Forecasting of stock return prices with sparse representation of financial time series over redundant dictionaries

• A new predictive model for time series within the financial sector is presented.
• The method is based on learned redundant dictionaries for sparse representation of financial time series.
• The overall return gain generated by the predictive model exceeds the gain generated by the market.
• Untrained dictionaries outperform dictionaries trained with the KSV-D method.
• Untrained dictionaries require a reduced number of atoms to achieve successful results.

This paper presents the theory, methodology and application of a new predictive model for time series within the financial sector, specifically data from 20 companies listed on the U.S. stock exchange market. The main impact of this article is (1) the proposal of a recommender system for financial investment to increase the cumulative gain; (2) an artificial predictor that beats the market in most cases; and (3) the fact that, to the best of our knowledge, this is the first effort to predict time series by learning redundant dictionaries to sparsely reconstruct these signals. The methodology is conducted by finding the optimal set of predicting model atoms through two directions for dictionaries generation: the first one by extracting atoms from past daily return price values in order to build untrained dictionaries; and the second one, by atom extraction followed by training of dictionaries though K-SVD. Prediction of financial time series is a periodic process where each cycle consists of two stages: (1) training of the model to learn the dictionary that maximizes the probability of occurrence of an observation sequence of return values, (2) prediction of the return value for the next coming trading day. The motivation for such research is the fact that a tool, which might generate confidence of the potential benefits obtained from using formal financial services, would encourage more participation in a formal system such as the stock market. Theory, issues, challenges and results related to the application of sparse representation to the prediction of financial time series, as well as the performance of the method, are presented.