对局部至单位自回归模型中系数随机性的检验
Testing for Coefficient Randomness in Local-to-Unity Autoregressions
AI总结：
本文提出一种检验局部至单位自回归模型中系数随机性的方法，分析随机系数与扰动项相关性对检验性能的影响，并改进检验统计量以提高其稳健性。
摘要：
在本文中，我们提出了一种检验自回归模型中局部至单位系数随机性的检验方法。在该规范下，我们理论分析了随机系数与扰动项之间的相关性对检验属性的影响，这在文献中尚未被广泛探讨。我们的分析表明，相关性对检验随机性系数的检验功效有关键影响，而早期提出的检验方法在相关性程度中等或较大时表现较差。本文提出的检验方法设计为具有对相关性的稳健功效函数。由于我们的检验统计量的渐近原分布依赖于扰动项与其平方之间的相关性ψ，如同早期检验方法，我们还提出了一种修改后的检验统计量，使其渐近原分布不受 nuisance 参数ψ的影响。修改后的检验在大样本和有限样本中均表现出比现有方法更好的功效特性。
英文摘要：
In this study, we propose a test for the coefficient randomness in autoregressive models where the autoregressive coefficient is local to unity, which is empirically relevant given the results of earlier studies. Under this specification, we theoretically analyze the effect of the correlation between the random coefficient and disturbance on tests' properties, which remains largely unexplored in the literature. Our analysis reveals that the correlation crucially affects the power of tests for coefficient randomness and that tests proposed by earlier studies can perform poorly when the degree of the correlation is moderate to large. The test we propose in this paper is designed to have a power function robust to the correlation. Because the asymptotic null distribution of our test statistic depends on the correlation $ψ$ between the disturbance and its square as earlier tests do, we also propose a modified version of the test statistic such that its asymptotic null distribution is free from the nuisance parameter $ψ$. The modified test is shown to have better power properties than existing ones in large and finite samples.
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