Semiparametric robust tests on seasonal or cyclical long memory time series

The concept of SCLM (seasonal or cyclical long memory) implies the existence of one or more spectral poles or zeros. The processes traditionally used to model such a behaviour assume the same persistence across different frequencies. In this paper, we propose semiparametric Wald and Lagrange multiplier (LM) tests of the equality of memory parameters at different frequencies (extendable to other linear restrictions) which are standard in the sense that they have well known χ2 distributions under the null hypothesis – although Gaussianity is nowhere assumed – and are consistent against constant and local alternatives. They have also the advantage of being robust against misspecification at frequencies distant from those of interest. Their finite sample performance is compared with the asymptotically locally efficient Robinson's tests (1994). An empirical application to a UK inflation series is also included.