GARTFIMA Process and its Empirical Spectral Density Based Estimation

TL;DR

This paper introduces the GARTFIMA process, a new time series model, and develops spectral density-based estimation methods, demonstrating improved modeling of real-world data over existing models.

Contribution

The paper proposes the GARTFIMA process and applies empirical spectral density methods for parameter estimation, enhancing modeling accuracy for complex time series.

Findings

Estimation methods perform well on simulated data.

GARTFIMA models real-world data more effectively.

Spectral density approach improves parameter accuracy.

Abstract

In this article, we introduce a Gegenbauer autoregressive tempered fractionally integrated moving average (GARTFIMA) process. We work on the spectral density and autocovariance function for the introduced process. The parameter estimation is done using the empirical spectral density with the help of the nonlinear least square technique and the Whittle likelihood estimation technique. The performance of the proposed estimation techniques is assessed on simulated data. Further, the introduced process is shown to better model the real-world data in comparison to other time series models.