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.

摘要

混合跃迁分布 (MTD) 时间序列模型通过对指定数量的滞后中的每一个进行一阶跃迁密度的加权组合来构建高阶相关性。我们提出了一个框架来构建超越线性高斯动力学的固定 MTD 模型。我们研究了一阶严格平稳性的条件，该条件允许在给定边际密度的预先指定族的情况下，对于一阶过渡密度具有连续或离散族的不同构造，并且对于由此产生的条件期望具有一般形式。推理和预测是在贝叶斯框架下开发的，特别强调混合权重的灵活、结构化先验。模型属性通过分析和合成数据示例进行研究。最后，Poisson 和 Lomax 示例通过真实的数据应用来说明。本文的补充文件可在线获取。