## Asymptotic analysis for bifurcating autoregressive processes via a martingale approach.(English)Zbl 1190.60019

Summary: We study the asymptotic behavior of the least squares estimators of the unknown parameters of general $$p$$th-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.

### MSC:

 60F15 Strong limit theorems 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 60G42 Martingales with discrete parameter 62F12 Asymptotic properties of parametric estimators
Full Text: