Introduces a Wasserstein-space multivariate autoregressive model for distributional time series, proving second-order stationarity via iterated random functions and providing a simplex-constrained consistent estimator that enables graph learning.
(7.2) Note thatϵt,t P Z are i.i.d, thus for any fixedX P X, we haverΦt,mpXq d“ rΦt1,mpXq,@t,t1P Z
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Wasserstein multivariate auto-regressive models for modeling distributional time series
Introduces a Wasserstein-space multivariate autoregressive model for distributional time series, proving second-order stationarity via iterated random functions and providing a simplex-constrained consistent estimator that enables graph learning.