Paper: arXiv 2511.14408

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.

Complexity vs Empirical Score

  • Math Complexity: 7.0/10
  • Empirical Rigor: 5.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a sophisticated mathematical model using renewal theory and Poisson processes to derive a scaling constant, but it also implements a concrete empirical analysis on real cryptocurrency data with specific statistical tests and reproducibility references.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Identify origin of stable<br>scaling laws in Intrinsic Time"] --> B["Key Methodology<br>Directional-change Intrinsic Time<br>Analysis & Poisson Process Modeling"]
  B --> C["Data Inputs<br>Empirical Intrinsic Time Series<br>Directional Changes & Total Events"]
  C --> D["Computational Process<br>Measure Ratio of Directional<br>Changes to Total Events"]
  D --> E{"Analysis"}
  E --> F["Evidence: Ratio stabilizes near<br><b>1 - 1/e = 0.632</b>"]
  E --> G["Interpretation<br>Market activity modeled as<br>Memoryless Exponential Hazard Process"]
  F --> H["Key Findings/Outcomes<br>1. Identified Hidden Constant<br>2. Natural heuristic for scaling regimes<br>3. Renewal Process interpretation"]
  G --> H

Cited References (17)

  1. A Directional-Change Events Approach for Studying Financial Time Series (2012) — link
  2. A Modern Paradigm for Algorithmic Trading — → 2501.06032
  3. Volatility Measurement with Directional Change in Chinese Stock Market: Statistical Property and Investment Strategy (2017) — link
  4. Instantaneous Volatility Seasonality of High-Frequency Markets in Directional-Change Intrinsic Time (2019) — link
  5. Intrinsic Time Directional-Change Methodology in Higher Dimensions (2019) — link
  6. Agent-based modelling in directional-change intrinsic time (2020) — link
  7. The Theory of Intrinsic Time: Market Microstructure 2.0 (2024) — link
  8. From the bird’s eye to the microscope: A survey of new stylized facts of the intra-daily foreign exchange markets (1997) — link
and 9 more
  1. Patterns in high-frequency FX data: Discovery of 12 empirical scaling laws (2011) — link
  2. Robust inference for nondestructive one-shot device testing under step-stress model with exponential lifetimes (2023) — link
  3. Queueing Systems, Volume I: Theory (1975)
  4. Non-exponential and oscillatory decays in quantum mechanics (2014) — link
  5. The Transient Response of Damped Linear Networks with Particular Regard to Wideband Amplifiers (1948) — link
  6. Stopping at the Last Renewal up to a Terminal Time (2007)
  7. Power-law distributions in empirical data (2009) — link
  8. Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data (1998) — link
  9. Econometric analysis of realized volatility and its use in estimating stochastic volatility models (2002) — link

1 of 17 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.