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A \(\text{LARCH}(\infty)\) vector valued process. (English) Zbl 1113.60038

Bertail, Patrice (ed.) et al., Dependence in probability and statistics. New York, NY: Springer (ISBN 0-387-31741-4/pbk). Lecture Notes in Statistics 187, 245-258 (2006).
The purpose of this paper is to propose a unified framework for the study of \(\text{ARCH}(\infty)\) processes that are commonly used in the financial econometrics. The extension of the univariate \(\text{ARCH}(\infty)\) processes to the multidimensional case based in Volterra expansions is proposed. Existence and uniqueness in \(L^p\) sense is studied. Coupling, Markovian approximation and weak dependence conditions are discussed.
For the entire collection see [Zbl 1092.60002].

MSC:

60G10 Stationary stochastic processes
60F05 Central limit and other weak theorems
60G12 General second-order stochastic processes
60G25 Prediction theory (aspects of stochastic processes)
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