GARTFIMA Models: A Class of Observation-Driven Models with Tempered Fractional Dynamics

This paper introduces a class of observation-driven models whose systematic component includes a tempered fractional differencing term. This specification generalizes long-range dependent models based on the fractional differencing operator, enabling a more general and robust model specification while offering theoretical advantages. We propose a partial maximum likelihood approach for parameter estimation and address hypothesis testing, confidence intervals, goodness-of-fit assessment, and both in-sample and out-of-sample forecasting. A Monte Carlo simulation study evaluates the finite-sample performance of the proposed estimation method, and an empirical application illustrates the model's practical utility.