Seasonal and Cyclical Long Memory - (Now published in S Ghosh (ed): Asymptotics, Nonparametrics and Time Series: A Tribute to Madam Lal Puri (Marcel Decker, 1999), pp.115-145.)

There has recently been great interest in time series with long memory, namely series whose dependence decays slowly in the sense that autocovariances are not summable and the spectral density is unbounded. This concept has been extended to SCLM (Seasonal/Cyclical Long Memory) where the dependence between seasonal or cyclic observations decays similarly slowly. We discuss issues related to SCLM processes such as modelling, estimation, statistical inference, applications and extensions.Long memory, seasonal time series, cyclic time series

Semiparametric Inference in Seasonal and Cyclical Long Memory Processes - (Now published in Journal of Time Series Analysis, 21 (2000), pp.1-25.)

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, long-range dependence can appear as a spectral pole at any Nyqvist frequency (reflecting seasonal or cyclical long memory), where the spectrym 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 log-periodogram and Gaussian or Whittle methods. We also provide three tests of symmetry. Monte Carlo analysis of finite sample behaviour and an empirical application to UK inflation data are included. Our models and methods allow also for the posssibility of negative dependence, described by a possibly asymmetric spectral zero.Semiparametric inference, long memory, seasonality