Spurious seasonality detection: a non-parametric test proposal

TL;DR

This paper introduces a non-parametric, symbolic dynamics-based test to detect day-of-the-week effects in financial data, revealing that such seasonality may be an artifact of data correlation structures rather than genuine patterns.

Contribution

It proposes a novel ordinal pattern-based test for seasonality detection that does not rely on distributional assumptions, offering a practical alternative to traditional methods.

Findings

The day-of-the-week effect can be partly explained by hidden correlations.

White noise signals do not show day-of-the-week patterns.

The test was successfully applied to 83 global stock indices.

Abstract

This paper offers a general and comprehensive definition of the day-of-the-week effect. Using symbolic dynamics, we develop a unique test based on ordinal patterns in order to detect it. This test uncovers the fact that the so-called "day-of-the-week" effect is partly an artifact of the hidden correlation structure of the data. We present simulations based on artificial time series as well. Whereas time series generated with long memory are prone to exhibit daily seasonality, pure white noise signals exhibit no pattern preference. Since ours is a non parametric test, it requires no assumptions about the distribution of returns so that it could be a practical alternative to conventional econometric tests. We made also an exhaustive application of the here proposed technique to 83 stock indices around the world. Finally, the paper highlights the relevance of symbolic analysis in economic time series studies.