A comparison of three Hurst exponent approaches to predict nascent bubbles in S&P500 stocks

Área de investigación: Applied Mathematics Año: 2017
Tipo de publicación: Artículo Palabras clave: Hurst Exponent; Market Bubble; Herding Behavior; Forecasting; SP500
Autores: Fernández Martínez, Manuel; Sánchez-Granero, M. A.; Torrecillas, M. J. Muñoz; McKelvey, Bill
Journal: Fractals Volumen: 25
Número: 1 Páginas: 1-10
Mes: February
BibTex:
Abstract:
Since the pioneer contributions due to Vandewalle and Ausloos, the Hurst exponent has been applied by econophysicists as a useful indicator to deal with investment strategies when such a value is above or below 0.5 0 . 5 , the Hurst exponent of a Brownian motion. In this paper, we hypothesize that the self-similarity exponent of financial time series provides a reliable indicator for herding behavior (HB) in the following sense: if there is HB, then the higher the price, the more the people will buy. This will generate persistence in the stocks which we shall measure by their self-similarity exponents. Along this work, we shall explore whether there is some connections between the self-similarity exponent of a stock (as a HB indicator) and the stock’s future performance under the assumption that the HB will last for some time. With this aim, three approaches to calculate the self-similarity exponent of a time series are compared in order to determine which performs best to identify the transition from random efficient market behavior to HB and hence, to detect the beginning of a bubble. Generalized Hurst Exponent, Detrended Fluctuation Analysis, and GM2 algorithms have been tested. Traditionally, researchers have focused on identifying the beginning of a crash. We study the beginning of the transition from efficient market behavior to a market bubble, instead. Our empirical results support that the higher (respectively the lower) the self-similarity index, the higher (respectively the lower) the mean of the price change, and hence, the better (respectively the worse) the performance of the corresponding stock. This would imply, as a consequence, that the transition process from random efficient market to HB has started. For experimentation purposes, S&P500 stock Index constituted our main data source.
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