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Article Dans Une Revue New Mathematics and Natural Computation Année : 2021

S-ARMA model and Wold decomposition for covariance stationary interval-valued time series processes

Résumé

The main purpose of this work is to contribute to the study of set-valued random variables by providing a kind of Wold decomposition theorem for interval-valued processes. As the set of set-valued random variables is not a vector space, the Wold decomposition theorem as established in 1938 by Herman Wold is not applicable for them. So, a notion of pseudovector space is introduced and used to establish a generalization of the Wold decomposition theorem that works for interval-valued covariance stationary time series processes. Before this, set-valued autoregressive moving-average (S-ARMA) time series process is defined by taking into account an arithmetical difference between random sets and random real variables.
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Dates et versions

hal-02901595 , version 1 (17-07-2020)

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Jules Sadefo-Kamdem, Babel Raïssa Guemdjo Kamdem, Carlos Ougouyandjou. S-ARMA model and Wold decomposition for covariance stationary interval-valued time series processes. New Mathematics and Natural Computation, 2021, 17 (1), pp.191-213. ⟨10.1142/S1793005721500101⟩. ⟨hal-02901595⟩
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