A new time-varying model for forecasting long-memory series

In this work we propose a new class of long-memory models with time-varying fractional parameter. In particular, the dynamics of the long-memory coefficient, d, is specified through a stochastic recurrence equation driven by the score of the predictive likelihood, as suggested by Creal et al. (J Appl Econom 28:777–795, 2013) and Harvey (Dynamic models for volatility and heavy tails: with applications to financial and economic time series, Cambridge University Press, Cambridge, 2013). We demonstrate the validity of the proposed model by a Monte Carlo experiment and an application to two real time series.