On the Cyclostationary Linear Inverse Models: A Mathematical Insight and Implication
<|reference_start|>On the Cyclostationary Linear Inverse Models: A Mathematical Insight and Implication: Cyclostationary linear inverse models (CS-LIMs), generalized versions of the classical (stationary) LIM, are advanced data-driven techniques for extracting the first-order time-dependent dynamics and random forcing relevant information from complex non-linear stochastic processes. Though CS-LIMs lead to a breakthrough in climate sciences, their mathematical background and properties are worth further exploration. This study focuses on the mathematical perspective of CS-LIMs and introduces two variants: e-CS-LIM and l-CS-LIM. The former refines the original CS-LIM using the interval-wise linear Markov approximation, while the latter serves as an analytic inverse model for the linear periodic stochastic systems. Although relying on approximation, e-CS-LIM converges to l-CS-LIM under specific conditions and shows noise-robust performance. Numerical experiments demonstrate that each CS-LIM reveals the temporal structure of the system. The e-CS-LIM optimizes the original model for better dynamics performance, while l-CS-LIM excels in diffusion estimation due to reduced approximation reliance. Moreover, CS-LIMs are applied to real-world ENSO data, yielding a consistent result aligning with observations and current ENSO understanding.<|reference_end|>
@article{lien2024on,
    title={On the Cyclostationary Linear Inverse Models: A Mathematical Insight and
  Implication},
    author={Justin Lien, Yan-Ning Kuo, Hiroyasu Ando},
    journal={arXiv preprint arXiv:2407.10931},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.10931},
    primaryClass={math.NA cs.NA}
}