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Updated: Oct 11, 2025

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Linear response theory in stock markets.

Antonio M Puertas1, Juan E Trinidad-Segovia2, Miguel A Sánchez-Granero3

  • 1Departamento de Química y Física, Universidad de Almería, 04.120, Almería, Spain. apuertas@ual.es.

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|November 30, 2021
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Summary

Linear response theory successfully predicts stock price and return dynamics after critical events. However, it does not fully capture volatility changes, indicating phenomena beyond linear response in financial markets.

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Area of Science:

  • * Physics
  • * Financial Markets
  • * Complex Systems

Background:

  • * Linear response theory connects system response to external forces with equilibrium dynamics and fluctuations.
  • * Applying this theory to financial markets requires adapting the concept of external forces.
  • * Critical events in stock prices are used as proxies for these forces.

Purpose of the Study:

  • * To apply linear response theory to analyze stock market dynamics.
  • * To identify critical events as external forces and study subsequent stock behavior.
  • * To define and observe the relaxation of perturbation energy in a stock system.

Main Methods:

  • * Analysis of NASDAQ stock price data over 20 years.
  • * Identification of critical events as sudden changes in stock prices.
  • * Application of linear response theory using log-return as the conjugate variable.
  • * Definition and observation of perturbation energy.

Main Results:

  • * Linear response theory accurately predicts average stock price and return responses post-event.
  • * The theory's predictions align with observed market behavior.
  • * Volatility changes are not adequately described, suggesting limitations beyond linear response.
  • * Perturbation energy was defined and its relaxation after events was observed.

Conclusions:

  • * Linear response theory provides a valuable framework for understanding average stock market responses to critical events.
  • * The study highlights the limitations of linear response theory in explaining market volatility.
  • * Identifying conjugate variables is crucial for defining and analyzing system perturbations in financial markets.