Statistical inference for ARTFIMA time series with stable innovations

TL;DR

This paper introduces a new stationary time series model called ARTFIMA with stable innovations, incorporating exponential tempering to modify long-range dependence, and develops its theoretical properties and parameter estimation methods.

Contribution

It provides the first comprehensive theoretical framework for ARTFIMA models with stable innovations, including dependence structure and estimation techniques.

Findings

Model exhibits semi-long-range dependence.

Developed estimation methods for model parameters.

Established dependence structure of the tempered process.

Abstract

Autoregressive tempered fractionally integrated moving average with stable innovations modifies the power-law kernel of the fractionally integrated time series model by adding an exponential tempering factor. The tempered time series is a stationary model that can exhibits semi-long-range dependence. This paper develops the basic theory of the tempered time series model, including dependence structure and parameter estimation.