Scaling Laws

The Hidden Constant of Market Rhythms: How $1-1/e$ Defines Scaling in Intrinsic Time ArXiv ID: 2511.14408 “View on arXiv” Authors: Thomas Houweling Abstract Directional-change Intrinsic Time analysis has long revealed scaling laws in market microstructure, but the origin of their stability remains elusive. This article presents evidence that Intrinsic Time can be modeled as a memoryless exponential hazard process. Empirically, the proportion of directional changes to total events stabilizes near $1 - 1/e = 0.632$, matching the probability that a Poisson process completes one mean interval. This constant provides a natural heuristic to identify scaling regimes across thresholds and supports an interpretation of market activity as a renewal process in intrinsic time. ...

Universal Patterns in the Blockchain: Analysis of EOAs and Smart Contracts in ERC20 Token Networks ArXiv ID: 2508.04671 “View on arXiv” Authors: Kundan Mukhia, SR Luwang, Md. Nurujjaman, Tanujit Chakraborty, Suman Saha, Chittaranjan Hens Abstract Scaling laws offer a powerful lens to understand complex transactional behaviors in decentralized systems. This study reveals distinctive statistical signatures in the transactional dynamics of ERC20 tokens on the Ethereum blockchain by examining over 44 million token transfers between July 2017 and March 2018 (9-month period). Transactions are categorized into four types: EOA–EOA, EOA–SC, SC-EOA, and SC-SC based on whether the interacting addresses are Externally Owned Accounts (EOAs) or Smart Contracts (SCs), and analyzed across three equal periods (each of 3 months). To identify universal statistical patterns, we investigate the presence of two canonical scaling laws: power law distributions and temporal Taylor’s law (TL). EOA-driven transactions exhibit consistent statistical behavior, including a near-linear relationship between trade volume and unique partners with stable power law exponents ($γ\approx 2.3$), and adherence to TL with scaling coefficients ($β\approx 2.3$). In contrast, interactions involving SCs, especially SC-SC, exhibit sublinear scaling, unstable power-law exponents, and significantly fluctuating Taylor coefficients (variation in $β$ to be $Δβ= 0.51$). Moreover, SC-driven activity displays heavier-tailed distributions ($γ< 2$), indicating bursty and algorithm-driven activity. These findings reveal the characteristic differences between human-controlled and automated transaction behaviors in blockchain ecosystems. By uncovering universal scaling behaviors through the integration of complex systems theory and blockchain data analytics, this work provides a principled framework for understanding the underlying mechanisms of decentralized financial systems. ...

A Modern Paradigm for Algorithmic Trading ArXiv ID: 2501.06032 “View on arXiv” Authors: Unknown Abstract We introduce a novel framework for developing fully-automated trading model algorithms. Unlike the traditional approach, which is grounded in analytical complexity favored by most quantitative analysts, we propose a paradigm shift that embraces real-world complexity. This approach leverages key concepts relating to self-organization, emergence, complex systems theory, scaling laws, and utilizes an event-based reframing of time. In closing, we describe an example algorithm that incorporates the outlined elements, called the Delta Engine. ...

Machine learning in weekly movement prediction ArXiv ID: 2407.09831 “View on arXiv” Authors: Unknown Abstract To predict the future movements of stock markets, numerous studies concentrate on daily data and employ various machine learning (ML) models as benchmarks that often vary and lack standardization across different research works. This paper tries to solve the problem from a fresh standpoint by aiming to predict the weekly movements, and introducing a novel benchmark of random traders. This benchmark is independent of any ML model, thus making it more objective and potentially serving as a commonly recognized standard. During training process, apart from the basic features such as technical indicators, scaling laws and directional changes are introduced as additional features, furthermore, the training datasets are also adjusted by assigning varying weights to different samples, the weighting approach allows the models to emphasize specific samples. On back-testing, several trained models show good performance, with the multi-layer perception (MLP) demonstrating stability and robustness across extensive and comprehensive data that include upward, downward and cyclic trends. The unique perspective of this work that focuses on weekly movements, incorporates new features and creates an objective benchmark, contributes to the existing literature on stock market prediction. ...

The Theory of Intrinsic Time: A Primer ArXiv ID: 2406.07354 “View on arXiv” Authors: Unknown Abstract The concept of time mostly plays a subordinate role in finance and economics. The assumption is that time flows continuously and that time series data should be analyzed at regular, equidistant intervals. Nonetheless, already nearly 60 years ago, the concept of an event-based measure of time was first introduced. This paper expands on this theme by discussing the paradigm of intrinsic time, its origins, history, and modern applications. Departing from traditional, continuous measures of time, intrinsic time proposes an event-based, algorithmic framework that captures the dynamic and fluctuating nature of real-world phenomena more accurately. Unsuspected implications arise in general for complex systems and specifically for financial markets. For instance, novel structures and regularities are revealed, otherwise obscured by any analysis utilizing equidistant time intervals. Of particular interest is the emergence of a multiplicity of scaling laws, a hallmark signature of an underlying organizational principle in complex systems. Moreover, a central insight from this novel paradigm is the realization that universal time does not exist; instead, time is observer-dependent, shaped by the intrinsic activity unfolding within complex systems. This research opens up new avenues for economic modeling and forecasting, paving the way for a deeper understanding of the invisible forces that guide the evolution and emergence of market dynamics and financial systems. An exciting and rich landscape of possibilities emerges within the paradigm of intrinsic time. ...