Nonparametric Entropy-Based Tests of Independence Between Stochastic Processes
提出一种非参数检验方法，用于判断两个随机过程是否独立，利用广义熵度量联合密度与边际密度乘积的差异，并推导渐近性质，通过蒙特卡洛模拟验证了有限样本下的良好表现。
This article develops nonparametric tests of independence between two stochastic processes satisfying β-mixing conditions. The testing strategy boils down to gauging the closeness between the joint and the product of the marginal stationary densities. For that purpose, we take advantage of a generalized entropic measure so as to build a whole family of nonparametric tests of independence. We derive asymptotic normality and local power using the functional delta method for kernels. As a corollary, we also develop a class of entropy-based tests for serial independence. The latter are nuisance parameter free, and hence also qualify for dynamic misspecification analyses. We then investigate the finite-sample properties of our serial independence tests through Monte Carlo simulations. They perform quite well, entailing more power against some nonlinear AR alternatives than two popular nonparametric serial-independence tests.