Consistent Order Selection for Arfima Processes

Abstract

Estimating the orders of the autoregressive fractionally integrated moving average (ARFIMA) model has been a long-standing challenge in time series analysis. This study tackles the challenge by establishing the consistency of the Bayesian information criterion (BIC) in the ARFIMA model with independent errors.?Since we allow the model’s memory parameter to be any unknown real number, our consistency result can apply simultaneously to short-memory, long-memory, and non-stationary time series. We further extend BIC’s consistency to the ARFIMA model with conditional heteroskedastic errors, thereby broadening the criterion’s range of applications. Finally, the finite-sample implications of our theoretical results is illustrated using numerical examples.