On Construction and Estimation of Stationary Mixture Transition Distribution Models

Mixture transition distribution (MTD) time series models build high-order dependence through a weighted combination of first-order densities for each one specified number lags. We present framework to construct stationary MTD that extend beyond linear, Gaussian dynamics. study conditions strict stationarity which allow different constructions with either continuous or discrete families the given prespecified family marginal density, and general forms resulting conditional expectations. Inference prediction are developed under Bayesian particular emphasis on flexible, structured priors mixture weights. Model properties investigated both analytically synthetic data examples. Finally, Poisson Lomax examples illustrated real applications. Supplementary files this article available online.