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Asymptotic Analysis for Bifurcating AutoRegressive Processes via a Martingale Approach

   
@article{EJP717,
	author = {Bernard Bercu and Benoîte de Saporta and Anne Gégout-Petit},
	title = {Asymptotic Analysis for Bifurcating AutoRegressive Processes via a Martingale Approach},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {14},
	year = {2009},
	keywords = {bifurcating autoregressive process; tree-indexed times series; martingales; least squares estimation; almost sure convergence; quadratic strong law; central limit theorem},
	abstract = {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.},
	pages = {no. 87, 2492-2526},
	issn = {1083-6489},
	doi = {10.1214/EJP.v14-717},    
        url = {http://ejp.ejpecp.org/article/view/717}}