scholarly journals Extremal behavior of Archimedean copulas

2011 ◽  
Vol 43 (1) ◽  
pp. 195-216 ◽  
Author(s):  
Martin Larsson ◽  
Johanna Nešlehová
Keyword(s):  
Domain Of Attraction ◽  
Tail Dependence ◽  
Dependence Structure ◽  
Tail Behavior ◽  
Archimedean Copulas ◽  
Radial Part ◽  
Stochastic Representation ◽  
Lower Tail ◽  
Extremal Behavior ◽  
Practical Implications

We show how the extremal behavior of d-variate Archimedean copulas can be deduced from their stochastic representation as the survival dependence structure of an ℓ1-symmetric distribution (see McNeil and Nešlehová (2009)). We show that the extremal behavior of the radial part of the representation is determined by its Williamson d-transform. This leads in turn to simple proofs and extensions of recent results characterizing the domain of attraction of Archimedean copulas, their upper and lower tail-dependence indices, as well as their associated threshold copulas. We outline some of the practical implications of their results for the construction of Archimedean models with specific tail behavior and give counterexamples of Archimedean copulas whose coefficient of lower tail dependence does not exist.

scholarly journals Extremal behavior of Archimedean copulas

2011 ◽  
Vol 43 (01) ◽  
pp. 195-216 ◽  
Author(s):  
Martin Larsson ◽  
Johanna Nešlehová
Keyword(s):  
Domain Of Attraction ◽  
Tail Dependence ◽  
Dependence Structure ◽  
Tail Behavior ◽  
Archimedean Copulas ◽  
Radial Part ◽  
Stochastic Representation ◽  
Lower Tail ◽  
Extremal Behavior ◽  
Practical Implications

We show how the extremal behavior of d-variate Archimedean copulas can be deduced from their stochastic representation as the survival dependence structure of an ℓ1-symmetric distribution (see McNeil and Nešlehová (2009)). We show that the extremal behavior of the radial part of the representation is determined by its Williamson d-transform. This leads in turn to simple proofs and extensions of recent results characterizing the domain of attraction of Archimedean copulas, their upper and lower tail-dependence indices, as well as their associated threshold copulas. We outline some of the practical implications of their results for the construction of Archimedean models with specific tail behavior and give counterexamples of Archimedean copulas whose coefficient of lower tail dependence does not exist.

Simulation for Mixture of Archimedean Copulas

2012 ◽  
Vol 195-196 ◽  
pp. 738-743
Author(s):  
Shi De Ou
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Tail Dependence ◽  
Likelihood Estimation ◽  
Numerical Results ◽  
Dependence Structure ◽  
Archimedean Copulas ◽  
Copula Models ◽  
Random Samples ◽  
Dependence Structures

Many dependence structures can consist of mixed copulas. In order to analyze the dependence of stock, we present the method of estimation for mixed copula models. Via generating random samples and using maximum likelihood estimation, the parameters of mixture of Archimedean copulas are estimated. Numerical results show that this method estimates effectively the parameters and tail dependence coefficients. Therefore we can use the method to analyze dependence structure for stocks.

scholarly journals Spatial Tail Dependence and Survival Stability in a Class of Archimedean Copulas

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Diakarya Barro ◽  
Moumouni Diallo ◽  
Remi Guillaume Bagré
Keyword(s):  
Dimensional Analysis ◽  
Tail Dependence ◽  
High Dimensional ◽  
Archimedean Copulas ◽  
Lower Tail

This paper investigates properties of extensions of tail dependence of Archimax copulas to high dimensional analysis in a spatialized framework. Specifically, we propose a characterization of bivariate margins of spatial Archimax processes while spatial multivariate upper and lower tail dependence coefficients are modeled, respectively, for Archimedean copulas and Archimax ones. A property of stability is given using convex transformations of survival copulas in a spatialized Archimedean family.

scholarly journals Dependence Structure between Conventional and Islamic Indexes: A Copula Approach

2020 ◽  
Vol 4 (2) ◽  
pp. 22-30
Author(s):  
Samia Ben Messaoud ◽  
Mondher Kouki
Keyword(s):  
Empirical Analysis ◽  
Tail Dependence ◽  
Dependence Structure ◽  
Lower Tail ◽  
Copula Models ◽  
Conditional Dependence ◽  
Copula Approach ◽  
Upper Tail Dependence ◽  
Stock Indexes

This article examines the conditional dependence structure between Islamic stock indexes and conventional counterparts. Our empirical analysis relies on Islamic and conventional indexes of dependence distribution using copula methods over the period 1999–2014. The results from the copula models denote that the dependence is not formally symmetric in that the lower tail dependence is significantly larger than the upper tail dependence.

scholarly journals Assessing Market Risk in BRICS and Oil Markets: An Application of Markov Switching and Vine Copula

2021 ◽  
Vol 9 (2) ◽  
pp. 30
Author(s):  
John Weirstrass Muteba Mwamba ◽  
Sutene Mwambetania Mwambi
Keyword(s):  
South Africa ◽  
Crude Oil ◽  
South African ◽  
Asset Allocation ◽  
Markov Switching ◽  
Tail Dependence ◽  
Lower Tail ◽  
Oil Market ◽  
Oil Markets ◽  
Vine Copula

This paper investigates the dynamic tail dependence risk between BRICS economies and the world energy market, in the context of the COVID-19 financial crisis of 2020, in order to determine optimal investment decisions based on risk metrics. For this purpose, we employ a combination of novel statistical techniques, including Vector Autoregressive (VAR), Markov-switching GJR-GARCH, and vine copula methods. Using a data set consisting of daily stock and world crude oil prices, we find evidence of a structure break in the volatility process, consisting of high and low persistence volatility processes, with a high persistence in the probabilities of transition between lower and higher volatility regimes, as well as the presence of leverage effects. Furthermore, our results based on the C-vine copula confirm the existence of two types of tail dependence: symmetric tail dependence between South Africa and China, South Africa and Russia, and South Africa and India, and asymmetric lower tail dependence between South Africa and Brazil, and South Africa and crude oil. For the purpose of diversification in these markets, we formulate an asset allocation problem using raw returns, MS GARCH returns, and C-vine and R-vine copula-based returns, and optimize it using a Particle Swarm optimization algorithm with a rebalancing strategy. The results demonstrate an inverse relationship between the risk contribution and asset allocation of South Africa and the crude oil market, supporting the existence of a lower tail dependence between them. This suggests that, when South African stocks are in distress, investors tend to shift their holdings in the oil market. Similar results are found between Russia and crude oil, as well as Brazil and crude oil. In the symmetric tail, South African asset allocation is found to have a well-diversified relationship with that of China, Russia, and India, suggesting that these three markets might be good investment destinations when things are not good in South Africa, and vice versa.

Dependence structure between money and economic activity: A Markov-switching copula VEC approach

2021 ◽  
pp. 1-17
Author(s):  
Apostolos Serletis ◽  
Libo Xu
Keyword(s):  
Error Correction ◽  
Economic Activity ◽  
Regime Switching ◽  
Markov Switching ◽  
Tail Dependence ◽  
Error Correction Model ◽  
Dependence Structure ◽  
Copula Models ◽  
Correction Model ◽  
Dependence Structures

Abstract This paper examines correlation and dependence structures between money and the level of economic activity in the USA in the context of a Markov-switching copula vector error correction model. We use the error correction model to focus on the short-run dynamics between money and output while accounting for their long-run equilibrium relationship. We use the Markov regime-switching model to account for instabilities in the relationship between money and output, and also consider different copula models with different dependence structures to investigate (upper and lower) tail dependence.

scholarly journals Tail Behavior and Dependence Structure in the APARCH Model

2016 ◽  
Vol 9 (2) ◽  
Author(s):  
Farrukh Javed ◽  
Krzysztof Podgórski
Keyword(s):  
Statistical Inference ◽  
Dependence Structure ◽  
Leverage Effect ◽  
Tail Behavior ◽  
News Shocks ◽  
Negative News ◽  
Asymmetric Responses ◽  
Heavy Tailed ◽  
European Economies ◽  
Theoretical Results

AbstractThe APARCH model attempts to capture asymmetric responses of volatility to positive and negative ‘news shocks’ – the phenomenon known as the leverage effect. Despite its potential, the model’s properties have not yet been fully investigated. While the capacity to account for the leverage is clear from the defining structure, little is known how the effect is quantified in terms of the model’s parameters. The same applies to the quantification of heavy-tailedness and dependence. To fill this void, we study the model in further detail. We study conditions of its existence in different metrics and obtain explicit characteristics: skewness, kurtosis, correlations and leverage. Utilizing these results, we analyze the roles of the parameters and discuss statistical inference. We also propose an extension of the model. Through theoretical results we demonstrate that the model can produce heavy-tailed data. We illustrate these properties using S&P500 data and country indices for dominant European economies.

Sign in / Sign up

Export Citation Format

Share Document