an:05712388
Zbl 1187.62083
Fernandes, Marcelo; N??ri, Breno
Nonparametric entropy-based tests of independence between stochastic processes
EN
Econ. Rev. 29, No. 3, 276-306 (2010).
00261635
2010
j
62G10 62M07 62B10 62G20 65C05 62M10 62P05
independence; misspecification testing; nonparametric theory; Tsallis entropy
Summary: This article develops nonparametric tests of independence between two stochastic processes satisfying \(\beta \)-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.