Deviation inequalities and moderate deviations for estimators of parameters in bifurcating autoregressive models

Abstract

The purpose of this paper is to investigate the deviation inequalities and the moderate deviation principle of the least squares estimators of the unknown parameters of general pth-order asymmetric bifurcating autoregressive processes, under suitable assumptions on the driven noise of the process. Our investigation relies on the moderate deviation principle for martingales. © Association des Publications de l'Institut Henri Poincaré, 2014.