Asymptotic Analysis for Bifurcating AutoRegressive Processes via a Martingale Approach | Zendy

Bernard Bercu | Zendy; Benoîte de Saporta | Zendy; Anne GégoutPetit | Zendy

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Asymptotic Analysis for Bifurcating AutoRegressive Processes via a Martingale Approach

Author(s) -

Bernard Bercu,

Benoîte de Saporta,

Anne GégoutPetit

Publication year - 2009

Publication title -

electronic journal of probability

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.666

H-Index - 53

ISSN - 1083-6489

DOI - 10.1214/ejp.v14-717

Subject(s) - mathematics , autoregressive model , martingale (probability theory) , estimator , central limit theorem , martingale difference sequence , setar , weak convergence , convergence of random variables , asymptotic analysis , law of large numbers , quadratic equation , moment (physics) , quadratic variation , mathematical analysis , star model , econometrics , statistics , autoregressive integrated moving average , random variable , time series , brownian motion , asset (computer security) , geometry , computer security , computer science , physics , classical mechanics

We study the asymptotic behavior of the least squares estimators of the unknown parameters of general pth-order bifurcating autoregressive processes. Under very weak assumptions on the driven noise of the process, namely conditional pair-wise independence and suitable moment conditions, we establish the almost sure convergence of our estimators together with the quadratic strong law and the central limit theorem. All our analysis relies on non-standard asymptotic results for martingales.

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