Nonparametric Approach for Non-Gaussian Vector Stationary Processes

✍ Scribed by Masanobu Taniguchi; Madan L. Puri; Masao Kondo

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 743 KB
• Volume: 56
• Category: Article
• ISSN: 0047-259X
• DOI: 10.1006/jmva.1996.0014

✦ Synopsis

Suppose that [z(t)] is a non-Gaussian vector stationary process with spectral density matrix f (*). In this paper we consider the testing problem H: ? &? K[ f (*)] d*=c against A: ? &? K[ f (*)] d*{c, where K[ } ] is an appropriate function and c is a given constant. For this problem we propose a test T n based on ? &? K[ f n (*)] d*, where f n (*) is a nonparametric spectral estimator of f (*), 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 Z 4 of z(t). If it does not depend on f Z 4 , we say that T n is non-Gaussian robust. We will give sufficient conditions for T n to be non-Gaussian robust. Since our test setting is very wide we can apply the result to many problems in time series. We discuss interrelation analysis of the components of [z(t)] and eigenvalue analysis of f (*). The essential point of our approach is that we do not assume the parametric form of f (*). Also some numerical studies are given and they confirm the theoretical results.