On Tail Dependence and Multifractality
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...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/10/1767 |
| _version_ | 1797551122137743360 |
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| author | Krenar Avdulaj Ladislav Kristoufek |
| author_facet | Krenar Avdulaj Ladislav Kristoufek |
| author_sort | Krenar Avdulaj |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T15:39:15Z |
| format | Article |
| id | doaj.art-2cb661ceb7d54c60b300a190e80dc716 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T15:39:15Z |
| publishDate | 2020-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-2cb661ceb7d54c60b300a190e80dc7162023-11-20T16:54:59ZengMDPI AGMathematics2227-73902020-10-01810176710.3390/math8101767On Tail Dependence and MultifractalityKrenar Avdulaj0Ladislav Kristoufek1Institute of Information Theory and Automation, Czech Academy of Sciences, Pod Vodarenskou Vezi 4, 182 08 Prague, Czech RepublicInstitute of Information Theory and Automation, Czech Academy of Sciences, Pod Vodarenskou Vezi 4, 182 08 Prague, Czech RepublicWe 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.https://www.mdpi.com/2227-7390/8/10/1767multifractalitytail dependenceserial correlationcopulas |
| spellingShingle | Krenar Avdulaj Ladislav Kristoufek On Tail Dependence and Multifractality Mathematics multifractality tail dependence serial correlation copulas |
| title | On Tail Dependence and Multifractality |
| title_full | On Tail Dependence and Multifractality |
| title_fullStr | On Tail Dependence and Multifractality |
| title_full_unstemmed | On Tail Dependence and Multifractality |
| title_short | On Tail Dependence and Multifractality |
| title_sort | on tail dependence and multifractality |
| topic | multifractality tail dependence serial correlation copulas |
| url | https://www.mdpi.com/2227-7390/8/10/1767 |
| work_keys_str_mv | AT krenaravdulaj ontaildependenceandmultifractality AT ladislavkristoufek ontaildependenceandmultifractality |