High-Dimensional Mutual Information Estimation

Background: Estimating the forecastability profile involves estimating mutual information from data, which can be challenging, especially in high-dimensional settings where the information set is rich.

Question / Future Work: Developing reliable and computationally tractable methods for estimating the mutual information that defines the forecastability profile ($\mathcal{F}(h; \mathcal{I}_t)$) in high-dimensional information sets or for complex time series remains an open problem in practical application of this framework. Finite-sample bias and variance increase substantially in these regimes.