Modeling and Generating Extreme Fluctuations in Time Series with a Multilayer Linear Response Model

A multilayer linear response model (MLRM) is proposed to generate time-series data based on linear response theory. The proposed MLRM is designed to generate data for anomalous dynamics by extending the conventional single-layer linear response model (SLRM) into multiple layers. While the SLRM is a linear equation with respect to external forces, the MLRM introduces nonlinear interactions, enabling the generation of a wider range of dynamics. The MLRM is applicable to various fields, such as finance, as it does not rely on machine learning techniques and maintains interpretability. We investigated whether the MLRM could generate anomalous dynamics, such as those observed during the coronavirus disease 2019 (COVID-19) pandemic, using pre-pandemic data. Furthermore, an analysis of the log returns and realized volatility derived from the MLRM-generated data demonstrated that both exhibited heavy-tailed characteristics, consistent with empirical observations. These results indicate that the MLRM can effectively reproduce the extreme fluctuations and tail behavior seen during high-volatility periods.