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Title: A dual parameter long memory time series model Authors:  Rajendra Bhansali - Imperial College London (United Kingdom) [presenting]
David Natsios - University of Liverpool (United Kingdom)
Abstract: A new model for long-memory time series that characterizes the correlation decay as a mixture of polynomial and logarithmic rates is introduced. This model includes as a special case the standard single-parameter model in which the correlations may decay only at a polynomial rate. Examples illustrating situations where the standard model does not apply, but the new model does do so are presented. A mathematical definition of the class of dual parameter long memory models is given, and extended to include also the class of dual parameter intermediate memory models. The dual parameter fractional ARMA models are also introduced, and the notions of strong, weak and intermediate memory are defined. Non-parametric and semi-parametric estimation of the parameters of this new class of models by suitable extensions of the standard log-periodogram and local Whittle methods is considered, together with the maximum likelihood estimation of the parameters of the dual parameter fractional ARMA model. Asymptotic, and finite sample, properties of the estimates are investigated, and it is shown that the standard single-parameter estimation methods can be badly biased when the dual parameter model applies. The question of discriminating between these two classes of models for observed time series is examined and an application to internet packet traffic is discussed.