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

58 Pages Posted: 5 Jan 2011

Date Written: December 1999

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

Suggested Citation

Lacroix, Renaud, Testing for Zeros in the Spectrum of an Univariate Stationary Process: Part I (December 1999). Banque de France Working Paper No. 70, Available at SSRN: https://ssrn.com/abstract=1734311 or http://dx.doi.org/10.2139/ssrn.1734311

Renaud Lacroix (Contact Author)

Banque de France ( email )

Paris
France

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