🤖 AI Summary
This study addresses the limited flexibility of traditional fractionally differenced models in capturing long memory, which often fail to accommodate faster-decaying dependence structures observed in real-world data. To overcome this limitation, the authors propose a class of observation-driven models incorporating tempered fractional differencing, thereby preserving long-memory modeling capabilities while substantially enhancing flexibility and theoretical robustness. Parameter estimation is carried out via partial maximum likelihood, enabling hypothesis testing, confidence interval construction, and predictive evaluation. Monte Carlo simulations demonstrate favorable finite-sample performance, and empirical analyses confirm the model’s effectiveness and practical utility in modeling real time series data.
📝 Abstract
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.