On Distributional Autoregression and Iterated Transportation
分布值自回归与迭代运输
We consider the problem of defining and fitting models of autoregressive time series of probability distributions on a compact interval of $\mathbb{R}$. 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…