Implementation of potentials of unbalanced complex kinetics model with particle filter in detecting critical transition in financial market time series

Abstract

As a complex system, a real financial market consists of many interacting agents that can be differentiated into buyers, sellers, and brokers. Each of them drives the market with their strategies, which are affected by various factors. However, sometimes these agents’ behavior may lead to an uncontrollable market price movement, which eventually leads to financial bubbles or crashes. These events, which can be regarded as a critical transition in analogy to statistical physics, may damage the economy, which has led researchers to develop techniques to quantify the financial risk and detect these abnormal market states. In 2006, Takayasu et al. introduced the Potentials of Unbalanced Complex Kinetics (PUCK) model, which is understood as a simple modification to the random walk theory by adding a potential force term that varies over time. This potential function reflects the state of the market participants, and its functional form can be estimated from the data. However, with the conventional PUCK model, we require at least 1,000 latest data points to obtain a reasonable estimate for the model parameters, which is too long for a real-time application. Hence, to achieve a more rapid estimation, the particle filter version of PUCK model was introduced by Yura et al., where Monte Carlo simulation is incorporated to the estimation. We observe that the particle filter simulation can detect the critical transition within roughly 50 time steps with an appropriate choice of simulation parameters. We also find out that the PUCK model replicates the actual situation in the market fairly well, especially at the times of financial bubbles and crashes, compared to a normal random walk model that has been used by analysts over the last century.