arXiv subjects

Samuel W. Akingbade

Publications and source records attributed to Samuel W. Akingbade.

3 recordsLinked to original sources

arXiv2026

Null-Validated Topological Signatures of Financial Market Dynamics

Financial markets exhibit temporal organization that is not fully captured by volatility measures or linear correlation structure. We study a null-validated topological approach for quantifying financial market complexity using Bitcoin daily log returns and the S&P 500 index as examples of cryptocurrency and broad U.S. equity market dynamics. The analysis uses the $L^1$ norm of the persistence landscapes computed from sliding-window delay embeddings. This quantity co-moves strongly with stochastic volatility during periods of market stress, but the strength and form of this relationship vary over time and differ between the two markets. Surrogate-based null models provide statistical validation of these observations. Rejection of shuffle surrogates rules out explanations based on marginal distributions alone, while departures from phase randomized surrogates indicate sensitivity to nonlinear and phase-dependent temporal organization beyond linear correlations. These results demonstrate that persistence landscape norms provide complementary information about market dynamics across market conditions.

q-fin.ST↗

arXiv2023

Why Topological Data Analysis Detects Financial Bubbles?

We present a heuristic argument for the propensity of Topological Data Analysis (TDA) to detect early warning signals of critical transitions in financial time series. Our argument is based on the Log-Periodic Power Law Singularity (LPPLS) model, which characterizes financial bubbles as super-exponential growth (or decay) of an asset price superimposed with oscillations increasing in frequency and decreasing in amplitude when approaching a critical transition (tipping point). We show that whenever the LPPLS model is fitting with the data, TDA generates early warning signals. As an application, we illustrate this approach on a sample of positive and negative bubbles in the Bitcoin historical price.

q-fin.ST↗

arXiv2023

Arnold diffusion in a model of dissipative system

For a mechanical system consisting of a rotator and a pendulum coupled via a small, time-periodic Hamiltonian perturbation, the Arnold diffusion problem asserts the existence of `diffusing orbits' along which the energy of the rotator grows by an amount independent of the size of the coupling parameter, for all sufficiently small values of the coupling parameter. There is a vast literature on establishing Arnold diffusion for such systems. In this work, we consider the case when an additional, dissipative perturbation is added to the rotator-pendulum system with coupling. Therefore, the system obtained is not symplectic but conformally symplectic. We provide explicit conditions on the dissipation parameter, so that the resulting system still exhibits energy growth. The fact that Arnold diffusion may play a role in systems with small dissipation was conjectured by Chirikov. In this work, the coupling is carefully chosen, however the mechanism we present can be adapted to general couplings and we will deal with the general case in future work.

math.DS↗