Local stationarity and time-inhomogeneous Markov chains
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局部平稳性与时变 Markov 链
- 研究问题
- 如何为类别型、整数型及更一般状态空间的数据建立局部平稳 Markov 模型，并支持随时间变化的统计建模与推断？
- 方法与思路
- 作者以收缩且缓慢变化的转移核构造时变 Markov 链三角阵，用遍历齐次链局部近似其分布，并研究混合性质与核平滑推断。
- 材料陈述的贡献
- 摘要称，框架提供局部分布近似、混合性质和中心极限定理，支持有限状态链的快速实现，并展示计数及二元时间序列等例子。
- 阅读关注点
- 应核对转移核的收缩与缓变条件、局部近似误差及中心极限定理范围，并检查核平滑推断和具体模型实例的要求。
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- 仅据版本未注明的 OpenAlex 摘要；具体条件、带宽及实现细节未提供，不能推断框架覆盖任意时变链或突发结构变化。
原文摘要
A primary motivation of this contribution is to define new locally stationary Markov models for categorical or integer-valued data. For this initial purpose, we propose a new general approach for dealing with time-inhomogeneity that extends the local stationarity notion developed in the time series literature. We also introduce a probabilistic framework which is very flexible and allows us to consider a much larger class of Markov chain models on arbitrary state spaces, including most of the locally stationary autoregressive processes studied in the literature. We consider triangular arrays of time-inhomogeneous Markov chains, defined by some families of contracting and slowly-varying Markov kernels. The finite-dimensional distribution of such Markov chains can be approximated locally with the distribution of ergodic Markov chains and some mixing properties are also available for these triangular arrays. As a consequence of our results, some classical geometrically ergodic homogeneous Markov chain models have a locally stationary version, which lays the theoretical foundations for new statistical modeling. Statistical inference of finite-state Markov chains can be based on kernel smoothing and we provide a complete and fast implementation of such models, directly usable by the practitioners. We also illustrate the theory on a real data set. A central limit theorem for Markov chains on more general state spaces is also provided and illustrated with the statistical inference in INAR models, Poisson ARCH models and binary time series models. Additional examples such as locally stationary regime-switching or SETAR models are also discussed.