Working Paper Series no. 72: Testing the null hypothesis of stationarity in fractionally integrated models

Abstract

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

Renaud Lacroix
December 1999

Classification JEL : C22.

Keywords : Fractional integration, Long memory parameter, Spectral density, Moving average unit root, Non parametric tests