[PDF] On Distributional Autoregression and Iterated Transportation-论文阅读讨论-ReadPaper

摘要

We consider the problem of defining and fitting models of autoregressive timeseries of probability distributions on a compact interval of $\mathbb{R}$. Anorder-$1$ autoregressive model in this context is to be understood as a Markovchain, where one specifies a certain structure (regression) for the one-stepconditional Fr\'echet mean with respect to a natural probability metric. Weconstruct and explore different models based on iterated random functionsystems of optimal transport maps. While the properties and interpretation ofthese models depend on how they relate to the iterated transport system, theycan all be analyzed theoretically in a unified way. We present such atheoretical analysis, including convergence rates, and illustrate ourmethodology using real and simulated data. Our approach generalises or extendscertain existing models of transportation-based regression and autoregression,and in doing so also provides some additional insights on existing models.

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