Informational predictability, and an application to the intensity of high-resolution temporal rainfall

Abstract
In an effort to solidly define predictability, and the estimation thereof, in different processes, and considering the interpretation of mutual information as an expected value of the logarithm of joint probability, we show that, in the light of causality, the expected value of the logarithm of conditional probability fulfills the desirable properties of a predictability descriptor. An application to high-resolution rainfall intensity time series is presented.