Copula Representation of Bivariate L-Moments: A New Estimation Method for Multiparameter 2-Dimensional Copula Models

Brahimi, Brahim; Chebana, Fateh; Necir, Abdelhakim

doi:10.2139/ssrn.1866569

Cited by 8 publications

(12 citation statements)

References 30 publications

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“…This means that, if two consecutive values in a time series are chosen for small time lag k (day), these two values are likely to be less correlated for high values but more correlated for low values, which leads to negative value of A 1 (k). This implies that the intrinsic temporal distribution of precipitation can be investigated based on this asymmetry, possibly with advanced asymmetry functions such as bivariate moments based on L-moments (Brahimi et al, 2015;Serfling and Xiao, 2007).…”

Section: Asymmetry and Catchment Characteristicsmentioning

confidence: 99%

Investigation of hydrological time series using copulas for detecting catchment characteristics and anthropogenic impacts

Sugimoto

Bàrdossy

Pegram

et al. 2016

Hydrol. Earth Syst. Sci.

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Abstract. Global climate change can have impacts on characteristics of rainfall-runoff events and subsequently on the hydrological regime. Meanwhile, the catchment itself changes due to anthropogenic influences. However, it is not easy to prove the link between the hydrology and the forcings. In this context, it might be meaningful to detect the temporal changes of catchments independent from climate change by investigating existing long-term discharge records. For this purpose, a new stochastic system based on copulas for time series analysis is introduced in this study.A statistical tool like copula has the advantage to scrutinize the dependence structure of the data and, thus, can be used to attribute the catchment behavior by focusing on the following aspects of the statistics defined in the copula domain: (1) copula asymmetry, which can capture the nonsymmetric property of discharge data, differs from one catchment to another due to the intrinsic nature of both runoff and catchment; and (2) copula distances can assist in identifying catchment change by revealing the variability and interdependency of dependence structures. These measures were calculated for 100 years of daily discharges for the Rhine River and these analyses detected epochs of change in the flow sequences. In a follow-up study, we compared the results of copula asymmetry and copula distance applied to two flow models: (i) antecedent precipitation index (API) and (ii) simulated discharge time series generated by a hydrological model. The results of copula-based analysis of hydrological time series seem to support the assumption that the Neckar catchment had started to change around 1976 and stayed unusual until 1990.

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Section: Asymmetry and Catchment Characteristicsmentioning

confidence: 99%

Investigation of hydrological time series using copulas for detecting catchment characteristics and anthropogenic impacts

Sugimoto

Bàrdossy

Pegram

et al. 2016

Hydrol. Earth Syst. Sci.

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“…The vector parameter

θ \in Θ \subset ℝ^{p}, p \geq 1

of the copula family

C_{θ}

can be estimated using a nonparametric, semiparametric, or fully parametric approach. In this study, the focus is on the maximum pseudo‐likelihood (MPL) method, however, other estimation methods may be applied, for instance the moment method based on the inversion of dependence measures such as the Spearman's rho and Kendall's tau [ Nelsen , ], minimum‐distance method [ Tsukahara , ], inference function for margins method [ Joe and Xu , ], and method based on bivariate L‐moments [ Brahimi et al ., ]. The MPL estimator is determined by maximizing the log pseudo‐likelihood function:

l (θ) = \sum_{i = 1}^{n} \log c_{θ} ({\overset{U}{true}}_{i 1}, {\overset{U}{true}}_{i 2}),

where

{\overset{U}{true}}_{i j} = R_{i j} / (n + 1)

are pseudo‐observations ( R ij is the rank of X ij among

(X_{1 j}, \dots, X_{n j}))

and

c (u, v) = \frac{\partial C (u, v)}{\partial u \partial v}

is the corresponding copula density that is absolutely continuous.…”

Section: Methodsmentioning

confidence: 99%

Homogeneity testing for spatially correlated data in multivariate regional frequency analysis

Šimková

2017

Water Resources Research

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Identification of homogeneous regions is a key task in regional frequency analysis (RFA) to obtain adequate quantile estimates for an event of interest. Recently, the frequently used univariate Hosking‐Wallis L‐moment homogeneity test was extended to the multivariate case. Multivariate L‐moments are used as a tool to define the test statistic and copula models to describe the statistical behavior of the analyzed dependent variables. To avoid drawbacks in fitting a parametric joint distribution to the data and a rejection threshold which is based on simulations, its nonparametric alternatives were also proposed. Although the simulation studies performed demonstrated the usefulness of both the parametric and nonparametric tests, the powers obtained were valid only for regions without intersite dependence. Examples from practice nevertheless demonstrate that intersite correlation may be expected for some kinds of data. To overcome the problem of cross correlation between stations, the parametric testing procedure is generalized using D‐vine copulas to model intersite dependence when generating synthetic homogeneous regions during the testing procedure. Monte Carlo simulations were performed and illustrate how intersite dependence negatively impacts the multivariate L‐moment homogeneity tests by significantly reducing their powers. The results of simulations also demonstrate the superiority of the proposed modification over both the original parametric and nonparametric procedures inasmuch as it improves the heterogeneity detection and avoids miscategorization of a region. The modified test is also applied in a case study for meteorological data in the Czech Republic.

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“…In a similar line of study, Brahimi et al . [] introduced a new L ‐moment‐based approach to estimate the copula parameters, which outperforms the traditional approaches in terms of bias and computational costs, and is less sensitive to data outliers. However, these methods are not usually capable of characterizing the underlying uncertainties.…”

Section: Introductionmentioning

confidence: 98%

“…Local optimization approaches benefit from efficient (mostly gradient-based) search algorithms, but suffer from susceptibility to getting trapped in local optima [Duan et al, 1992]. In a similar line of study, Brahimi et al [2015] introduced a new L-moment-based approach to estimate the copula parameters, which outperforms the traditional approaches in terms of bias and computational costs, and is less sensitive to data outliers. However, these methods are not usually capable of characterizing the underlying uncertainties.…”

Section: Introductionmentioning

confidence: 99%

Multivariate Copula Analysis Toolbox (MvCAT): Describing dependence and underlying uncertainty using a Bayesian framework

Sadegh

Ragno

AghaKouchak

2017

Water Resources Research

273

142

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We present a newly developed Multivariate Copula Analysis Toolbox (MvCAT) which includes a wide range of copula families with different levels of complexity. MvCAT employs a Bayesian framework with a residual-based Gaussian likelihood function for inferring copula parameters and estimating the underlying uncertainties. The contribution of this paper is threefold: (a) providing a Bayesian framework to approximate the predictive uncertainties of fitted copulas, (b) introducing a hybrid-evolution Markov Chain Monte Carlo (MCMC) approach designed for numerical estimation of the posterior distribution of copula parameters, and (c) enabling the community to explore a wide range of copulas and evaluate them relative to the fitting uncertainties. We show that the commonly used local optimization methods for copula parameter estimation often get trapped in local minima. The proposed method, however, addresses this limitation and improves describing the dependence structure. MvCAT also enables evaluation of uncertainties relative to the length of record, which is fundamental to a wide range of applications such as multivariate frequency analysis.

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Copula Representation of Bivariate L-Moments: A New Estimation Method for Multiparameter 2-Dimensional Copula Models

Cited by 8 publications

References 30 publications

Investigation of hydrological time series using copulas for detecting catchment characteristics and anthropogenic impacts

Investigation of hydrological time series using copulas for detecting catchment characteristics and anthropogenic impacts

Homogeneity testing for spatially correlated data in multivariate regional frequency analysis

Multivariate Copula Analysis Toolbox (MvCAT): Describing dependence and underlying uncertainty using a Bayesian framework

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