Variance of entropy for testing time-varying regimes with an application to meme stocks

Andrey Shternshis () and Piero Mazzarisi ()
Additional contact information
Andrey Shternshis: Scuola Normale Superiore
Piero Mazzarisi: Scuola Normale Superiore

Decisions in Economics and Finance, 2024, vol. 47, issue 1, No 9, 215-258

Abstract: Abstract Shannon entropy is the most common metric for assessing the degree of randomness of time series in many fields, ranging from physics and finance to medicine and biology. Real-world systems are typically non-stationary, leading to entropy values fluctuating over time. This paper proposes a hypothesis testing procedure to test the null hypothesis of constant Shannon entropy in time series data. The alternative hypothesis is a significant variation in entropy between successive periods. To this end, we derive an unbiased sample entropy variance, accurate up to the order $$O(n^{-4})$$ O ( n - 4 ) with n the sample size. To characterize the variance of the sample entropy, we first provide explicit formulas for the central moments of both binomial and multinomial distributions describing the distribution of the sample entropy. Second, we identify the optimal rolling window length to estimate time-varying Shannon entropy. We optimize this choice using a novel self-consistent criterion based on counting significant entropy variations over time. We corroborate our findings using the novel methodology to assess time-varying regimes of entropy for stock price dynamics by presenting a comparative analysis between meme and IT stocks in 2020 and 2021. We show that low entropy values correspond to periods when profitable trading strategies can be devised starting from the symbolic dynamics used for entropy computation, namely periods of market inefficiency.

Keywords: Market efficiency; Meme stocks; Multinomial distribution; Entropy distribution; Hypothesis testing (search for similar items in EconPapers)
JEL-codes: C12 C53 D84 G14 (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10203-023-00427-9 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:decfin:v:47:y:2024:i:1:d:10.1007_s10203-023-00427-9

Ordering information: This journal article can be ordered from
http://www.springer. ... ry/journal/10203/PS2

DOI: 10.1007/s10203-023-00427-9

Access Statistics for this article

Decisions in Economics and Finance is currently edited by Paolo Ghirardato

More articles in Decisions in Economics and Finance from Springer, Associazione per la Matematica
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().