Financial multifractality and its subtleties: an example of DAX

TL;DR

This paper investigates the complex multifractal properties of the DAX stock index's high-frequency data, revealing that market dynamics are more intricate than simple multifractality, through various advanced analysis methods.

Contribution

It provides a comprehensive analysis of multifractal characteristics of financial time series using multiple exponents and highlights the complex nature of stock market dynamics.

Findings

Stock market exhibits more complex behavior than simple multifractality.

Different multifractal measures show consistent complex patterns.

High-frequency data reveals nuanced multifractal features.

Abstract

Detailed study of multifractal characteristics of the financial time series of asset values and of its returns is performed using a collection of the high frequency Deutsche Aktienindex data. The tail index ($\alpha$), the Renyi exponents based on the box counting algorithm for the graph ($d_q$) and the generalized Hurst exponents ($H_q$) are computed in parallel for short and daily return times. The results indicate a more complicated nature of the stock market dynamics than just consistent multifractal.