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Limit theorems for bifurcating integer-valued autoregressive processes

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  • Bernard Bercu
  • Vassili Blandin

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

Suggested Citation

  • Bernard Bercu & Vassili Blandin, 2015. "Limit theorems for bifurcating integer-valued autoregressive processes," Statistical Inference for Stochastic Processes, Springer, vol. 18(1), pages 33-67, April.
    • Handle: RePEc:spr:sistpr:v:18:y:2015:i:1:p:33-67
    DOI: 10.1007/s11203-014-9105-6
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    References listed on IDEAS

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    4. Zhou, J. & Basawa, I.V., 2005. "Least-squares estimation for bifurcating autoregressive processes," Statistics & Probability Letters, Elsevier, vol. 74(1), pages 77-88, August.
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    6. J. Zhou & I. V. Basawa, 2005. "Maximum Likelihood Estimation for a First‐Order Bifurcating Autoregressive Process with Exponential Errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(6), pages 825-842, November.
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