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

## TL;DR

This paper introduces a novel class of long-memory models with a time-varying fractional parameter, where the dynamics are driven by a stochastic recurrence based on the score of the predictive likelihood, validated through simulations and real data.

## Contribution

It proposes a new long-memory model with a stochastic, score-driven evolution of the fractional parameter, enhancing flexibility over traditional fixed-parameter models.

## Key findings

- Model successfully captures time-varying long-memory behavior.
- Monte Carlo simulations confirm the model's validity.
- Application to real series demonstrates practical usefulness.

## Abstract

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. (2013) and Harvey (2013). We demonstrate the validity of the proposed model by a Monte Carlo experiment and an application to two real time series.