Locally stationary long memory estimation

François Roueff (1) , Rainer von Sachs (2)

1 LTCI - Laboratoire Traitement et Communication de l'Information
2 Institut de Statistique, Biostatistique et Sciences Actuarielles (ISBA)

There exists a wide literature on modelling strongly dependent time series using a longmemory parameter d, including more recent work on semiparametric wavelet estimation. As a generalization of these latter approaches, in this work we allow the long-memory parameter d to be varying over time. We embed our approach into the framework of locally stationary processes. We show weak consistency and a central limit theorem for our log-regression wavelet estimator of the time-dependent d in a Gaussian context. Both simulations and a real data example complete our work on providing a fairly general approach.

Keywords: locally stationary process; long memory; semi-parametric estimation; wavelets

Domains: Mathematics [math]; Statistics [math.ST]; Statistics [stat]; Statistics Theory [stat.TH]

François Roueff, Rainer von Sachs. Locally stationary long memory estimation. Stochastic Processes and their Applications, 2011, 121 (4), pp.Pages 813-844. ⟨10.1016/j.spa.2010.12.004⟩. ⟨hal-00408224v2⟩