Statistical Analysis of Autoregressive Fractionally Integrated Moving Average Models

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.