Asymptotic analysis for bifurcating autoregressive processes via a martingale approach
Probability
2009-06-29 v2 Statistics Theory
Statistics Theory
Abstract
We study the asymptotic behavior of the least squares estimators of the unknown parameters of 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.
Cite
@article{arxiv.0807.0528,
title = {Asymptotic analysis for bifurcating autoregressive processes via a martingale approach},
author = {Bernard Bercu and Benoite de Saporta and Anne Gegout-Petit},
journal= {arXiv preprint arXiv:0807.0528},
year = {2009}
}