Abstract
In this article, we propose a test of the dynamics of stock market indexes typical of the US and EU capital markets in order to determine which of the two fundamental hypotheses, efficient market hypothesis (EMH) or fractal market hypothesis (FMH), best describes market behavior. The article’s major goal is to show how to appropriately model return distributions for financial market indexes, specifically which geometric Brownian motion (GBM) and geometric fractional Brownian motion (GFBM) dynamic equations best define the evolution of the S&P 500 and Stoxx Europe 600 stock indexes. Daily stock index data were acquired from the Thomson Reuters Eikon database during a ten-year period, from January 2011 to December 2020. The main contribution of this work is determining whether these markets are efficient (as defined by the EMH), in which case the appropriate stock indexes dynamic equation is the GBM, or fractal (as described by the FMH), in which case the appropriate stock indexes dynamic equation is the GFBM. In this paper, we consider two methods for calculating the Hurst exponent: the rescaled range method (RS) and the periodogram method (PE). To determine which of the dynamics (GBM, GFBM) is more appropriate, we employed the mean absolute percentage error (MAPE) method. The simulation results demonstrate that the GFBM is better suited for forecasting stock market indexes than the GBM when the analyzed markets display fractality. However, while these findings cannot be generalized, they are verisimilar.
Highlights
Modeling and forecasting stock price movements has been a key issue in financial studies
Using the geometric fractional Brownian motion (GFBM) to derive the Hurst exponent produces reasonable forecasts for the Stoxx Eur 600 index, with the exception of the 3-year period, where the forecast is considered good. The latter circumstance is observed when the Hurst exponent is assumed to be 0.5, in which case the geometric Brownian motion (GBM) provides the dynamics of the Stoxx Eur
The calculations on the dynamics of stock market indexes value were performed in Matlab using GBM, GFBM, Hurst index, and mean absolute percentage error (MAPE) calculation, and the validation of our study’s results will be done on the basis of the results obtained from determining the average
Summary
Modeling and forecasting stock price movements has been a key issue in financial studies. In order to make financial and investment decisions, investors use prediction models to assure low investment risk and to have a picture of the market trends. This has inspired a great deal of research into the development and design of prediction models. The efficient financial market, according to EMH theory, is the market that fully reflects the available information, and one of the models of the efficient financial market is the random walk model [4]. Because the EMH is based on standard Brownian motion processes that assume prices evolve through random walk, one obvious consequence is that forecasting future price movements is impossible because market movements are independent and lack autocorrelation, rendering technical analysis useless to investors [6]
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