Estimating the memory parameter for possibly non-linear and non-Gaussian time series with wavelets

Abstract

The asymptotic theory for the memory parameter estimator constructed from the log-regression with wavelets is incomplete for 1/f processes that are not necessarily Gaussian or linear. Such a theory is necessary due to the importance of non-Gaussian and non-linear long memory models in describing financial time series. To fill this gap, we prove that under some mild assumptions, the newly designed memory estimator, named as LRMW in this paper, is asymptotically consistent. The performances of LRMW on three simulated long-memory processes indicate the efficiency of this new estimator.