Testing for independence between two covariance stationary time series

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A Kernel Independence Test for Random Processes (2014, methodology): “Prior work in the context of dependency tests of two time series includes cross covariance based tests e.g. (Haugh, 1976; Hong, 1996; Shao, 2009); and a Generalized Association Measure based criterion (Fadlallah et al., 2012).”
Testing nonparametric and semiparametric hypotheses in vector stationary processes (2008, methodology): “[40] Y. Hong, Testing for independence between two covariance stationary time series, Biometrika 83 (1996) 615–625.”
A GENERALIZED PORTMANTEAU TEST FOR INDEPENDENCE BETWEEN TWO STATIONARY TIME SERIES (2008, methodology): “We conjecture that for fixed alternatives, the rate at which Tn (Tn(θ̂ ), Tn(γ̂ )) diverges is n/ √ Bn ; compare Theorem 4 in Hong (1996) and Theorem 2 in Bouhaddioui and Roy (2006).”
Granger Causality in Risk and Detection of Extreme Risk Spillover Between Financial Markets (2009, background): “Hong (1996) shows that over a class of kernels K(τ ) = { k(·) : k(0) = 1, ∫ ∞ −∞ k(z)dz ∞, k2 ≡ lim z→0 1− k(z) z2 ∈ (0,∞) } which includes the Parzen and Quadratic-Spectral kernels (but not the Bartlett kernel), the Daniell kernel kD(z) = sin(πz)/πz minimizes ∫ ∞ 0 k 4(z)dz.”