The current work investigates the discovery of causal relationships in time series data through a deep learning approach. Traditionally, uncovering such dependencies requires extensive analytical work, including model construction, solving differential equations, hypothesis testing and relational analysis. These processes can be automated using transformer-based models with a large number of training parameters, such as CausalFormer. The main contribution of this work is the adaptation of this model to support incremental learning, allowing it to update with new data without full retraining on the entire dataset. This is particularly valuable in real-world applications where data arrives continuously and resources for retraining are limited. Using a functional magnetic resonance imaging (fMRI) dataset, a comparative analysis between full and incremental training was performed, which showed similar results between the two methods. This indicates that the combination of interpretable deep learning models and incremental learning provides an effective and adaptive alternative for causal analysis in real time and under continuously evolving data conditions. This opens new opportunities for applying such models in dynamic domains like environmental monitoring, healthcare, finance and beyond, where it is crucial not only to identify dependencies, but also to ensure that models are adaptive and interpretable by domain experts and end users.