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
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.
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Research supported by DAAD (German Academic Exchange Service) grant A/01/26875.
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Dehling, H., Sharipov, O.S. Estimation of Mean and Covariance Operator for Banach Space Valued Autoregressive Processes with Dependent Innovations. Stat Infer Stoch Process 8, 137–149 (2005). https://doi.org/10.1007/s11203-003-0382-8
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DOI: https://doi.org/10.1007/s11203-003-0382-8