1. Although I am quite familiar with regime-switching, identification, and financial markets, the logical structure of this paper is challenging to follow. The introduction directly presents model definitions and the authors’ proposed improvements without first providing an overview of related work, the motivation, or the current state of research. This structure makes it difficult for readers to understand the unique contributions of this work and distinguish them from existing models. A clearer, more organized flow would greatly enhance readability and clarify the authors’ contributions.
2. The paper lacks a detailed motivation explaining why Regularised K-means, specifically, is optimal for adapting into the Jump Model framework. A comparison of Regularised K-means with alternative approaches could clarify why it is most suitable in this context.
3. The paper briefly mentions Hidden Markov Models (HMM) and other regime-switching models but does not provide a thorough comparison, such as the latest model - RHINE: A Regime-Switching Model with Nonlinear Representation for Discovering and Forecasting Regimes in Financial Markets (SIAM SDM2024). Besides, although feature selection is central to the model, there is limited discussion on alternative feature selection methods in time series analysis.
4. The formulas (such as those in Eq. 1.6) lack detailed explanations for how each component, including the penalty terms $ P(\mu) $, specifically enhances feature selection and regime accuracy.
5. The experimental part does not demonstrate how regime identification or interpretability is achieved. Additionally, there are no actual experimental results presented in the main text, yet the pseudo-code of the algorithms takes up several pages.
6. Appendix A is left blank, and the purpose of Proposition B.1 in Appendix B is unclear—is it merely meant to illustrate the classic partitioning principle of K-means? This is a well-known concept in machine learning, and furthermore, the authors’ so-called “proof” is missing.
6. Appendix A is left blank, and the purpose of Proposition B.1 in Appendix B is unclear—is it merely meant to illustrate the classic partitioning principle of K-means? This is a well-known concept in machine learning, and furthermore, the authors’ so-called “proof” is missing.