Emergence of Randomness in Temporally Aggregated Financial Tick Sequences

TL;DR

This paper introduces a comprehensive, model-free methodology using statistical randomness tests to analyze how time aggregation affects the randomness of high-frequency financial data, revealing new patterns and increasing unpredictability.

Contribution

It extends randomness analysis in financial data with extensive statistical tests, demonstrating how aggregation transforms correlated data into more random streams and uncovering novel predictability patterns.

Findings

Randomness increases with higher aggregation levels.

Non-monotonic predictability patterns are observed in some assets.

The methodology can generate pseudo-random sequences from financial data.

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.