Dynamic copula quantile regressions and tail area dynamic dependence in Forex markets

Abstract

We introduce a general approach to nonlinear quantile regression modelling based on the copula function that defines the dependency structure between the variables of interest. Hence, we extend Koenker and Bassett's (1978. Regression quantiles. Econometrica, 46, no. 1: 33-50.) original statement of the quantile regression problem by determining a distribution for the dependent variable Y conditional on the regressors X, and hence the specification of the quantile regression functions. The approach exploits the fact that the joint distribution function can be split into two parts: the marginals and the dependence function (or copula). We then deduce the form of the (invariably nonlinear) conditional quantile relationship implied by the copula. This can be achieved with arbitrary distributions assumed for the marginals. Some properties of the copula-based quantiles or c-quantiles are derived. Finally, we examine the conditional quantile dependency in the foreign exchange market and compare our quantile approach with standard tail area dependency measures.Copula, Quantile, Regression, dependence, foreign exchange markets,

Archimedean Copulas and Temporal Dependence

“…Chen and Fan (2006) introduced copula-based Markov models to the econometric literature. Following that contribution, a number of related papers have appeared, including Fentaw and Naik-Nimbalkar (2008), Gagliardini and Gouriéroux (2008), Bouyé and Salmon (2009), Chen, Koenker and Xiao (2009), Chen, Wu andYi (2009), Ibragimov (2009), Ibragimov andLentzas (2009), andBeare (2010).…”

Time Irreversible Copula-Based Markov Models

“…This class of models was introduced to the econometric literature by Chen and Fan (2006); subsequent contributions to the subject include Fentaw and NaikNimbalkar (2008), Gagliardini and Gouriéroux (2008), Bouyé and Salmon (2009), Chen, Koenker and Xiao (2009), Chen, Wu and Yi (2009), Ibragimov (2009), Beare (2010Beare ( , 2012, and the recent book by Cherubini et al (2011). The time series of interest is assumed to be a stationary real valued Markov chain.…”

Modelling the bivariate dependence structure of exchange rates before and after the introduction of the euro: a semi-parametric approach

“…For example, stock returns appear to become more related when they are large and negative (lower tail dependence) than when they are large and positive (upper tail dependence), a phenomenon which is known as financial contagion and which cannot be captured by simple correlation (see, for example, Ang and Chen, 2002, Login and Solnik, 2001, Granger and Silvapulle, 2001 and references therein). Copulas are emerging as attractive models for capturing and measuring various forms of dependence, and have found useful applications, especially for the analysis of the behaviour of returns on financial assets (a partial list of recent contributions includes Bouyé and Salmon, 2002, Ang and Bekaert, 2002, Jondeau and Rockinger, 2006, Campbell et al, 2008, Sun et al, 2008.…”