  In this paper, we present a recurrent neural system named Long Short-term
Cognitive Networks (LSTCNs) as a generalization of the Short-term Cognitive
Network (STCN) model. Such a generalization is motivated by the difficulty of
forecasting very long time series efficiently. The LSTCN model can be defined
as a collection of STCN blocks, each processing a specific time patch of the
(multivariate) time series being modeled. In this neural ensemble, each block
passes information to the subsequent one in the form of weight matrices
representing the prior knowledge. As a second contribution, we propose a
deterministic learning algorithm to compute the learnable weights while
preserving the prior knowledge resulting from previous learning processes. As a
third contribution, we introduce a feature influence score as a proxy to
explain the forecasting process in multivariate time series. The simulations
using three case studies show that our neural system reports small forecasting
errors while being significantly faster than state-of-the-art recurrent models.
