The Hidden Constant of Market Rhythms: How 1−1/e Defines Scaling in Intrinsic Time

Battle Count: 71

The paper provides a theoretically grounded heuristic (the 1-1/e constant) for identifying the appropriate threshold range in multi-scale DcOS analyses, which is directly applicable to algorithmic trading systems using Intrinsic Time. It helps practitioners avoid ad hoc threshold selection and provides a diagnostic for detecting when market dynamics deviate from memoryless behavior (e.g., trending vs. choppy regimes). However, it is primarily a theoretical/empirical characterization paper rather than a direct trading strategy paper. The scaling exponent β≈-1.91 and the stable Dc share provide quantitative anchors for model calibration in trading systems.

The core methodology (DcOS event extraction, threshold scanning, statistical tests) is implemented in the open-source IntrinsicTime Python package, making practical implementation straightforward. The theoretical framework (renewal processes, exponential hazard, geometric distributions) requires graduate-level probability theory understanding. The statistical diagnostics (chi-squared, KS tests, log-log regression) are standard. The main complexity lies in interpreting results across the full threshold range and understanding the renormalized hazard rate interpretation.

The paper provides a publicly available Python package (IntrinsicTime v1.3) on both PyPI and GitHub (github.com/THouwe/IntrinsicTime). All analyses are reproducible using the dcos core, dcos fractal, and dcos tests modules. Datasets are standard 1-second sampled cryptocurrency midprice data from public exchanges. Full supplementary tables with all numerical results are provided.