Entropy serves as a measure of chaos in systems by representing the average rate of information loss about a phase point's position on the attractor. When dealing with a multifractal system, a single exponent cannot fully describe its dynamics, necessitating a continuous spectrum of exponents, known as the singularity spectrum. From an investor's point of view, a rise in entropy is a signal of abnormal and possibly negative returns. This means he has to expect the unexpected and prepare for it. To explore this, we analyse the New York Stock Exchange (NYSE) U.S. Index as well as its constituents. Through this examination, we assess their multifractal characteristics and identify market conditions (bearish/bullish markets) using entropy, an effective method for recognizing fluctuating fractal markets. Our findings challenge conventional beliefs by demonstrating that price declines lead to increased entropy, contrary to some studies in the literature that suggest that reduced entropy in market crises implies more determinism. Instead, we propose that bear markets are likely to exhibit higher entropy, indicating a greater chance of unexpected extreme events. Moreover, our study reveals a power-law behaviour and indicates the absence of variance.

Department of Applied Mathematics VSB Technical University of Ostrava 17 Listopadu 2172 15 708 00 Ostrava Czech Republic

Department of Economics HSE University 3A Kantemirovskaya Ulitsa St Petersburg 190121 Russia

Department of Mathematics University of Bari Via Edoardo Orabona 4 70125 Bari Italy

Department of Mathematics University of Jaen Campus Las Lagunillas s n 23071 Jaén Spain

IT4Innovations VSB Technical University of Ostrava 17 Listopadu 2172 15 708 00 Ostrava Czech Republic

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