Recurrent dictionary learning for state-space models with an application in stock forecasting.

• We introduce a new tool, called recurrent dictionary learning, whose core idea is to rely on a linear state-space model whose state transition and observation matrices are sequentially inferred, jointly with the resolution of the inherent probabilistic filtering problem, using an expectation-minimization approach. • Our numerical results on financial time series prediction from stock market data, show that our proposed method excels over state-of-the-art stock analysis models. • The advantages of our method are (i) the available uncertainty quantification on the estimates, (ii) the ease for dealing with multivariate input and output vectors, (iii) the automatic nature of the joint estimation problem (model parameters and sequence of the states). In this work, we introduce a new modeling and inferential tool for dynamical processing of time series. The approach is called recurrent dictionary learning (RDL). The proposed model reads as a linear Gaussian Markovian state-space model involving two linear operators, the state evolution and the observation matrices, that we assumed to be unknown. These two unknown operators (that can be seen interpreted as dictionaries) and the sequence of hidden states are jointly learnt via an expectation–maximization algorithm. The RDL model gathers several advantages, namely online processing, probabilistic inference, and a high model expressiveness which is usually typical of neural networks. RDL is particularly well suited for stock forecasting. Its performance is illustrated on two problems: next day forecasting (regression problem) and next day trading (classification problem), given past stock market observations. Experimental results show that our proposed method excels over state-of-the-art stock analysis models such as CNN-TA, MFNN, and LSTM. [ABSTRACT FROM AUTHOR]