Mixture transition distribution 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 transition mixture distribution 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 pre-specified 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.

翻译：混合过渡分布时间序列模型通过对每个特定滞后点的一级过渡密度进行加权组合,建立高度依赖性。我们提出了一个框架,以构建超越直线和高斯动态的固定过渡混合分布模型。我们研究一阶严格固定状态条件,允许在第一阶过渡密度方面与连续或离散家庭进行不同的构造,为边缘密度预先指定的家庭提供连续或离散家庭,并采用一般形式来预测由此产生的有条件期望。贝叶斯框架下制定了推论和预测,特别强调混合物重量的灵活、结构前期;对模型特性进行了分析研究,并通过合成数据实例进行了调查。最后,Poisson和Lomax的例子通过实际数据应用加以说明。