Price predictability at ultra-high frequency: Entropy-based randomness test

ArXiv ID: 2312.16637 “View on arXiv”

Authors: Unknown

Abstract

We use the statistical properties of Shannon entropy estimator and Kullback-Leibler divergence to study the predictability of ultra-high frequency financial data. We develop a statistical test for the predictability of a sequence based on empirical frequencies. We show that the degree of randomness grows with the increase of aggregation level in transaction time. We also find that predictable days are usually characterized by high trading activity, i.e., days with unusually high trading volumes and the number of price changes. We find a group of stocks for which predictability is caused by a frequent change of price direction. We study stylized facts that cause price predictability such as persistence of order signs, autocorrelation of returns, and volatility clustering. We perform multiple testing for sub-intervals of days to identify whether there is predictability at a specific time period during the day.

Keywords: ultra-high frequency data, Shannon entropy, Kullback-Leibler divergence, predictability, order flow, Equities

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 4.0/10
  • Quadrant: Lab Rats
  • Why: The paper is highly mathematical, featuring rigorous statistical derivations of entropy estimators, Neyman-Pearson tests, and asymptotic distributions (e.g., χ²), but it lacks implementation details, backtest results, or transaction cost analysis, making it more theoretical than backtest-ready.
  flowchart TD
    A["Research Goal: Test for price predictability<br>in ultra-high frequency data"] --> B["Methodology: Shannon Entropy &<br>Kullback-Leibler Divergence"]
    B --> C["Data Input: Ultra-High Frequency<br>Equity Transaction Data"]
    C --> D["Computational Process:<br>1. Calculate Entropy at various<br>aggregation levels<br>2. Perform statistical tests<br>3. Analyze stylized facts<br>(order signs, autocorrelation, volatility)"]
    D --> E["Key Findings:<br>- Randomness increases with aggregation<br>- Predictable days = high trading activity<br>- Persistence in order flow causes predictability<br>- Predictability varies by time of day"]