scholarly journals Trivariate copula to design coastal structures

2020 ◽  
Author(s):  
Olivier Orcel ◽  
Philippe Sergent ◽  
François Ropert
Keyword(s):  
Return Period ◽  
Tail Dependence ◽  
Structure Design ◽  
Likelihood Method ◽  
Dependence Structure ◽  
Practical Case ◽  
Coastal Structures ◽  
Copula Parameter ◽  
Bivariate Copula ◽  
Survival Copula

Abstract. Some coastal structures must be redesigned in the future due to rising sea levels caused by global warming. The design of structures subjected to the actions of waves requires an accurate estimate of the long return period of such parameters as wave height, wave period, storm surge and more specifically their joint exceedance probabilities. The Defra method that is currently used makes it possible to directly connect the joint exceedance probabilities to the product of the univariate probabilities by means of a simple factor. These schematic correlations do not, however, represent all the complexity of the reality and may lead to damaging errors in coastal structure design. The aim of this paper is therefore to remedy the lack of accuracy of these current approaches. To this end, we use copula theory with a copula function that aggregates joint distribution function to its univariate margins. We select a bivariate copula that is adapted to our application by the likelihood method with a copula parameter that is obtained by the error method. In order to integrate extreme events, we also resort to the notion of tail dependence. We can select the copulas with the same tail dependence as data. In the event of an opposite tail dependence structure, we resort to the survival copula. The tail dependence parameter makes it possible to estimate the optimal copula parameter. The most accurate copulas for our practical case with applications in Saint-Malo and Le Havre (France), are the Clayton normal copula and the Gumbel survival copula. The originality of this paper is the creation of a new and accurate trivariate copula. Firstly, we select the fittest bivariate copula with its parameter for the two most correlated univariate margins. Secondly, we build a trivariate function. For this purpose, we aggregate the bivariate function with the remaining univariate margin with its parameter. We show that this trivariate function satisfies the mathematical properties of the copula. We can finally represent joint trivariate exceedance probabilities for a return period of 10, 100 and 1000 years.

scholarly journals Trivariate copula to design coastal structures

2021 ◽  
Vol 21 (1) ◽  
pp. 239-260
Author(s):  
Olivier Orcel ◽  
Philippe Sergent ◽  
François Ropert
Keyword(s):  
Return Period ◽  
Tail Dependence ◽  
Copula Function ◽  
Structure Design ◽  
Distribution Functions ◽  
Likelihood Method ◽  
Practical Case ◽  
Single Factor ◽  
Coastal Structures ◽  
Bivariate Copula

Abstract. Some coastal structures must be redesigned in the future due to rising sea levels caused by climate change. The design of structures subjected to the actions of waves requires an accurate estimate of the long return period of such parameters as wave height, wave period, storm surge and more specifically their joint exceedance probabilities. The simplified Defra method that is currently used in particular for European coastal structures makes it possible to directly connect the joint exceedance probabilities to the product of the univariate probabilities by means of a single factor. These schematic correlations do not, however, represent all the complexity of the reality because of the use of this single factor. That may lead to damaging errors in coastal structure design. The aim of this paper is therefore to remedy the lack of robustness of these current approaches. To this end, we use copula theory with a copula function that aggregates joint distribution functions to their univariate margins. We select a bivariate copula that is adapted to our application by the likelihood method. In order to integrate extreme events, we also resort to the notion of tail dependence. The optimal copula parameter is estimated through the analysis of the tail dependence coefficient, the likelihood method and the mean error. The most robust copulas for our practical case with applications in Saint-Malo and Le Havre (in northern France) are the Clayton copula and the survival Gumbel copula. The originality of this paper is the creation of a new and robust trivariate copula with an analysis of the sensitivity to the method of construction and to the choice of the copula. Firstly, we select the best fitting of the bivariate copula with its parameter for the two most correlated univariate margins. Secondly, we build a trivariate function. For this purpose, we aggregate the bivariate function with the remaining univariate margin with its parameter. We show that this trivariate function satisfies the mathematical properties of the copula. We finally represent joint trivariate exceedance probabilities for a return period of 10, 100 and 1000 years. We finally conclude that the choice of the bivariate copula is more important for the accuracy of the trivariate copula than its own construction.

Ignoring spatial dependence misestimates flood risk at the European scale

2020 ◽  
Author(s):  
Viet Dung Nguyen ◽  
Ayse Duha Metin ◽  
Lorenzo Alfieri ◽  
Sergiy Vorogushyn ◽  
Bruno Merz
Keyword(s):  
Return Period ◽  
Flood Risk ◽  
Spatial Dependence ◽  
Large Scale ◽  
Spatial Scales ◽  
Tail Dependence ◽  
Flood Protection ◽  
Economic Losses ◽  
Dependence Structure ◽  
Spatial Homogeneity

<p>Flooding is a major problem worldwide causing many fatalities and economic losses. The quantification of flood risk can be difficult for large spatial scales due to its spatial variability. The traditional risk assessment approaches assuming unrealistic spatial homogeneity of flood return period for the entire catchment are often used and hence in many cases lead to misleading results especially for large-scale applications. In this study, we aim at investigating the influences of spatial dependence in flood risk estimation over national and continental scales by comparing the assessments under three spatial dependence assumptions: modelled dependence (MD), complete dependence (CD) and complete independence (CI) of flow return periods. In order to achieve the aim, we develop a copula-based model representing the dependence structure of annual maximum stream flow (AMS) at 507 stations (with basin area > 500km2) across Europe and use it to generate long-term (10000 years) spatially coherent AMS at these locations. The generated series at multiple sites are then used for estimating associated flood loss considering two levels (with and without) of flood protection. The flood risk is estimated and aggregated for the representative 3 regions (England, Germany and Europe) and for the three dependence assumptions considering also the role of tail dependence of the used copulas. The results highlight that ignoring spatial dependence misestimates flood risk. The deviation from the modelled risk (under-/over-estimation) depends differently on the assumptions of spatial dependence, tail dependence, flood protection level and spatial scales. For example, under CD assumption for 200-year return period and considering flood protection, approximately 2.5-, 3- and 3.5-fold overestimation of flood risk in England, Germany and Europe, respectively, is found.</p>

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 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 A Method for Systemic Risk Estimation Based on CDS Indices

2015 ◽  
Vol 8 (1) ◽  
pp. 103-124
Author(s):  
Gabriel Gaiduchevici
Keyword(s):  
Goodness Of Fit ◽  
Risk Estimation ◽  
Multivariate Time Series ◽  
Tail Dependence ◽  
Dependence Structure ◽  
Parameter Estimates ◽  
Copula Models ◽  
Goodness Of Fit Tests ◽  
Multi Stage ◽  
Stage Estimation

AbstractThe copula-GARCH approach provides a flexible and versatile method for modeling multivariate time series. In this study we focus on describing the credit risk dependence pattern between real and financial sectors as it is described by two representative iTraxx indices. Multi-stage estimation is used for parametric ARMA-GARCH-copula models. We derive critical values for the parameter estimates using asymptotic, bootstrap and copula sampling methods. The results obtained indicate a positive symmetric dependence structure with statistically significant tail dependence coefficients. Goodness-of-Fit tests indicate which model provides the best fit to data.

scholarly journals Copula-Based Assessment of Co-Movement and Tail Dependence Structure Among Major Trading Foreign Currencies in Ghana

Risks ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 55
Author(s):  
Prince Osei Mensah ◽  
Anokye M. Adam
Keyword(s):  
Exchange Rates ◽  
Foreign Currency ◽  
Tail Dependence ◽  
Time Range ◽  
Dependence Structure ◽  
Joint Movement ◽  
Positive Dependence ◽  
Study Results ◽  
Foreign Currencies ◽  
Dependence Measures

This paper examines the joint movement and tail dependence structure between the pair of foreign exchange rates (EUR, USD and GBP) against the GHS, using daily exchange rates data expressed in GHS per unit of foreign currencies (EUR, USD and GBP) between the time range of 24 February 2009 and 19 December 2019. We use different sets of both static (time-invariant) and time-varying copulas with different levels of dependence and tail dependence measures, and the study results reveal positive dependence between all exchange rates pairs, though the dependencies for EUR-USD and GBP-USD pairs are not as strong as the EUR-GBP pair. The findings also reveal symmetric tail dependence, and dependence evolves over time. Notwithstanding this, the asymmetric tail dependence copulas provide evidence of upper tail dependence. We compare the copula results to DCC(1,1)-GARCH(1,1) model result and find the copula to be more sensitive to extreme co-movement between the currency pairs. The afore-mentioned findings, therefore, offer forex market players the opportunity to relax in hoarding a particular foreign currency in anticipation of domestic currency depreciation.

scholarly journals Streamflow estimation at partially gaged sites using multiple dependence conditions via vine copulas

2020 ◽  
Author(s):  
Kuk-Hyun Ahn
Keyword(s):  
Missing Values ◽  
The Other ◽  
Dependence Structure ◽  
Proposed Model ◽  
Pee Dee ◽  
Streamflow Estimation ◽  
Vine Copula ◽  
Bivariate Copula ◽  
Pee Dee River ◽  
Vine Copulas

Abstract. Reliable estimates of missing streamflow values are relevant for water resources planning and management. This study proposes a multiple dependence condition model via vine copulas for the purpose of estimating streamflow at partially gaged sites. The proposed model is attractive in modeling the high dimensional joint distribution by building a hierarchy of conditional bivariate copulas when provided a complex streamflow gage network. The usefulness of the proposed model is firstly highlighted using a synthetic streamflow scenario. In this analysis, the bivariate copula model and a variant of the vine copulas are also employed to show the ability of the multiple dependence structure adopted in the proposed model. Furthermore, the evaluations are extended to a case study of 54 gages located within the Yadkin-Pee Dee River Basin, the eastern U. S. Both results inform that the proposed model is better suited for infilling missing values. After that, the performance of the vine copula is compared with six other infilling approaches to confirm its applicability. Results demonstrate that the proposed model produces more reliable streamflow estimates than the other approaches. In particular, when applied to partially gaged sites with sufficient available data, the proposed model clearly outperforms the other models. Even though the model is illustrated by a specific case, it can be extended to other regions with diverse hydro-climatological variables for the objective of infilling.

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