Testing for Zeros in the Spectrum of an Univariate Stationary Process: Part I

Abstract

It is well-known that traditional inference do not apply when the spectral density of a stationary process vanishes for some frequency. This paper examines some properties of several new non parametric tests of this hypothesis which have been recently proposed by Lacroix (1999). These tests exploit the asymptotic behavior of the periodigram for some well-chosen sequence of frequencies. In particular, we investigate the power properties of the tests from both theoretical and empirical approach.