Blandin. Limit theorems for bifurcating integer-valued autoregressive processes. Statistical Inference for Stochastic Processes, Springer Verlag, 2014, 17, pp.1-37. ⟨hal-01023462⟩

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