Nonparametric Conditional Association Measures
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 widely-used 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 kernel-based conditional copula estimators under α-mixing, the asymptotic normality of nonparametric estimators of these local measures is deduced and asymptotically valid confidence intervals are built; tests of local non-causality 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.
Dr Félix Lemyre, Université de Sherbrooke