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

Abstract

Non parametric and parametric estimation for the spectral density of a stationary process is a well-known topic, except when the spectrum vanishes for some frequency. Indeed, for this frequency, the limit law degenerates, and traditional inference no longer applies. The paper introduces non parametric tests of this hypothesis, which exploit the asymptotic behavior of the periodogram for some well-chosen sequence of frequencies. In particular, statistics free from nuisance parameters are derived, and conditional heteroskedasticity of unknown form is allowed. As an application, stationarity tests against seasonal unit-root alternatives are developed.

Keywords: Stationarity, Spectral density, Moving average unit root, Non parametric tests

JEL Classification: C12, C14, C22