Model Selection and Estimation of Long-Memory Time-Series Models

An exploratory estimation of ARFIMA(p,d,q) models on agricultural spot and futures markets showed us that the estimated d is quite sensitive to the number of lags included in the short-term dynamics. AIC and SIC agreed there were many lags but, familiarly, disagreed on how many. To address this issue, I run a series of Monte Carlo experiments and test the performance (i) of the AIC and the SIC in selecting p and q and (ii) of the AIC, the SIC and the multimodel-inference approach of Burnham and Anderson (2002) in estimating d. I contribute to the literature by studying high-order data generating processes-up to (8,d,8) rather than (2,d,0); by testing also the MMI-approach; and by studying the impact of excluding models close to the data generating process from the set of candidate models. Three findings stand out. First, the familiar result that, in terms of order selection, the SIC outperforms the AIC for low-order models gets reversed for high-order models. Second, for inference on the presence or absence of fractional integration, I find that the SIC still dominates both the AIC and the MMI-approach. Third, set-up snooping (if the true model is also a candidate model) has little impact