Testing for Independence between Two stationary Time Series
via the Empirical Characteristic Function

Yongmiao Hong

This paper proposes an asymptotic one-sided $N(0,1)$ test for independence between two stationary time series using the empirical characteristic function. Unlike the tests based on the cross-correlation function (e.g. Haugh, 1976; Hong, 1996; Koch & Yang 1986), the proposed test has power against all pairwise cross-dependencies, including those with zero cross-correlation. By differentiating the empirical characteristic function at the origin, the present approach yields a modified version of Hong's (1996) test, which in turn generalizes Haugh's (1976) test. Other new tests can be derived by further differentiating the empirical characteristic function properly. A simulation study compares the new test with those of Haugh (1976), Hong (1996) and Koch & Yang (1986) in finite samples; the results show that the new test has reasonable sizes and good powers against linear and nonlinear cross-dependencies.

Key Words: Asymptotic normality; Cramer-von Mises statistic; Empirical characteristic function; Independence; Kernel function; Multivariate time series.
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