Recursive predictive tests for structural change of long-memory ARFIMA processes with unknown break points

This paper considers the theoretical justifications of Lütkpohl’s (1988) test statistics when the data-generating process is relaxed to be a stationary ARFIMA process. Under suitable regularity conditions, we prove the applicability of Lütkpohl’s (1988) method to the stationary ARFIMA (p, d, q) process with d∈ (−0.5, 0.5). The practical advantages of our results imply that the potential one or more change points of an ARFIMA process can be detected via recursive predictive tests based on AR regression, even though the exact order of the ARFIMA (p, d, q) is unknown. The spurious break considered in Kuan and Hsu (1998) can also be resolved by Lütkpohl’s (1988) predictive tests, and the simulations conducted in this paper confirm our theoretical results.