Locally stationary long memory estimation

There exists a wide literature on parametrically or semi-parametrically modelling strongly dependent time series using a long-memory parameter dd, including more recent work on wavelet estimation. As a generalization of these latter approaches, in this work we allow the long-memory parameter dd to be varying over time. We adopt a semi-parametric approach in order to avoid fitting a time-varying parametric model, such as tvARFIMA, to the observed data. We study the asymptotic behavior of a local log-regression wavelet estimator of the time-dependent dd. Both simulations and a real data example complete our work on providing a fairly general approach.