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We study online prediction of bounded stationary ergodic processes. To do so, we consider the setting of prediction of individual sequences and build a deterministic regression tree that performs asymptotically as well as the best L-Lipschitz constant predictors. Then, we show why the obtained regret bound entails the asymptotical optimality with respect to the class of bounded stationary ergodic processes.
We derive generalization error bounds for traditional time-series forecasting models. Our results hold for many standard forecasting tools including autoregressive models, moving average models, and, more generally, linear state-space models. These n
We present a simple randomized procedure for the prediction of a binary sequence. The algorithm uses ideas from recent developments of the theory of the prediction of individual sequences. We show that if the sequence is a realization of a stationary
We consider the problem of estimating the predictive density of future observations from a non-parametric regression model. The density estimators are evaluated under Kullback--Leibler divergence and our focus is on establishing the exact asymptotics
The current work is motivated by the need for robust statistical methods for precision medicine; as such, we address the need for statistical methods that provide actionable inference for a single unit at any point in time. We aim to learn an optimal
We introduce new quantities for exploratory causal inference between bivariate time series. The quantities, called penchants and leanings, are computationally straightforward to apply, follow directly from assumptions of probabilistic causality, do n