Complex statistical signatures of stock markets: Scaling laws, multifractality, temporal recurrence networks of price and the Ising model

Author

Jude Maria V. Antenorcruz, De La Salle University, ManilaFollow

Date of Publication

1-2025

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Physics

Subject Categories

Physics

College

College of Science

Department/Unit

Physics

Defense Panel Member

Maria Carla Manzano
Romeric Pobre
Johnrob Bantang

Abstract/Summary

Financial markets, such as stock markets, are good representative examples of complex systems because they are composed of a large number of agents interacting in a non-linear manner. As such, there has now been a paradigm shift towards the treatment of stock markets as complex systems. A defining feature of complex systems is emergence, presenting themselves as statistical signatures in the macroscopic scale. In financial markets, this is observed in the main stylized facts: fat-tails in the distribution of large returns, volatility clustering, absence of autocorrelation in daily returns, and multifractality. Using log-returns data on sixteen global market indices over varying time scales, we verify the main stylized facts and found empirical results consistent with previous works. In addition to the main stylized facts, this work has uncovered nearly-universal statistical properties in financial markets from the perspective of the theory of records and complex networks. By creating a temporally directed network of prices using global stock market data, we recover robust power-law statistics in the distribution of records and link separation times, and find Poisson statistics in the in- and out-degree link distributions, quantifying a high level of activity in financial markets, i.e., price recurrences are retrieved over fewer connections than that of completely random sequences. These empirical facts are benchmarks of complex and agent-based financial market models. As such, valid models must be able to retrieve the main stylized facts. In this work, we demonstrate that the self-organizing Ising model is one such model capable of replicating the empirical stylized facts. We generate synthetic return series over a broad set of model parameters (b_max, σ_max,CV) and identified b_max ∈ [0.2,03], σ_max ∈ [0.15,0.45] and CV = 0.50 as the range of parameters that retrieve the main stylized facts with a minimal degree of multifractality. These simulated findings imply that agents in stock markets tend to follow the external news, conform with neighborhood trends, and that agents are neither too timid or too bold in introducing idiosyncratic actions when making decisions.

Abstract Format

html

Language

English

Format

Electronic

Keywords

Stock exchanges—Mathematical models; Fractals; Ising model

Recommended Citation

Antenorcruz, J. V. (2025). Complex statistical signatures of stock markets: Scaling laws, multifractality, temporal recurrence networks of price and the Ising model. Retrieved from https://animorepository.dlsu.edu.ph/etdd_physics/8

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Embargo Period

4-7-2026