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The Mathematical Model of Cyclic Signals in Dynamic Systems as a Cyclically Correlated Random Process

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  • Serhii Lupenko

    (Faculty of Electrical Engineering, Automatic Control and Informatics of Opole University of Technology, 45-758 Opole, Poland)

Abstract

This work is devoted to the procedure for constructing of a cyclically correlated random process of a continuous argument as a mathematical model of cyclic signals in dynamic systems, which makes it possible to consistently describe cyclic stochastic signals, both with regular and irregular rhythms, not separating them, but complementing them within the framework of a single integrated model. The class of cyclically correlated random processes includes the subclass of cyclostationary (periodically) correlated random processes, which enable the use of a set of powerful methods of analysis and the forecasting of cyclic signals with a stable rhythm. Mathematical structures that model the cyclic, phase and rhythmic structures of a cyclically correlated random process are presented. The sufficient and necessary conditions that the structural function and the rhythm function of the cyclically correlated random process must satisfy have been established. The advantages of the cyclically correlated random process in comparison with other mathematical models of cyclic signals with a variable rhythm are given. The obtained results contribute to the emergence of a more complete and rigorous theory of this class of random processes and increase the validity of the methods of their analysis and computer simulation.

Suggested Citation

  • Serhii Lupenko, 2022. "The Mathematical Model of Cyclic Signals in Dynamic Systems as a Cyclically Correlated Random Process," Mathematics, MDPI, vol. 10(18), pages 1-27, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:18:p:3406-:d:919021
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    References listed on IDEAS

    as
    1. Eric Ghysels, 1993. "A time series model with periodic stochastic regime switching," Discussion Paper / Institute for Empirical Macroeconomics 84, Federal Reserve Bank of Minneapolis.
    2. Ghysels, Eric, 1994. "On the Periodic Structure of the Business Cycle," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 289-298, July.
    3. Peter Bloomfield & Harry L. Hurd & Robert B. Lund, 1994. "Periodic Correlation In Stratospheric Ozone Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(2), pages 127-150, March.
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