Random coefficients bifurcating autoregressive processes. (3rd October 2014)

• Record Type: Journal Article
• Authors: Saporta, Benoîte de; Gégout-Petit, Anne; Marsalle, Laurence
• Is Part Of: ESAIM. Volume 18(2014)
• Page Start: 365
• Page End: 399
• Publication Date: 2014-10-03
• Subjects: Autoregressive process, -- branching process, -- missing data, -- least squares estimation, -- limit theorems, -- bifurcating Markov chain, -- martingale; Probabilities -- Periodicals; Mathematical statistics -- Periodicals; 519.2
• DOI: 10.1051/ps/2013042
• Languages: English
• ISSNs: 1292-8100

Abstract

Abstract : This paper presents a new model of asymmetric bifurcating autoregressive process with random coefficients. We couple this model with a Galton−Watson tree to take into account possibly missing observations. We propose least-squares estimators for the various parameters of the model and prove their consistency, with a convergence rate, and asymptotic normality. We use both the bifurcating Markov chain and martingale approaches and derive new results in both these frameworks.