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

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 periodogram for some well-chosen sequence of frequencies. In particular, we investigate the power properties of the tests from both theoretical and empirical approach. We first derive the limiting properties of the tests under a sequence of local alternatives. Then, we use Monte Carlo experiments to study the size and power of the tests for two particular ARMA models. The distribution of the statistics in finite sample is also investigated.