Tensorial products of functional ARMA processes

Denis Bosq

Journal of Multivariate Analysis, 2010, vol. 101, issue 6, 1352-1363

Abstract: We study the structure of tensorial products for the autoregressive and moving average processes (Xn), with values in a Hilbert space H and with innovations that are martingale differences. The obtained models are ARMA(H[circle times operator]H) processes, possibly non standard. We provide criteria for the standardness of these models, we specify the results in the real case, give some examples and consider some applications.

Keywords: Autoregressive; Hilbertian; processes; Hilbertian; moving; averages; Tensorial; products; Hilbert-Schmidt; operators; Standard; processes; Autocovariance; operators (search for similar items in EconPapers)
Date: 2010
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