Determinace přítomnosti deterministického chaosu ve finančních časových řadách

This study examines the presence of deterministic chaos in the hourly logarithmic returns of seven cryptocurrency assets (BTC, ETH, XRP, LTC, LINK, DOGE, and ADA) during the period from May 2025 to May 2026. The main research hypothesis is the assumption that the estimated nonlinear invariants are sensitive to the temporal arrangement of the series, which implies the presence of a deterministic structure. The analysis utilizes estimates of the correlation dimension, the largest Lyapunov exponent, and recurrent quantification analysis (RQA). The statistical significance of the invariants is verified by testing on three types of surrogate data (random permutation, normal distribution, Student’s t-distribution with 3.5 degrees of freedom). The study presents three main findings. First, the logarithmic returns of cryptocurrency pairs exhibit a demonstrable nonlinear structure that cannot be explained by a random or linear process with heavy tails. Second, the existence of a low-dimensional chaotic attractor is not robustly demonstrated across assets; the conclusions depend heavily on the chosen methodology. Third, RQA provides the most consistent evidence of deterministic patterns. The results suggest a certain presence of a deterministic component in the dynamics of cryptocurrency markets; however, its unambiguous classification as low-dimensional chaos remains an open question.