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Tensorial products of functional ARMA processes

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  • Bosq, Denis

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.

Suggested Citation

  • Bosq, Denis, 2010. "Tensorial products of functional ARMA processes," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1352-1363, July.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:6:p:1352-1363
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    References listed on IDEAS

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    1. In-Bong Choi & Masanobu Taniguchi, 2003. "Prediction Problems for Square-Transformed Stationary Processes," Statistical Inference for Stochastic Processes, Springer, vol. 6(1), pages 43-64, January.
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    Cited by:

    1. Ruiz-Medina, M.D., 2011. "Spatial autoregressive and moving average Hilbertian processes," Journal of Multivariate Analysis, Elsevier, vol. 102(2), pages 292-305, February.

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