Omnibus Goodness-of-Fit Tests for Copulas: A Review and a Power Study
01 Nov 2006-pp 1-43
TL;DR: In this paper, the authors present a critical review of blanket tests for goodness-of-fit testing of copula models and suggest new ones, and conclude with a number of practical recommendations.
Abstract: Many proposals have been made recently for goodness-of-fit testing of copula models. After reviewing them briefly, the authors concentrate on "blanket tests", i.e., those whose implementation requires neither an arbitrary categorization of the data nor any strategic choice of smoothing parameter, weight function, kernel, window, etc. The authors present a critical review of these procedures and suggest new ones. They describe and interpret the results of a large Monte Carlo experiment designed to assess the effect of the sample size and the strength of dependence on the level and power of the blanket tests for various combinations of copula models under the null hypothesis and the alternative. To circumvent problems in the determination of the limiting distribution of the test statistics under composite null hypotheses, they recommend the use of a double parametric bootstrap procedure, whose implementation is detailed. They conclude with a number of practical recommendations.
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TL;DR: This work uses the pair-copula decomposition of a general multivariate distribution and proposes a method for performing inference, which represents the first step towards the development of an unsupervised algorithm that explores the space of possible pair-Copula models, that also can be applied to huge data sets automatically.
Abstract: Building on the work of Bedford, Cooke and Joe, we show how multivariate data, which exhibit complex patterns of dependence in the tails, can be modelled using a cascade of pair-copulae, acting on two variables at a time. We use the pair-copula decomposition of a general multivariate distribution and propose a method for performing inference. The model construction is hierarchical in nature, the various levels corresponding to the incorporation of more variables in the conditioning sets, using pair-copulae as simple building blocks. Pair-copula decomposed models also represent a very flexible way to construct higher-dimensional copulae. We apply the methodology to a financial data set. Our approach represents the first step towards the development of an unsupervised algorithm that explores the space of possible pair-copula models, that also can be applied to huge data sets automatically.
1,744 citations
TL;DR: This article examined the extent of the current global crisis and the contagion effects it induces by conducting an empirical investigation of the extreme financial interdependences of some selected emerging markets with the US.
Abstract: The paper examines the extent of the current global crisis and the contagion effects it induces by conducting an empirical investigation of the extreme financial interdependences of some selected emerging markets with the US. Several copula functions that provide the necessary flexibility to capture the dynamic patterns of fat tail as well as linear and nonlinear interdependences are used to model the degree of cross-market linkages. Using daily return data from Brazil, Russia, India, China (BRIC) and the US, our empirical results show strong evidence of time-varying dependence between each of the BRIC markets and the US markets, but the dependency is stronger for commodity-price dependent markets than for finished-product export-oriented markets. We also observe high levels of dependence persistence for all market pairs during both bullish and bearish markets.
504 citations
TL;DR: This survey reviews the large and growing literature on copula-based models for economic and financial time series and surveys estimation and inference methods and goodness-of-fit tests for such models, as well as empirical applications of these copulas.
500 citations
TL;DR: In this paper, the role of gold as a safe haven or hedge against the US dollar (USD) using copulas to characterize average and extreme market dependence between gold and the USD was assessed.
Abstract: We assess the role of gold as a safe haven or hedge against the US dollar (USD) using copulas to characterize average and extreme market dependence between gold and the USD. For a wide set of currencies, our empirical evidence revealed (1) positive and significant average dependence between gold and USD depreciation, consistent with the fact that gold can act as hedge against USD rate movements, and (2) symmetric tail dependence between gold and USD exchange rates, indicating that gold can act as an effective safe haven against extreme USD rate movements. We evaluate the implications for mixed gold-currency portfolios, finding evidence of diversification benefits and downside risk reduction that confirms the usefulness of gold in currency portfolio risk management.
430 citations
TL;DR: The authors show how the possibility of ties that results from atoms in the probability distribution invalidates various familiar relations that lie at the root of copula theory in the continuous case.
Abstract: The authors review various facts about copulas linking discrete distributions. They show how the possibility of ties that results from atoms in the probability distribution invalidates various familiar relations that lie at the root of copula theory in the continuous case. They highlight some of the dangers and limitations of an undiscriminating transposition of modeling and inference practices from the continuous setting into the discrete one.
427 citations
References
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Book•
01 Jan 1999
TL;DR: This book discusses the fundamental properties of copulas and some of their primary applications, which include the study of dependence and measures of association, and the construction of families of bivariate distributions.
Abstract: The study of copulas and their role in statistics is a new but vigorously growing field. In this book the student or practitioner of statistics and probability will find discussions of the fundamental properties of copulas and some of their primary applications. The applications include the study of dependence and measures of association, and the construction of families of bivariate distributions. This book is suitable as a text or for self-study.
8,626 citations
TL;DR: Introduction.
Abstract: Introduction. Aspects of Interpretation. Technical Considerations. Statistical Analysis. Special Methods for Joint Responses. Some Examples. Strategical Aspects. More Specialized Topics. Appendices.
3,913 citations
Book•
01 Apr 1986
TL;DR: In this paper, a broad cross-section of the literature available on one-dimensional empirical processes is summarized, with emphasis on real random variable processes as well as a wide-ranging selection of applications in statistics.
Abstract: Here is the first book to summarize a broad cross-section of the large volume of literature available on one-dimensional empirical processes. Presented is a thorough treatment of the theory of empirical processes, with emphasis on real random variable processes as well as a wide-ranging selection of applications in statistics. Featuring many tables and illustrations accompanying the proofs of major results, coverage includes foundations - special spaces and special processes, convergence and distribution of empirical processes, alternatives and processes of residuals, integral tests of fit and estimated empirical processes and martingale methods.
2,774 citations
2,735 citations
TL;DR: In this article, a related model for association in bivariate survivorship time distributions is proposed for the analysis of familial tendency in disease incidence, which is related to more specifically epidemiological models.
Abstract: SUMMARY The application of Cox's (1972) regression model for censored survival data to epidemiological studies of chronic disease incidence is discussed. A related model for association in bivariate survivorship time distributions is proposed for the analysis of familial tendency in disease incidence. The possible extension of the model to general multivariate survivorship distributions is indicated. This paper is concerned with a problem in the analysis of epidemiological studies of chronic disease incidence. In contrast with problems in the epidemiology of infectious disease, such analysis usually assumes that incidence of disease in different individuals represents independent events, the occurrence of which is influenced by measurable factors describing individuals and their environment. However, in the study of familial tendency in chronic disease incidence, this assumption is called into question. Comparisons of parents and offspring and sibling comparisons investigate possible relationships between disease incidence in related individuals and such studies provide interesting analytical difficulties. Here, this problem is treated as one of estimating association in multivariate life tables. In ? 2 it is shown that epidemiological incidence studies may be regarded as being concerned primarily with the study of the distribution of the age at incidence and that Cox's (1972) regression model for the analysis of censored survival time data may readily be applied to incidence data and is closely related to more specifically epidemiological models. In later sections, a related model for bivariate life tables is developed and applied to the problem of demonstrating association in disease incidence in ordered pairs of individuals. The possible extension of the model into more dimensions is indicated.
2,013 citations