We investigate the problem of discovering and forecasting regular regime switches in a financial ecosystem comprising multiple time series. Such regime switches, indicative of varying market behaviors across distinct time intervals, are pivotal for a nuanced understanding of market dynamics, which in turn allows informed model selection for forecasting and enhanced interpretability of predictive outcomes. Despite strides in this domain, prevailing methodologies often falter due to: (1) an inability to effectively model the temporal behaviors inherent in financial series; and (2) neglecting the interdependencies among series when discovering regimes. In this paper, we propose RHINE, a Regime-switcHIng model with Nonlinear rEpresentation. RHINE stands out with its kernel-based representation, adept at capturing the dynamic shifts in market regimes. This representation encapsulates the nonlinear interplay across multiple financial time series. By leveraging the kernel representation, we introduce an eigengap thresholding measure, designed to automatically discern the optimal number of financial market regimes, enhancing the model's adaptability to market fluctuations. Empirical assessments on both synthetic and real-world stock market datasets underscore RHINE's prowess. The findings illuminate that the inherent structures governing financial market behaviors are dynamic, and harnessing these dynamics via RHINE leads to a regime-based model that outperforms both conventional and state-of-the-art neural network models in predictive capabilities.

These days, complex systems yield copious time series data, necessitating understanding co-generation, often assessed through pairwise comparisons. However, this method lacks scalability and temporal dynamics handling. In this paper, we advocate using a temporal graph to capture contiguous effects among multiple time series efficiently. Our two-step approach identifies patterns and temporal influences with low execution time, showcasing its potential in financial system incident prediction.

We investigate issues related to dynamic cross-sectional regime identification for financial market prediction. A financial market can be viewed as an ecosystem regulated by regimes that may switch at different time points. In most existing regime-based prediction models, regimes can only switch, according to a static transition probability matrix, among a fixed set of regimes identified on training data due to the fact that they lack in mechanism of identifying new regimes on test data. This prevents them from being effective as the financial markets are time-evolving and may fall into a new regime at any future time. Moreover, most of them only handle single time series, and are not capable of dealing with multiple time series. These shortcomings prompted us to devise a dynamic cross-sectional regime identification model for time series prediction. The new model is defined on a multi-time-series system, with time-varying transition probabilities, and can identify new cross-sectional regimes dynamically from the time-evolving financial market. Experimental results on real-world financial datasets illustrate the promising performance and suitability of our model.

The identification and prediction of complex behaviors in time series are fundamental problems of interest in the field of financial data analysis. Autoregressive (AR) model and Regime switching (RS) models have been used successfully to study the behaviors of financial time series. However, conventional RS models evaluate regimes by using a fixed-order Markov chain and underlying patterns in the data are not considered in their design. In this paper, we propose a novel RS model to identify and predict regimes based on a weighted conditional probability distribution (WCPD) framework capable of discovering and exploiting the significant underlying patterns in time series. Experimental results on stock market data, with 200 stocks, suggest that the structures underlying the financial market behaviors exhibit different dynamics and can be leveraged to better define regimes with superior prediction capabilities than traditional models.