Testing for equality between two copulas

Tests are proposed for the hypothesis that the underlying copula of a continuous random pair is symmetric. The procedures are based on Cramér-von Mises and Kolmogorov-Smirnov functionals of a rank-based empirical process whose largesample behaviour is obtained. The asymptotic validity of a re-sampling method to compute P values is also established. The technical arguments supporting the use of a Chi-squared test due to Jasson are also presented. A power study suggests that the proposed tests are more powerful than Jasson's procedure under many scenarios of copula asymmetry. The methods are illustrated on a nutrient data set.

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“…,Rémillard and Scaillet (2009),, and.FollowingBücher and Dette (2010), fix M ∈ N and for each h ∈ {1, . .…”

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confidence: 99%

Tests of symmetry for bivariate copulas

2011

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“…It is important to note that the sample size played a key role in deciding whether empirical copulas can be regarded as different or not. In the answer to the first science question when the test of Remillard and Scaillet (2009) was adopted for the full data sets, we observed significantly different empirical copulas in a number of cases. When subsamples were drawn to verify the conclusions, however, the test showed decreased ability to yield significant results.…”

Section: Discussionmentioning

confidence: 93%

“…In this paper, we are interested in the similarity (equality, in statistical sense) of empirical copulas of pairs of flood peaks and corresponding event volumes, which is tested by the approach of Remillard and Scaillet (2009). It is based on a Cramér-von Mises type of distance measure:…”

Section: Copula Methods and Analysesmentioning

confidence: 99%

A regional comparative analysis of empirical and theoretical flood peak-volume relationships

Szolgay

Gaál

Bacigál

et al. 2016

Journal of Hydrology and Hydromechanics

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This paper analyses the bivariate relationship between flood peaks and corresponding flood event volumes modelled by empirical and theoretical copulas in a regional context, with a focus on flood generation processes in general, the regional differentiation of these and the effect of the sample size on reliable discrimination among models. A total of 72 catchments in North-West of Austria are analysed for the period . From the hourly runoff data set, 25 697 flood events were isolated and assigned to one of three flood process types: synoptic floods (including long-and short-rain floods), flash floods or snowmelt floods (both rain-on-snow and snowmelt floods). The first step of the analysis examines whether the empirical peak-volume copulas of different flood process types are regionally statistically distinguishable, separately for each catchment and the role of the sample size on the strength of the statements. The results indicate that the empirical copulas of flash floods tend to be different from those of the synoptic and snowmelt floods. The second step examines how similar are the empirical flood peak-volume copulas between catchments for a given flood type across the region. Empirical copulas of synoptic floods are the least similar between the catchments, however with the decrease of the sample size the difference between the performances of the process types becomes small. The third step examines the goodness-of-fit of different commonly used copula types to the data samples that represent the annual maxima of flood peaks and the respective volumes both regardless of flood generating processes (the traditional engineering approach) and also considering the three process-based classes. Extreme value copulas (Galambos, Gumbel and Hüsler-Reiss) show the best performance both for synoptic and flash floods, while the Frank copula shows the best performance for snowmelt floods. It is concluded that there is merit in treating flood types separately when analysing and estimating flood peak-volume dependence copulas; however, even the enlarged dataset gained by the process-based analysis in this study does not give sufficient information for a reliable model choice for multivariate statistical analysis of flood peaks and volumes.

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“…For the rest of the cases, i.e., excluding the first tree, the conditional models include different copulas with Independent, Gaussian, Gumbel, and Frank [71] accounting for around 70% of the selected families. A test developed by [72] is applied to assess the goodness of fit of the different Vine copulas. The authors propose a test of equality between two dependence structures estimated based on empirical copulas.…”

Section: Modeling Of Events Occurring Simultaneouslymentioning

confidence: 99%

Spatio-Temporal Synthesis of Continuous Precipitation Series Using Vine Copulas

Poduje

Haberlandt

2018

Water

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Long and continuous series of precipitation in a high temporal resolution are required for several purposes, namely, urban hydrological applications, design of flash flood control structures, etc. As data of the temporally required resolution is often available for short period, it is advantageous to develop a precipitation model to allow for the generation of long synthetic series. A stochastic model is applied for this purpose, involving an alternating renewal process (ARP) describing a system consisting of spells that can take two possible states: wet or dry. Stochastic generation of rainfall time series using ARP models is straight forward for single site simulation. The aim of this work is to present an extension of the model to spatio-temporal simulations. The proposed methodology combines an occurrence model to define in which locations rainfall events occur simultaneously with a multivariate copula to generate synthetic events. Rainfall series registered in different regions of Germany are used to develop and test the methodology. Results are compared with an existing method in which long independent time series of rainfall events are transformed to spatially dependent ones by permutation of their order. The proposed model shows to perform as a satisfactory extension of the ARP model for multiple sites simulations.

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Testing for equality between two copulas

Cited by 158 publications

References 22 publications

Tests of symmetry for bivariate copulas

Tests of symmetry for bivariate copulas

A regional comparative analysis of empirical and theoretical flood peak-volume relationships

Spatio-Temporal Synthesis of Continuous Precipitation Series Using Vine Copulas

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