Asymptotic analysis for bifurcating autoregressive processes via a martingale approach

被引：24

作者：

Bercu, Bernard ^{[1
,2
]}

de Saporta, Benoite ^{[1
,2
]}

Gegout-Petit, Anne ^{[2
]}

机构：

[1] Univ Bordeaux, IMB, CNRS, GREThA,UMR 5113,UMR 5251, Bordeaux, France

[2] INRIA Bordeaux, Team CQFD, Bordeaux, France

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2009年 / 14卷

关键词：

bifurcating autoregressive process; tree-indexed times series; martingales; least squares estimation; almost sure convergence; quadratic strong law; central limit theorem; MODELS;

D O I：

10.1214/EJP.v14-717

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.

引用

页码：2492 / 2526

页数：35

共 50 条

[41] A MARTINGALE APPROACH TO THE PROBLEM OF DIMENSIONALITY AND PERFORMANCE OF BAYESIAN CLASSIFIERS - ASYMPTOTIC RESULTS
KOKOLAKIS, GE
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 1985, 14 (04) : 927 - 935
[42] ASYMPTOTIC-BEHAVIOR OF NEYMAN-PEARSON TESTS FOR AUTOREGRESSIVE PROCESSES
LUSCHGY, H
SCANDINAVIAN JOURNAL OF STATISTICS, 1994, 21 (04) : 461 - 473
[43] On Asymptotic Normality of Sequential LS-Estimates of Unstable Autoregressive Processes
Galtchouk, L.
Konev, V.
SEQUENTIAL ANALYSIS-DESIGN METHODS AND APPLICATIONS, 2011, 30 (02): : 117 - 144
[44] THE ASYMPTOTIC DISTRIBUTION OF SERIAL CORRELATION COEFFICIENTS FOR AUTOREGRESSIVE PROCESSES WITH DEPENDENT RESIDUALS
WALKER, AM
PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1954, 50 (01): : 60 - 64
[45] ASYMPTOTIC CONDITIONAL INFERENCE FOR REGULAR NONERGODIC MODELS WITH AN APPLICATION TO AUTOREGRESSIVE PROCESSES
BASAWA, IV
BROCKWELL, PJ
ANNALS OF STATISTICS, 1984, 12 (01): : 161 - 171
[46] Asymptotic inference for dynamic panel estimators of infinite order autoregressive processes
Lee, Yoon-Jin
Okui, Ryo
Shintani, Mototsugu
JOURNAL OF ECONOMETRICS, 2018, 204 (02) : 147 - 158
[47] The local asymptotic normality of a class of generalized random coefficient autoregressive processes
Hwang, SY
Basawa, IV
STATISTICS & PROBABILITY LETTERS, 1997, 34 (02) : 165 - 170
[48] Analytical solutions for stochastic differential equations via Martingale processes
Farnoosh, Rahman
Rezazadeh, Hamidreza
Sobhani, Amirhossein
Behboudi, Maryam
MATHEMATICAL SCIENCES, 2015, 9 (02) : 87 - 92
[49] A unified approach to asymptotic behaviors for the autoregressive model with fuzzy data
Jung, Hye Young
Lee, Woo Joo
Yoon, Jin Hee
INFORMATION SCIENCES, 2014, 257 : 127 - 137
[50] Detrended fluctuation analysis of autoregressive processes
Morariu, Vasile V.
Buimaga-Iarinca, Luiza
Vamos, Calin
Soltuz, Stefan M.
FLUCTUATION AND NOISE LETTERS, 2007, 7 (03): : L249 - L255

← 1 2 3 4 5 →