Nonparametric Conditional Association Measures
Seminar/Forum
The study of the causal relationships in a stochastic process (Yt, Zt)t∈Z is a subject of a particular interest in finance and economy. A widelyused approach is to consider the notion of Granger causality, which in the case of first order Markovian processes is based on the joint distribution function of (Yt, Zt−1) given Yt−1. The measures of Granger causality proposed so far are global in the sense that if the relationship between Yt and Zt−1 changes with the value taken by Yt−1, this may not be captured. To circumvent this limitation, this paper proposes local causality measures based on the conditional copula of (Yt, Zt−1) given Yt−1 = x. Exploiting results on the asymptotic behavior of two kernelbased conditional copula estimators under αmixing, the asymptotic normality of nonparametric estimators of these local measures is deduced and asymptotically valid confidence intervals are built; tests of local noncausality are also developed. The suitability of the proposed methods is investigated with simulations and their usefulness is illustrated on the time series of Standard & Poor’s 500 prices and trading volumes.
Presenter

Dr Félix Lemyre, Université de Sherbrooke