S-ARMA Model and Wold Decomposition for Covariance Stationary Interval-Valued Time Series Processes

Jules Sadefo Kamdem, Babel Raïssa Guemdjo Kamdem and Carlos Ougouyandjou
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Babel Raïssa Guemdjo Kamdem: #x2020;Institut de Mathématiques et de Sicence Physique, UAC, Dangbo, Benin
Carlos Ougouyandjou: Université de Montpellier (MRE EA 7491), Montpellier, France

New Mathematics and Natural Computation (NMNC), 2021, vol. 17, issue 01, 191-213

Abstract: 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.

Keywords: Wold decomposition; stationary time series; interval-valued time series processes; ARMA model (search for similar items in EconPapers)
Date: 2021
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Working Paper: S-ARMA model and Wold decomposition for covariance stationary interval-valued time series processes (2021)
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DOI: 10.1142/S1793005721500101

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