Asymptotics of bivariate local Whittle estimators with applications to fractal connectivity

Several methodological and numerical issues behind the local Whittle estimation of long and short memory in bivariate stationary time series with possible fractional cointegration are reexamined. These issues include the asymptotic normality for all model parameters, local Whittle plots for phase parameter and fractal connectivity, and others. For fractal connectivity, in particular, it is advocated to work with a model parametrization for which the model parameters associated with this phenomenon are identifiable and could be tested naturally within the local Whittle estimation framework. A simulation study and data applications are also considered. (C) 2019 Elsevier B.V. All rights reserved.