摘要翻译：
当制度转换概率被指定为常数（“混合模型”）或由有限状态马尔可夫链控制（“马尔可夫转换模型”）时，制度转换的测试是一个长期存在的问题，也是最近引起兴趣的问题。本文考虑了当状态切换概率随时间变化且依赖于观测数据时，状态切换的检验问题（与观测相关的状态切换）。具体来说，我们考虑了混合自回归模型中观测依赖的状态切换的似然比检验。该测试问题是高度非标准的，涉及到零点下未识别的干扰参数、边界上的参数、奇异信息矩阵和对数似然的高阶近似。在一般混合自回归条件下，我们利用允许系统切换概率对过去观测的各种形式依赖的高级条件，导出了似然比检验统计量的渐近零分布，并用两个特殊的混合自回归模型来说明该理论。似然比检验具有易于模拟的非标准渐近分布，Monte Carlo研究表明，该检验具有令人满意的有限样本量和幂性质。
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英文标题：
《Testing for observation-dependent regime switching in mixture
  autoregressive models》
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作者：
Mika Meitz and Pentti Saikkonen
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最新提交年份：
2017
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分类信息：

一级分类：Economics        经济学
二级分类：Econometrics        计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics        统计学
二级分类：Methodology        方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
  Testing for regime switching when the regime switching probabilities are specified either as constants (`mixture models') or are governed by a finite-state Markov chain (`Markov switching models') are long-standing problems that have also attracted recent interest. This paper considers testing for regime switching when the regime switching probabilities are time-varying and depend on observed data (`observation-dependent regime switching'). Specifically, we consider the likelihood ratio test for observation-dependent regime switching in mixture autoregressive models. The testing problem is highly nonstandard, involving unidentified nuisance parameters under the null, parameters on the boundary, singular information matrices, and higher-order approximations of the log-likelihood. We derive the asymptotic null distribution of the likelihood ratio test statistic in a general mixture autoregressive setting using high-level conditions that allow for various forms of dependence of the regime switching probabilities on past observations, and we illustrate the theory using two particular mixture autoregressive models. The likelihood ratio test has a nonstandard asymptotic distribution that can easily be simulated, and Monte Carlo studies show the test to have satisfactory finite sample size and power properties.
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PDF链接：
https://arxiv.org/pdf/1711.03959