On distributional autoregression and iterated transportation
研究如何在紧区间上对概率分布的自回归时间序列建模，基于最优运输映射的迭代随机函数系统构建模型，并给出理论分析和实证示例。
We consider the problem of defining and fitting models of autoregressive time series of probability distributions on a compact interval of . An order‐1 autoregressive model in this context is to be understood as a Markov chain, where one specifies a certain structure (regression) for the one‐step conditional Fréchet mean with respect to a natural probability metric. We construct and explore different models based on iterated random function systems of optimal transport maps. While the properties and interpretation of these models depend on how they relate to the iterated transport system, they can all be analyzed theoretically in a unified way. We present such a theoretical analysis, including convergence rates, and illustrate our methodology using real and simulated data. Our approach generalizes or extends certain existing models of transportation‐based regression and autoregression, and in doing so also provides some additional insights on existing models.