Statistical Analysis of Autoregressive Fractionally Integrated Moving Average Models

TL;DR

This paper discusses statistical tools for analyzing ARFIMA models, which are used to model long-range dependence in time series, including estimation, autocovariance, prediction, and impulse response analysis, demonstrated with real data.

Contribution

The paper introduces the afmtools R package that implements various statistical methods for ARFIMA models, facilitating analysis of long-memory time series.

Findings

Implementation of parameter estimation functions

Exact autocovariance calculation methods

Application to real-life time series data

Abstract

In practice, several time series exhibit long-range dependence or persistence in their observations, leading to the development of a number of estimation and prediction methodologies to account for the slowly decaying autocorrelations. The autoregressive fractionally integrated moving average (ARFIMA) process is one of the best-known classes of long-memory models. In the package afmtools for R, we have implemented some of these statistical tools for analyzing ARFIMA models. In particular, this package contains functions for parameter estimation, exact autocovariance calculation, predictive ability testing, and impulse response function, amongst others. Finally, the implemented methods are illustrated with applications to real-life time series.