A1352
Title: Wasserstein auto-regressive models for modeling multivariate distributional time series
Authors: Yiye Jiang - INRIA (France) [presenting]
Jeremie Bigot - Bordeaux University (France)
Abstract: Statistical analysis of data consisting of multiple time series of probability measures indexed by distinct time instants and supported over a bounded interval of the real line is considered. By modeling these time-dependent probability measures as random objects in the Wasserstein space, an auto-regressive model for statistical analysis of multivariate distributional time series is proposed. Using the theory of iterated random function systems, results on the second-order stationarity of the solution of such a model are established. A consistent estimator for the autoregressive coefficients of this model is also developed. Due to the simplex constraints imposed on the model coefficients, the proposed estimator learned under these constraints naturally has a sparse structure. The sparsity enables the application of the model in learning a graph of temporal dependency from multivariate distributional time series. Numerical performances of the estimation procedure are explored using simulated data. To demonstrate the benefits of the approach for real data analysis, the methodology is applied to two datasets: observations of age distributions in different countries and data from the bike-sharing network in Paris.
