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On Tail Dependence and Multifractality

by 1,† and 1,2,*,†
Institute of Information Theory and Automation, Czech Academy of Sciences, Pod Vodarenskou Vezi 4, 182 08 Prague, Czech Republic
Institute of Economic Studies, Faculty of Social Sciences, Charles University, Opletalova 26, 110 00 Prague, Czech Republic
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2020, 8(10), 1767;
Received: 31 August 2020 / Revised: 22 September 2020 / Accepted: 29 September 2020 / Published: 13 October 2020
(This article belongs to the Special Issue Advanced Methods in Mathematical Finance)
We study whether, and if yes then how, a varying auto-correlation structure in different parts of distributions is reflected in the multifractal properties of a dynamic process. Utilizing the quantile autoregressive process with Gaussian copula using three popular estimators of the generalized Hurst exponent, our Monte Carlo simulation study shows that such dynamics translate into multifractal dynamics of the generated series. The tail-dependence of the auto-correlations forms strong enough non-linear dependencies to be reflected in the estimated multifractal spectra and separated from the case of the standard auto-regressive process. With a quick empirical example from financial markets, we argue that the interaction is more important for the asymmetric tail dependence. In addition, we discuss and explain the often reported paradox of higher multifractality of shuffled series compared to the original financial series. In short, the quantile-dependent auto-correlation structures qualify as sources of multifractality and they are worth further theoretical examination. View Full-Text
Keywords: multifractality; tail dependence; serial correlation; copulas multifractality; tail dependence; serial correlation; copulas
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MDPI and ACS Style

Avdulaj, K.; Kristoufek, L. On Tail Dependence and Multifractality. Mathematics 2020, 8, 1767.

AMA Style

Avdulaj K, Kristoufek L. On Tail Dependence and Multifractality. Mathematics. 2020; 8(10):1767.

Chicago/Turabian Style

Avdulaj, Krenar, and Ladislav Kristoufek. 2020. "On Tail Dependence and Multifractality" Mathematics 8, no. 10: 1767.

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