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We consider a single-step Lagrange multiplier (LM) test for joint breaks (at known or unknown dates) in the long memory parameter, the short-run dynamics, and the level of a fractionally integrated time-series process. The regression version of this test is easily implementable and allows to identify the specific sources of the break when the null hypothesis of parameter stability is rejected. However, its size and power properties are sensitive to the correct specification of short-run dynamics under the null. To address this problem, we propose a slight modification of the LM test (labeled LMW-type test) which also makes use of some information under the alternative (in the spirit of a Wald test). This test shares the same limiting distribution as the LM test under the null and local alternatives but achieves higher power by facilitating the correct specification of the short-run dynamics under the null and any alternative (either local or fixed). Monte Carlo simulations provide support for these theoretical results. An empirical application, concerning the origin of shifts in the long-memory properties of forward discount rates in five G7 countries, illustrates the usefulness of the proposed LMW-type test.

LM Tests for Joint Breaks in the Dynamics and Level of a Long-Memory Time Series