A consistent deterministic regression tree for non-parametric prediction of time series
This work addresses time series prediction for applications in forecasting and statistical modeling, but it appears incremental as it builds on existing prediction frameworks.
The paper tackles the problem of online prediction for bounded stationary ergodic time series by constructing a deterministic regression tree that achieves asymptotic performance matching the best L-Lipschitz constant predictors, with a regret bound proving optimality for this class of processes.
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.