Approximate Entropy as a Measure of Market Efficiency
Summary
The note discusses financial entropy through the lens of market efficiency and predictability, rather than treating money as a direct substitute for heat or information in physical entropy equations. It points to approximate entropy, introduced by Pincus, as a way to quantify the regularity of a time series and says prior studies have examined its relationship with established measures of market efficiency. The cited research concerns stock markets and information flow, crashes, and efficiency.
The response recommends using those studies and the foundational work on approximate entropy to investigate the measure, while noting that the empirical examples described are limited to equities and that broader applications would require adapting the procedure. The document provides no equations, sample details, or numerical findings, so it serves as a research direction rather than a practical estimation guide. It also does not establish that financial transactions obey thermodynamic entropy laws; its relevant contribution is the connection between time-series complexity and predictability.
Key ideas
- Approximate entropy can quantify regularity in financial time series.
- The note relates entropy measures to market efficiency and predictability.
- Prior cited research examines stock markets, including information flow and crashes.
- The suggested applications beyond equities are possibilities rather than demonstrated results in this note.
- Financial entropy here is an empirical information measure, not a direct thermodynamic model of spending.
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Full text
# Looking for a definition of financial entropy # Looking for a definition of financial entropy In Science, Entropy is generally considered to be the irreversibility of stuff. Google defines entropy as: > lack of order or predictability; gradual decline into disorder The 'gradual decline in to disorder', although pessimistic in its approach, fits with my idea of entropy. In finance, the idea of entropy is present in the idea of spending money - this is an energy exchange, and (in principle at least) once the transaction is completed, it cannot be reversed. This example is obviously at the micro-economic level. I am aiming to write a paper on the idea of Financial Entropy, and I am looking for macro-economic examples (financial relations where entropic properties are present between large corporations, e.g. Microsoft/Oracle, and/or governments. I am thinking all we really need to do is take existing definitions of entropy and thermodynamics for physics and maths, for example: - Wikipedia, Thermodynamics - Wikipedia, Information Theory and simply change the words 'heat' and 'information' to 'money'. My idea is that the equations should be equally applicable! The concept of this is similar to the translation of quantum mechanics into Quantum Economics. Any links to stories, experiences, papers, theories, etc.. are appreciated. Appendum : There is a motive to this question - the main change to financial entropy occurs when a purchase is made, and I am wondering if the entropy of a financial system is: - continuous before and after a trigger event (a spend event) - independent of external forces ## Answer by Quantopik (score 2, accepted) https://quant.stackexchange.com/a/18265 The concept of entropy in the financial field is related to the market efficiency and predictability one; the measure approximate entropy by Pincus (1991) is considered as a market efficiency measure and it has been empirically proven it is correlated to the main market efficiency measures as shown by Eon & Kim (2008) and Risso (2008). I suggest you to read: > Eom, Cheoljun, et al. "Effects of time dependency and efficiency on information flow in financial markets." Physica A: Statistical Mechanics and its Applications 387.21 (2008): 5219-5224. Risso, Wiston Adrián. "The informational efficiency and the financial crashes." Research in International Business and Finance 22.3 (2008): 396-408. to study the application of entropy in financial markets, that is what you asked for; the paper deals with the stock market only, but the procedure can be applied to all other markets. As you suggested in the question, according to me too, the idea is applicable also in financial markets, but there do not exist many studies about this topic. Read also Pincus (1991) and Pincus & Singer (1996) for a complete definition and further studies about the measure itself, while, if you are interested to know other measures of market efficiency, look at this question I asked some time ago on quant.SE in which I update periodically the market efficiency measures known in the academic literature
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