Abstract:
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The study of the causal relationships in a process (Y_t,Z_t)_{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 (Y_t,Z_{t?1}) given Y_{t?1}. The Granger causality measures proposed so far are global in the sense that if the relationship between Y_t and Z_{t?1} changes with the value taken by Y_{t?1}, this will not necessarily be captured. To circumvent this limitation, this paper proposes local causality measures based on the conditional copula of (Y_t,Z_{t?1}) given Y_{t?1} = x. Exploiting results on the asymptotic behavior of two kernel-based conditional copula estimators under ?-mixing processes, the asymptotic normality of nonparametric estimators of these local measures is deduced and confidence intervals are built; tests of local non-causality are developed as well. The efficiency of the proposed methods is investigated via simulations and their usefulness is illustrated on the time series of Standard & Poor's 500 prices and trading volumes.
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