We propose a new algorithm called the context-based predictive information (CBPI) for estimating the predictive information (PI) between time series, by utilizing a lossy compression algorithm. The advantage of this approach over existing methods resides in the case of sparse predictive information (SPI) conditions, where the ratio between the number of informative sequences to uninformative sequences is small. It is shown that the CBPI achieves a better PI estimation than benchmark methods by ignoring uninformative sequences while improving explainability by identifying the informative sequences. We also provide an implementation of the CBPI algorithm on a real dataset of large banks' stock prices in the U.S. In the last part of this paper, we show how the CBPI algorithm is related to the well-known information bottleneck in its deterministic version.
Keywords: context tree; information bottleneck; predictive information; time series analysis.