Fractal analysis of Dow Jones Industrial Index returns

Desogus, Marco and Conversano, Claudio and Pili, Ambrogio and Venturi, Beatrice (2022): Fractal analysis of Dow Jones Industrial Index returns. Published in: Applied Mathematical Sciences , Vol. 16, No. 10 (2022): pp. 473-495.

Abstract

The Dow Jones Industrial Average 30 (DJIA30) Index was analyzed to show that models based on the Fractal Market Hypothesis (FMH) are preferable to those based on the Efficient Market Hypothesis (EMH). In a first step, Rescaled Range Analysis was applied to search for long term dependence between index returns. The Hurst coefficient was computed as a measure of persistence in the trend of the observed time series. A Monte Carlo simulation based on both Geometric Brownian Motion (GBM) and Fractional Brownian Motion (FBM) models was used in the second step to investigate the forecasting ability of each model in a situation where information about future prices is lacking. In the third step, the volatility of the index returns obtained from the simulated GBM and FBM was considered together with that produced by a GARCH(1,1) model in order to determine the approach that minimizes the Value at Risk (VaR) and the Conditional Value at Risk (CVaR) of one asset portfolio where the DJIA30 index underlies an Exchange Traded Commodity (ETC). In the case observed returns could either follow a gaussian distribution or a Pareto distribution with a scale parameter equal to the inverse of the Hurst coefficient determined in the first step.

• Item Type: MPRA Paper
• Language: English
• Keywords: Fractal Analysis; Rescaled Range Analysis; Pareto distribution; Hurst coefficient; Geometric Brownian Motion; Fractional Brownian Motion; Value at Risk (VaR); Conditional Value at Risk (CVaR); Efficient Market Hypothesis; Fractal Market Hypothesis; Dow Jones Industrial Average Index.
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63 - Computational Techniques ; Simulation Modeling

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