LM tests for joint breaks in the dynamics and level of a long-memory time series*

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.

本文针对分整时间序列过程的长记忆参数、短期动态与水平项中的联合结构突变（突变时点已知或未知），构建单步拉格朗日乘数（Lagrange Multiplier, LM）检验。该检验的回归形式易于实现，当参数稳定性原假设被拒绝时，可用于识别结构突变的具体来源。然而，其显著性水平与检验势属性对原假设下短期动态的正确设定较为敏感。为解决该问题，本文提出对LM检验的小幅修正（记为LMW型检验），该检验同时利用备择假设下的部分信息，遵循沃尔德（Wald）检验的设计思路。在原假设与局部备择假设下，该检验与LM检验拥有相同的极限分布；且通过简化原假设及任意备择假设（局部或固定备择）下短期动态的正确设定流程，可获得更高的检验势。蒙特卡洛（Monte Carlo）模拟结果为上述理论结论提供了支撑。一项针对七国集团（G7）5个国家远期贴现率长记忆属性变动成因的实证应用，验证了所提出的LMW型检验的实用价值。