Doukhan, Paul; Teyssière, Gilles; Winant, Pablo 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]. Reviewer: Nikolai N. Leonenko (Cardiff) Cited in 9 Documents 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) Keywords:\(\text{ARCH}(\infty)\) processes; \(\text{LARCH}(\infty)\) processes; vector processes; Volterra expansions; weak dependence PDFBibTeX XMLCite \textit{P. Doukhan} et al., Lect. Notes Stat. 187, 245--258 (2006; Zbl 1113.60038) Full Text: DOI