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

Area of Science:

• Physics
• Econometrics
• Data Science

Background:

• Conventional single-layer linear response models (SLRM) have limitations in capturing complex dynamics.
• Anomalous dynamics, characterized by extreme fluctuations and heavy tails, are prevalent in various fields, including finance.
• The need for interpretable models that can generate realistic anomalous data is critical.

Purpose of the Study:

• To propose a multilayer linear response model (MLRM) capable of generating time-series data exhibiting anomalous dynamics.
• To extend the capabilities of traditional linear response theory to encompass nonlinear interactions.
• To demonstrate the MLRM's applicability in reproducing real-world phenomena, such as those observed during the COVID-19 pandemic.

Main Methods:

• Development of a multilayer linear response model (MLRM) by extending the single-layer linear response model (SLRM).
• Introduction of nonlinear interactions within the MLRM framework.
• Application of the MLRM to generate time-series data using pre-pandemic financial data.
• Analysis of log returns and realized volatility from MLRM-generated data.

Main Results:

• The MLRM successfully generated time-series data with anomalous dynamics.
• Log returns and realized volatility from MLRM-generated data exhibited heavy-tailed characteristics, consistent with empirical observations.
• The model demonstrated an ability to reproduce extreme fluctuations and tail behavior characteristic of high-volatility periods.

Conclusions:

• The proposed MLRM is an effective tool for generating interpretable time-series data with anomalous dynamics.
• The MLRM provides a valuable framework for studying complex systems in fields like finance without relying on machine learning.
• The model's ability to capture heavy-tailed distributions and extreme events offers insights into financial market behavior during crises.