Several semiparametric estimates of the memory parameter in standard long memory time series are now available. They consider only local behaviour of the spectrum near zero frequency, about which the spectrum is symmetric. However longrange dependence can appear as a spectral pole at any Nyqvist frequency (re¯ecting seasonal or cyclical long-memory), where the spectrum need display no such symmetry. We introduce Seasonal/Cyclical Asymmetric Long Memory (SCALM) processes that allow differing rates of increase on either side of such a pole. To estimate the two consequent memory parameters we extend two semiparametric methods that were proposed for the standard case of a spectrum diverging at the origin, namely the logperiodogram and Gaussian or Whittle methods. We also provide three tests of symmetry. Monte Carlo analysis of ®nite sample behaviour and an empirical application to UK in¯ation data are included. Our models and methods allow also for the possibility of negative dependence, described by a possibly asymmetric spectral zero.

This paper considers the persistence found in the volatility of many financial time series by means of a local Long Memory in Stochastic Volatility model and analyzes the performance of the Gaussian semiparametric or local Whittle estimator of the memory parameter in a long memory signal plus noise model which includes the Long Memory in Stochastic Volatility as a particular case. It is proved that this estimate preserves the consistency and asymptotic normality encountered in observable long memory series and under milder conditions it is more efficient than the estimator based on a log-periodogram regression. Although the asymptotic properties do not depend on the signal-to-noise ratio the finite sample performance rely upon this magnitude and an appropriate choice of the bandwidth is important to minimize the influence of the added noise. I analyze the effect of the bandwidth via Monte Carlo. An application to a Spanish stock index is finally included.JEL classification: C13; C22.

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 v 2 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.

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This paper describes semiparametric techniques recently proposed for the analysis of seasonal or cyclical long memory and applies them to a monthly Spanish inflation series. One of the conclusions is that this series has long memory not only at the origin but also at some but not all seasonal frequencies, suggesting that the fractional difference operator (1 - "L"-super-12)-super-"d" should be avoided. Moreover, different persistent cycles are observed before and after the first oil crisis. Whereas the cycles seem stationary in the former period, we find evidence of a unit root after 1973, which implies that a shock has a permanent effect. Finally, it is shown how to compute the exact impulse responses and the coefficients in the autoregressive expansion of parametric seasonal long memory models. These two quantities are important to assess the impact of aleatory shocks such as those produced by a change of economic policy and for forecasting purposes, respectively. Copyright 2007 Blackwell Publishing Ltd.