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...

In this paper, we show how to estimate consistently the degree of fractional integration at a given frequency K, for both stationary and non stationary long-memory process. The statistics used are the periodigram for values Kn which converge to K with an appropriate rate. We also introduce tests...

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...