Estimation of Mean and Covariance Operator for Banach Space Valued Autoregressive Processes with Dependent Innovations期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Estimation of Mean and Covariance Operator for Banach Space Valued Autoregressive Processes with Dependent Innovations

Authors:

Herold?Dehling author-information" > author-information__contact u-icon-before" > mailto:herold.dehling@rub.de" title=" herold.dehling@rub.de" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author,Olimjon?SH.?Sharipov

Affiliation:

1.Fakult?t für Mathematik,Ruhr-Universit?t Bochum,Bochum,Germany;2.Department of Probability Theory, Institute of Mathematics,Uzbek Academy of Sciences,Tashkent,Uzbekistan

Abstract:

In this paper we study autoregressive processes of order 1 with values in a separable Banach space it B. Such ARB(1)-processes ${(X_{n})}_{n in mathbb{Z}}$ are defined by the recursion equation

$X_n - m = T(x_{n-1}-m) + epsilon_n, n in mathbb{Z}$

where T : B → B is a bounded linear operator and m ∈ B. We analyze the asymptotic properties of the sample mean and of the sample covariance operator in case that the innovation process ${(epsilon_{n})}_{n in mathbb{Z}}$ is weakly dependent. This extends earlier results of Bosq (2000, 2002), who studied ARB(1)-processes with independent and orthogonal observations. Research supported by DAAD (German Academic Exchange Service) grant A/01/26875.

Keywords:

mixing conditions autoregressive process Banach space sample mean empirical covariance

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