Nonparametric Measures of Local Causality and Tests of Local Non-Causality in Time Series

• Activity Number: 87 - Invited ePoster Session: a Statistical Smörgåsbord
• Type: Invited
• Date/Time: Sunday, July 29, 2018 : 8:30 PM to 10:30 PM
• Sponsor: SSC
• Author(s): Felix Camirand Lemyre* and Taoufik Bouezmarni and Jean-François Quessy
• Companies: School of mathematics and statistics, University of Melbourne and Université de Sherbrooke and Université du Québec à Trois-Rivières
• Keywords: a-mixing processes; conditional copula; Kendall's tau; local linear kernel estimation; Spearman's rho; weak convergence

Abstract

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.