NONPARAMETRIC APPROACH FOR NON-GAUSSIAN VECTOR STATIONARY-PROCESSES

Suppose that {z(t)} is a non-Gaussian vector stationary process with s pectral density matrix f(lambda). In this paper we consider the testin g problem H: integral(-pi)(pi) K{f(lambda} d lambda = c against A: int egral(-pi)(pi) K{f(lambda)} d lambda not equal c, where K{.} is an app ropriate function and c is a given constant. For this problem we propo se a test T-n based on integral(-pi)(pi) K{(f) over cap(n)(lambda)} d lambda, where (f) over cap(n)$(lambda) is a nonparametric spectral est imator of f(lambda), and we define an efficacy of T-n under a sequence of nonparametric contiguous alternatives. The efficacy usually depnds on the fourth-order cumulant spectra f(4)(z) of z(t). If it does not depend on f(4)(z), we say that T-n is non-Gaussian robust. We will giv e sufficient conditions for T-n to be non-Gaussian robust. Since our t est setting is very wide we can apply the result to many problems in t ime series. We discuss interrelation analysis of the components of {z( t)} and eigenvalue analysis of f(lambda). The essential point of our a pproach is that we do not assume the parametric form of f(lambda). Als o some numerical studies are given and they confirm the theoretical re sults. (C) 1996 Academic Press, Inc.