On Tail Dependence and Multifractality

0533622 - ÚTIA 2021 RIV CH eng J - Journal Article
Avdulaj, Krenar - Krištoufek, Ladislav
On Tail Dependence and Multifractality.
Mathematics. Roč. 8, č. 10 (2020), č. článku 1767. E-ISSN 2227-7390
R&D Projects: GA ČR(CZ) GJ17-12386Y
Institutional support: RVO:67985556
Keywords : multifractality * tail dependence * serial correlation * copulas
OECD category: Economic Theory
Impact factor: 2.258, year: 2020
Method of publishing: Open access
http://library.utia.cas.cz/separaty/2020/E/kristoufek-0533622.pdf https://www.mdpi.com/2227-7390/8/10/1767

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.
Permanent Link: http://hdl.handle.net/11104/0312007