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A dependence metric for possibly nonlinear processes. (English) Zbl 1062.62178
The authors consider a normalization of the Bhattacharya-Matusita-Hellinger measure of dependence given by \(S_{\rho}=2^{-1}\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}(f_1^{1/2}- f_2^{1/2})^2dx\,dy\), where \(f_1=f(x,y)\) is the joint density and \(f_2=g(x)\cdot h(y)\) is the product of the marginal densities of the random variables. The authors consider, using the metric as the basis for permutations, tests for serial independence. Simulations designed to gauge the finite-sample performance of the estimator are considered for a number of popular dependent processes. An application to chaotic series is presented.

MSC:
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G10 Nonparametric hypothesis testing
Software:
NUMAL
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