Likelihood Ratio-Based Tests for Markov Regime Switching
Likelihood Ratio-Based Tests for Markov Regime Switching
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基于似然比的马尔可夫体制切换检验
DOI：
10.1093/restud/rdaa035
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Fan Zhuo
中科院分区：
文献类型：
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作者：
Zhongjun Qu;Fan Zhuo
马尔可夫状态转换模型在经济学和金融学中得到了广泛的研究。虽然一直有兴趣（例如，Hansen, 1992, Garcia, 1998， Cho和White， 2007），但基于似然比的检验的渐近分布仍然未知。本文考虑了这类检验，并在允许多个开关参数的非线性模型下建立了它们的渐近分布。分析同时解决了三个困难：(i)在零假设下无法识别一些讨厌的参数，（ii）零假设产生局部最优，以及（iii）条件制度概率遵循只能递归表示的随机过程。解决这些问题可以在经验相关的情况下获得可观的权力。除了得到检验的渐近分布外，本文还得到了四组独立的结果：(1)条件区域概率及其对模型参数的高阶导数的表征，(2)允许多个切换参数的对数似然比的高阶逼近，(3)渐近分布的改进，(4)模拟临界值的统一算法。对于零假设下的线性模型，算法所需的元素都可以解析计算。上述结果还揭示了为什么一些引导过程可能不一致，以及为什么标准信息准则（如贝叶斯信息准则（BIC））可能对假设和模型结构敏感。当应用于美国季度实际GDP增长率时，这些方法显示出相当有力的证据支持制度转换规范，该规范在一系列样本时期内保持一致。
Markov regime switching models are widely considered in economics and finance. Although there have been persistent interests (see e.g., Hansen, 1992, Garcia, 1998, and Cho and White, 2007), the asymptotic distributions of likelihood ratio based tests have remained unknown. This paper considers such tests and establishes their asymptotic distributions in the context of non- linear models allowing for multiple switching parameters. The analysis simultaneously addresses three difficulties: (i) some nuisance parameters are unidentified under the null hypothesis, (ii) the null hypothesis yields a local optimum, and (iii) conditional regime probabilities follow stochastic processes that can only be represented recursively. Addressing these issues permits substantial power gains in empirically relevant situations. Besides obtaining the tests' asymptotic distributions, this paper also obtains four sets of results that can be of independent interest: (1) a characterization of conditional regime probabilities and their high order derivatives with respect to the model's parameters, (2) a high order approximation to the log likelihood ratio permitting multiple switching parameters, (3) a refinement to the asymptotic distribution, and (4) a unified algorithm for simulating the critical values. For models that are linear under the null hypothesis, the elements needed for the algorithm can all be computed analytically. The above results also shed light on why some bootstrap procedures can be inconsistent and why standard information criteria, such as the Bayesian information criterion (BIC), can be sensitive to the hypothesis and the model's structure. When applied to the US quarterly real GDP growth rates, the methods suggest fairly strong evidence favoring the regime switching specification, which holds consistently over a range of sample periods.