B0793
Title: Autoregressive models for distributional time series
Authors: Changbo Zhu - University of Notre Dame (United States) [presenting]
Hans-Georg Mueller - University of California Davis (United States)
Abstract: Distributional time series consist of sequences of distributions indexed by time and are frequently encountered in modern data analysis. Two classes of autoregressive models are proposed for such time series based on the Wasserstein and Fisher-Rao geometry, respectively, where the former is an intrinsic model that operates in the space of optimal transport maps. The latter utilizes rotation operators that map distributional regressions to geodesics on the infinite-dimensional Hilbert sphere. While the Wasserstein geometry is popular in the literature due to its statistical utility and connections to optimal transport, its application for distributional time series has been limited to the case of univariate distributions, as optimal transport is unwieldy for multidimensional distributions in statistical applications. On the other hand, the Fisher-Rao geometry is not affected by the dimension of the distributions, and it is shown that it can be utilized not only for multidimensional distributional time series but also for compositional time series, giving rise to a new class of spherical time series. Theoretical properties of the ensuing autoregressive models are derived and these approaches are showcased with a time series of yearly observations of uni/bivariate distributions of the minimum/maximum temperatures for a period of 120 days during each summer for the years 1990-2018 and with U.S. energy mix time series.
