标题： 马尔可夫时间序列模型的拟合优度检验：中心极限理论与 bootstrap 近似 显示英文标题

标题： Goodness-of-fit tests for Markovian time series models: Central limit theory and bootstrap approximations

摘要： 本文发展了用于时间序列分析中标记模型拟合优度检验的新方法，这些方法基于观测过程的一阶转移分布函数的完全非参数估计与零假设下假定的模型类别的转移分布函数之间的差异。 在零假设下的模型设定允许标记模型，其转移机制依赖于未知参数向量和未指定的独立同分布创新分布。 测试统计量的渐近性质被推导出来，并利用适当的自助法方案找到检验的临界值。同时，关于马尔可夫过程的自助法的一般性质也被推导出来。 得到了一个关于弱相关随机变量三角阵列的新中心极限定理。 为了证明多维经验过程的随机一致连续性，我们采用了一种简单的基于空间各向异性镶嵌的方法。 所提出的检验方法在有限样本下的表现通过一些数值例子进行了说明，并给出了一个实际数据的应用实例。 显示英文摘要

摘要： New goodness-of-fit tests for Markovian models in time series analysis are developed which are based on the difference between a fully nonparametric estimate of the one-step transition distribution function of the observed process and that of the model class postulated under the null hypothesis. The model specification under the null allows for Markovian models, the transition mechanisms of which depend on an unknown vector of parameters and an unspecified distribution of i.i.d. innovations. Asymptotic properties of the test statistic are derived and the critical values of the test are found using appropriate bootstrap schemes. General properties of the bootstrap for Markovian processes are derived. A new central limit theorem for triangular arrays of weakly dependent random variables is obtained. For the proof of stochastic equicontinuity of multidimensional empirical processes, we use a simple approach based on an anisotropic tiling of the space. The finite-sample behavior of the proposed test is illustrated by some numerical examples and a real-data application is given.