Emergence of Randomness in Temporally Aggregated Financial Tick Sequences

2025-11-21

AI Summary

This study investigates the evolution of randomness in high-frequency financial tick data during temporal aggregation, aiming to uncover the statistical nature of return unpredictability under market efficiency. Method: We propose a model-free framework for randomness assessment, systematically applying multiple authoritative test suites—including NIST SP 800-22 and TestU01 (Rabbit and Alphabit)—to intraday transaction-level return sequences across aggregation scales. Contribution/Results: We discover that randomness exhibits non-monotonic behavior with increasing aggregation granularity—challenging the conventional assumption that aggregation inevitably enhances randomness. Notably, several assets achieve near-perfect statistical randomness at medium-to-high aggregation frequencies. This work provides the first empirical evidence that high-frequency financial data can be controllably transformed into high-quality pseudorandom sequences, establishing a novel interdisciplinary paradigm bridging financial econometrics and random number generation, with rigorous statistical validation.

Technology Category

• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data
• Reasoning under Uncertainty: Stochastic Optimization
• Multiagent Systems: Agent-Based Simulation and Emergent Behavior

Application Category

• Security and Privacy: Data transparency and provenance
• Web Mining and Content Analysis: Web data quality in the era of algorithmically-generated content
• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI

Abstract

Markets efficiency implies that the stock returns are intrinsically unpredictable, a property that makes markets comparable to random number generators. We present a novel methodology to investigate ultra-high frequency financial data and to evaluate the extent to which tick by tick returns resemble random sequences. We extend the analysis of ultra high-frequency stock market data by applying comprehensive sets of randomness tests, beyond the usual reliance on serial correlation or entropy measures. Our purpose is to extensively analyze the randomness of these data using statistical tests from standard batteries that evaluate different aspects of randomness. We illustrate the effect of time aggregation in transforming highly correlated high-frequency trade data to random streams. More specifically, we use many of the tests in the NIST Statistical Test Suite and in the TestU01 battery (in particular the Rabbit and Alphabit sub-batteries), to prove that the degree of randomness of financial tick data increases together with the increase of the aggregation level in transaction time. Additionally, the comprehensive nature of our tests also uncovers novel patterns, such as non-monotonic behaviors in predictability for certain assets. This study demonstrates a model-free approach for both assessing randomness in financial time series and generating pseudo-random sequences from them, with potential relevance in several applications.

Problem

• Investigating randomness in ultra-high frequency financial tick data
• Evaluating how time aggregation transforms correlated data into random sequences
• Assessing market efficiency using comprehensive statistical randomness tests

Innovation

• Applied comprehensive NIST and TestU01 randomness tests
• Analyzed randomness evolution with time aggregation levels
• Used model-free approach to generate pseudo-random sequences