Copula Construction Research Articles

A diagnostic test for specification of copulas under censorship

We propose a copula specification test for copula-based multivariate survival models under censorship. This flexible test is applicable to both Archimedean and non-Archimedean copulas and provides useful pointers for alternative copula construction when a null distribution is rejected. It is shown to be consistent and asymptotically distribution free. We demonstrate its good finite sample performance via Monte Carlo simulations. We apply this test to an insurance dataset on losses and expenses. Our test rejects the hypothesis of Gaussian copula. Furthermore, its diagnostic information suggests an alternative copula specification that captures the extreme-value dependence exhibited in the data.

Copula-based multivariate flood probability construction: a review

Basin perspective hydrology and hydraulic water-related queries often demanding an accurate estimation of flood exceedance probabilities or return periods for assessing hydrologic risk. The research on the advancements of flood probability modelling contributed to reduction of flood risk, damage property and human life losses associated with the occurrence of flood events. Higher degree of uncertainty and complex flood dependence structure did not facilitate for their accurate prediction through deterministic approaches, which often demand a probability distribution framework. Unreliability of univariate frequency analysis under parametric or non-parametric framework would be an attribute for underestimation or overestimation of flood risk. Multivariate distribution framework facilitating a comprehensive understanding of flood structure for various possible occurrence combinations among the flood-related random vectors (i.e. flood peak flow, volume and duration). In this literature, copula function is recognized as a highly flexible tool for establishing multivariate joint dependency and their associated return periods in comparison with traditional multivariate functions. The incorporation of vine or pair-copula constructions (or PCC) further exaggerated the efforts of higher dimension copula construction, in terms of precision level in their estimated quantiles, under the minimum information concept. This review explored the efficacy of copula-based methodology for tackling multivariate design problems and can be used as a guideline for water practioner and hydrologist.

The grammaticalisation of a copula in vernacular Arabic

It is standardly assumed that Arabic copula constructions with present tense interpretation involve either a null copula or a pronominal copula. This paper provides evidence that some Arabic vernaculars are developing a three-way split, with an additional copula form occurring in some predicational copula clauses. This form has grammaticalised out of the active participle form of the posture verb meaning ‘sit’. While at different stages of development in different varieties of Arabic, this emergent copula shows the characteristics of a locative (temporary and/or permanent, depending on the variety) or contingent state (stage-level) copula, standing in contrast with the use of a null copula strategy, which marks characterising/defining individual-level properties. We propose a grammaticalisation trajectory for this copula in the Arabic varieties based on the comparative patterns of variation across those dialects, showing that the trajectory postulated for other, typologically distinct languages is also applicable to Arabic and hence providing further support for it. We suggest that there is also evidence of a distinct but related trajectory in some varieties which have developed a semantically bleached lexical existential predicate from this same form. We provide further evidence of the importance of the temporary/permanent split in the copula systems of Arabic arguing that the developing split copula system based on the active participle of the ‘sit’ verb is in alignment with the development of two other parallel split copula systems in other geographically diverse Arabic varieties, which use different bases/strategies for grammaticalisation.

The efficiency of constructed bivariate copulas for MEWMA and Hotelling’s T2 control charts

A multivariate exponentially weighted moving average (MEWMA) and Hotelling’s T2 control charts are types of multivariate control charts for monitoring the mean vector. In this paper, we propose an efficient construction of bivariate copulas on MEWMA and Hotelling’s T2 control charts. Observations are classified with Kendall’s tau values as weak, moderate, and strong positive dependence by using a Monte Carlo simulation to measure the average run length as a performance metric. The numerical results obtained from the simulation show that the performances of the MEWMA and Hotelling’s T2 control charts were similar for small shifts () but the MEWMA control chart showed higher performance for moderate to large shifts.

Hierarchy effects in copula constructions

AbstractThis paper develops a generalization about agreement in German copula constructions described in Coon et al. (2017), and proposes an analysis that ties it to other well-established hierarchy phenomena. Specifically, we show that “assumed-identity” copula constructions in German exibit both person and number hierarchy effects, and that these extend beyond the “non-canonical” or “inverse” agreement patterns described in previous work on copula constructions (e.g., Béjar and Kahnemuyipour 2017 and works cited there). We present experimental evidence to support this generalization, and then develop an account that unifies it with hierarchy phenomena in other languages, with a focus on PCC effects. Specifically, we propose that what German copula constructions have in common with PCC environments is that there are multiple accessible DPs in the domain of a single agreement probe, the lower of which is more featurally specified than the higher (see, e.g., Béjar and Rezac 2003, 2009; Anagnostopoulou 2005; Nevins 2007). We also offer an explanation as to why number effects are present in German copula constructions but notably absent in PCC effects. We then place our account within the broader context of constraints on predication structures.

The key role of convexity in some copula constructions

We start with some binary (“outer”) copula, apply it to an arbitrary binary (“inner”) copula and its dual (the latter being transformed by some real function) and ask under which conditions the result is again a binary copula. Sufficient convexity conditions for the transformation function and for the “outer” copula (ultramodularity and Schur concavity) are given, thus generalizing the scenarios considered in Klement et al. (J Math Inequal 11(2):361–381, 2017) and Manstavičius and Bagdonas (Fuzzy Sets Syst 354:48–62, 2019). In general, these sufficient conditions are not necessary (and a counterexample is provided), but in some distinguished cases necessary and sufficient conditions can be given. Several well-known families of copulas can be obtained in this way. We also present a few extensions for special “outer”/“inner” copulas and/or transformation functions, as well as some counterexamples.

Modelling temporal dependence of realized variances with vines

Models for realized volatility that take the specific form of temporal dependence into account are proposed. Current popular methods use the idea of mixed frequencies for forecasting realized volatility, but neglect the potential non-linear and non-monotonic temporal dependence. The proposed approach utilizes vine copulas to mimic different memory properties. HAR, MIDAS and bivariate copulas, which can be seen as special cases of the suggested modeling framework, are chosen as benchmarks. All models are evaluated within an extensive empirical study both in- and out-of-sample and their forecasting ability is compared statistically. The results suggest that one specific vine copula construction is significantly superior over the considered benchmarks in modeling time dependencies of realized volatilities.

Remarks on the Historical Development and Syntax of the Copula in North-Eastern Neo-Aramaic Dialects

Abstract This paper examines some aspects of the morphology and syntax of the copula in the North-Eastern Neo-Aramaic (NENA) dialects. The first part proposes a possible pathway for the diachronic development of the morphology of the copula, with particular attention to the innovative inflection of the 3rd person. It is argued that this originated in deictic constructions that were reanalysed as deictic copulas. The second part offers a functional explanation for the position of the copula before or after the predicate. It is argued that many constructions that place the copula before the predicate should be interpreted as thetic sentences, whereas those that place the copula after the predicate should be interpreted as categorical sentences. The thetic structures are likely to have developed by the replication of the pattern of copula constructions in Kurdish.

Symmetry and asymmetry in the Hebrew copula construction

The copula construction in Hebrew has received much attention in the linguistic literature. Nevertheless, one non-canonical variant has been largely neglected. In this variant the copula, flanked by two NPs, exhibits agreement with the post-copular NP, contrary to the canonical variant, where the agreement controller is the initial NP. This phenomenon challenges the notion of subject and its relation to agreement. The current corpus-based study investigates the word order and agreement patterns exhibited by the Hebrew copular constructions and shows that their distribution is largely motivated by information structure considerations. The proposed analysis accounts for the syntactic symmetry and semantic asymmetry between the two NPs.

Generalized phi-transformations of aggregation functions

In this paper we present a new method of construction of aggregation functions based on the so-called bijective chains, that generalizes the standard isomorphic ϕ-transforms of aggregation functions. It covers, among others, several known construction methods, such as the construction of copulas based on ultramodular copulas, or particular ordinal sums of aggregation functions, e.g., of t-norms, copulas, t-conorms. Several properties of the proposed construction method are discussed and exemplified.

Soil Moisture Drought in Europe: A Compound Event of Precipitation and Potential Evapotranspiration on Multiple Time Scales

AbstractCompound events are extreme impacts that depend on multiple variables that need not be extreme themselves. In this study, we analyze soil moisture drought as a compound event of precipitation and potential evapotranspiration (PET) on multiple time scales related to both meteorological drought and heat waves in wet, transitional, and dry climates in Europe during summer. Drought indices that incorporate PET to account for the effect of temperature on drought conditions are sensitive to global warming. However, as evapotranspiration (ET) is moisture limited in dry climates, the use of such drought indices has often been criticized. We therefore assess the relevance of the contributions of both precipitation and PET to the estimation of soil moisture drought. Applying a statistical model based on pair copula constructions to data from FluxNet sites in Europe, we find at all sites that precipitation exerts the main control over soil moisture drought. At wet sites PET is additionally required to explain the onset, severity, and persistence of drought events over different time scales. At dry sites, where ET is moisture limited in summer, PET does not improve the estimation of soil moisture. In dry climates, increases in drought severity measured by indices incorporating PET may therefore not indicate further drying of soil but the increased availability of energy that can contribute to other environmental hazards such as heat waves and wildfires. We therefore highlight that drought indices including PET should be interpreted within the context of the climate and season in which they are applied in order to maximize their value.

Copula approaches for modeling cross-sectional dependence of data breach losses

Many experts claim that cyber risks are correlated, but there is not much supporting empirical evidence. We consider 3327 data breach events from 2005 to 2016 and identify a significant asymmetric dependence of monthly losses in two cross-sectional settings: cross-industry losses in four categories by breach types (hacking, lost electronic device, unintended disclosure and insider breach) and cross-breach type losses in five categories by industries (banking and insurance, government, medical service, retail/other business and educational institution). To identify the method that best fits the dependence structure of the dataset, we implement copula modeling by separating the dependence into pairwise non-zero losses and zero loss arrivals. We model the former by pair copula construction (PCC) allowing for the flexible choice of copula functions, whereas the latter is modeled by Gaussian copula. We illustrate the usefulness of our results in two applications to risk measurement and pricing. Our findings are important for risk managers and actuaries who are designing cyber-insurance policies.

Constructions of copulas with given diagonal (and opposite diagonal) sections and some generalizations

Abstract We review various methods for constructing bivariate copulas with given diagonal sections from seminal work to the most recent research on copulas with given diagonal and opposite diagonal sections. A survey on a generalization of copulas with given diagonal plane sections in higher dimensions and other sections that generalize the diagonal and opposite diagonal sections is of particular interest.

A class of bivariate copula mappings

We provide necessary and sufficient conditions on a function f:[0,1]→R+ so that Hf(C)(u,v)=C(u,v)f(1−u−v+C(u,v)), (u,v)∈[0,1]2 is a copula for any bivariate copula C. Then we discuss several important bivariate copula properties preserved or not by the mapping C↦Hf(C). The considered bivariate copula construction unifies many examples found in the literature and opens a qualitatively new way of obtaining new copulas by simply using a function f which has to satisfy a few easily verifiable properties.

Construction of bivariate asymmetric copulas

Construction of bivariate asymmetric copulas

Inversion copulas from nonlinear state space models with an application to inflation forecasting

We propose the construction of copulas through the inversion of nonlinear state space models. These copulas allow for new time series models that have the same serial dependence structure as a state space model, but with an arbitrary marginal distribution, and flexible density forecasts. We examine the time series properties of the copulas, outline serial dependence measures, and estimate the models using likelihood-based methods. Copulas constructed from three example state space models are considered: a stochastic volatility model with an unobserved component, a Markov switching autoregression, and a Gaussian linear unobserved component model. We show that all three inversion copulas with flexible margins improve the fit and density forecasts of quarterly U.S. broad inflation and electricity inflation.

Application of selection and estimation regular vine copula on go public company share

The accuracy of financial risk management involving a large number of assets is needed, but information about dependencies among assets cannot be adequately analyzed. To analyze dependencies on a number of assets, several tools have been added to standard multivariate copula. However, these tools have not been adequately used in apps with higher dimensions. The bivariate parametric copula families can be used to solve it. The multivariate copula can be built from the bivariate parametric copula which is connected by a graphical representation to become Pair Copula Constructions (PCCs) or vine copula. The application of C-vine and D-vine copula have been used in some researches, but the use of C-vine and D-vine copula is more limited than R-vine copula. Therefore, this study used R-vine copula to provide flexibility for modeling complex dependencies on a high dimension. Since copula is a static model, while stock values change over time, then copula should be combined with the ARMA- GARCH model for modeling the movement of shares (volatility). The objective of this paper is to select and estimate R-vine copula which is used to analyze PT Jasa Marga (Persero) Tbk (JSMR), PT Waskita Karya (Persero) Tbk (WSKT), and PT Bank Mandiri (Persero) Tbk (BMRI) from august 31, 2014 to august 31, 2017. From the method it is obtained that the selected copulas for 2 edges at the first tree are survival Gumbel and the copula for edge at the second tree is Gaussian.

Pair Copula Constructions for Insurance Experience Rating

ABSTRACTIn nonlife insurance, insurers use experience rating to adjust premiums to reflect policyholders’ previous claim experience. Performing prospective experience rating can be challenging when the claim distribution is complex. For instance, insurance claims are semicontinuous in that a fraction of zeros is often associated with an otherwise positive continuous outcome from a right-skewed and long-tailed distribution. Practitioners use credibility premium that is a special form of the shrinkage estimator in the longitudinal data framework. However, the linear predictor is not informative especially when the outcome follows a mixed distribution. In this article, we introduce a mixed vine pair copula construction framework for modeling semicontinuous longitudinal claims. In the proposed framework, a two-component mixture regression is employed to accommodate the zero inflation and thick tails in the claim distribution. The temporal dependence among repeated observations is modeled using a sequence of bivariate conditional copulas based on a mixed D-vine. We emphasize that the resulting predictive distribution allows insurers to incorporate past experience into future premiums in a nonlinear fashion and the classic linear predictor can be viewed as a nested case. In the application, we examine a unique claims dataset of government property insurance from the state of Wisconsin. Due to the discrepancies between the claim and premium distributions, we employ an ordered Lorenz curve to evaluate the predictive performance. We show that the proposed approach offers substantial opportunities for separating risks and identifying profitable business when compared with alternative experience rating methods. Supplementary materials for this article are available online.

The Formation of the Copula Function of Wei 为 and the Nature of the “Wei 为 V” Construction

This paper aims to explain the development of the copula function of wei 为and to show that wei in the “wei V” construction is a copula during pre-Han times, rather than a passive marker. Therefore, in essence, the “wei V” construction is a copula construction rather than a passive construction. In this analysis, we pay special attention to the “yi 以X wei 为Y” construction and draw the following conclusions: (1) the generalized copula function of wei derives from the “yi X wei Y” construction because of the disposal function of yi, and because wei absorbed the characteristics of the “yi X wei Y” construction. This conclusion is based on the observation that the unique features of wei as a copula are congruent with its function in the “yi X wei Y” construction, and that the change from “V yi wei” to “V wei” indicates that wei replaced “yi wei” to a certain degree. (2) “X wei V” is an alternative pattern of “yi X wei V” when a causer (C) does not appear in the same clause with wei. These observations are supported by the fact that “yi X wei V” and “X wei V” have the same (low) frequency, and are both very limited in their semantic range, and that their exchangeability does not have any influence on their semantics. (3) “Wei A V” is formed through the omission of yi in the “yi X wei A V” or, alternatively, through the addition of the agent A in “wei V”, whereas “wei A (zhi) suo V” is the consequence of “A (zhi) suo V” replacing “A V” in “wei A V”. Therefore, none of the wei constructions in pre-Qin should be regarded as syntactically functioning as passive constructions. Rather, “wei A suo V” became a common passive construction only in the Han Dynasty.

Bivariate quadratic copula constructions

In this study, we present the concept of quadratic copula constructions using two arbitrary copulas. We characterize all quadratic polynomials of four variables whose composition with any two copulas always results in a copula. We show that these polynomials form a compact convex set in a seven-dimensional vector space. We also apply the result to obtain a new family of copulas.