Generalized Additive Models for Conditional Dependence Structures

Abstract

We develop a generalized additive modeling framework for taking into account the effect of predictors on the dependence structure between two variables. We consider dependence or concordance measures that are solely functions of the copula, because they contain no marginal information: rank correlation coefficients or tail-dependence coefficients represent natural choices. We propose a maximum penalized log-likelihood estimator, derive its $\sqrt{n}$-consistency and asymptotic normality, discuss details of the estimation procedure and the selection of the smoothing parameter. Finally, we present the results from a simulation study and apply the new methodology to a real dataset. Using intraday asset returns, we show that an intraday dependence pattern, due to the cyclical nature of market activity, is shaped similarly to the individual conditional second moments.

Keywords: Conditional rank correlations, Copula, Penalized log-likelihood, Regression splines, Semiparametric modeling, Intraday financial returns

JEL Classification: C12, C13, C14, C51, C52, C53