Fitting a fractional ARIMA model to time series data

Abstract

This paper provides a time domain method to estimate the parameter d for fractionally differenced ARIMA (p, d, q) models. These models are considered better models to model long term persistence and to get long range forecasts. Two important results by Hosking(1984) are used to extend the estimator of d for an ARIMA (0, d, 0) model by Gupta and Ji(1992) to the range d∈(0, 0.5), the range in which the model is truly a long memory model. The asymptotic normality of our new estimator for d∈(0, 0.25) is derived. A simulation study is done to compare the performance of our new estimator with some of the other estimators that exist in the literature. We also make some comments about the general ARIMA (p, d, q) model and suggest a procedure to estimate such a model. The simulation results support our suggestion.