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    Area of Science:

    • Statistics
    • Time Series Analysis
    • Nonlinear System Modeling

    Background:

    • Existing nonlinear time series models often lack flexibility.
    • A unified framework for diverse nonlinear models is needed.
    • Efficient parameter estimation for complex models is challenging.

    Purpose of the Study:

    • To propose a novel framework for nonlinear time series and system modeling.
    • To demonstrate the flexibility of the proposed framework in encompassing known models.
    • To develop an efficient parameter estimation algorithm for the new model.

    Main Methods:

    • Introduction of the basis function matrix-based flexible coefficient autoregressive (BFM-FCAR) model.
    • Investigation of probabilistic properties, including geometrical ergodicity.
    • Application of the variable projection method for efficient parameter estimation.

    Main Results:

    • The BFM-FCAR model offers a highly flexible nonlinear structure.
    • Many existing nonlinear time series models can be derived within this framework.
    • An efficient parameter estimation algorithm is presented, leveraging the model's structure.

    Conclusions:

    • The BFM-FCAR framework provides a unified and flexible approach to nonlinear time series modeling.
    • The proposed estimation method is efficient and practical.
    • The framework facilitates the generation of new nonlinear time series models.