On Construction and Estimation of Stationary Mixture Transition Distribution Models
On Construction and Estimation of Stationary Mixture Transition Distribution Models
复制标题
DOI：
10.1080/10618600.2021.1981342
复制
发表时间：
2020-10
影响因子：
2.4
通讯作者：
Xiaotian Zheng;A. Kottas;Bruno Sans'o
中科院分区：
文献类型：
--
作者：
Xiaotian Zheng;A. Kottas;Bruno Sans'o
摘要混合转移分布（MTD）时间序列模型通过对指定数量的滞后中的每一个滞后的一阶转移密度的加权组合来建立高阶依赖。我们提出了一个框架来构建静态MTD模型，扩展到线性，高斯动态。我们研究条件一阶严格平稳，允许不同的建设与连续或离散家庭的一阶过渡密度给定一个预先指定的家庭的边缘密度，并与一般形式的条件期望。推理和预测的贝叶斯框架下，特别强调灵活的，结构化的混合权重先验。模型属性进行了研究分析，并通过合成数据的例子。最后，泊松和Lomax的例子说明通过真实的数据应用。本文的补充文件可在线获得。
Abstract Mixture transition distribution (MTD) time series models build high-order dependence through a weighted combination of first-order transition densities for each one of a specified number of lags. We present a framework to construct stationary MTD models that extend beyond linear, Gaussian dynamics. We study conditions for first-order strict stationarity which allow for different constructions with either continuous or discrete families for the first-order transition densities given a prespecified family for the marginal density, and with general forms for the resulting conditional expectations. Inference and prediction are developed under the Bayesian framework with particular emphasis on flexible, structured priors for the mixture weights. Model properties are investigated both analytically and through synthetic data examples. Finally, Poisson and Lomax examples are illustrated through real data applications. Supplementary files for this article are available online.