Open Access
2019 Inference on local causality and tests of non-causality in time series
Taoufik Bouezmarni, Félix Camirand Lemyre, Jean-François Quessy
Electron. J. Statist. 13(2): 4121-4156 (2019). DOI: 10.1214/19-EJS1623


The study of the causal relationships in a stochastic process $(Y_{t},Z_{t})_{t\in\mathbb{Z}}$ 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 ${{(Y_{t+1},Z_{t})}}$ given ${{Y_{t}}}$. The measures of Granger causality proposed so far are global in the sense that if the relationship between ${{Y_{t+1}}}$ and ${{Z_{t}}}$ changes with the value taken by ${{Y_{t}}}$, this may not be captured. To circumvent this limitation, this paper proposes local causality measures based on the conditional copula of ${{(Y_{t+1},Z_{t})}}$ given ${{Y_{t}}}=x$. Exploiting results by [5] on the asymptotic behavior of two kernel-based conditional copula estimators under $\alpha$-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.


Download Citation

Taoufik Bouezmarni. Félix Camirand Lemyre. Jean-François Quessy. "Inference on local causality and tests of non-causality in time series." Electron. J. Statist. 13 (2) 4121 - 4156, 2019.


Received: 1 May 2018; Published: 2019
First available in Project Euclid: 9 October 2019

zbMATH: 07116199
MathSciNet: MR4017530
Digital Object Identifier: 10.1214/19-EJS1623

Primary: 62G99
Secondary: 62M99

Keywords: $\alpha$-mixing processes , Bandwidth selection , conditional copula , Kendall and Spearman dependence measures , local linear kernel estimation , weak convergence

Vol.13 • No. 2 • 2019
Back to Top