The dataset is made primarily for the task of real-time low latency filtering of the EEG data in the closed loop neuroscience experiments and for EEG forecasting task. The dataset consists of a real data and 5 options of the synthetic data of varying difficulty. The real dataset consists of 25 people involved into the P4 alpha neurofeedback training. Its total size is about 16.3 hours. A more detailed instruction for this file is provided in the file Real dataset instructions.txt. Synthetic data is generated in 5 different ways: sine wave with white noise, sine wave with pink noise, narrow-band filtered pink noise sample with pink noise, state-space model with white noise and state-space model with pink noise. Each of these datasets has about 34.5 hours of data. It is generated similarly to (Wodeyar et al, 2021). A more detailed instruction for the synthetic dataset can be found in the file Synthetic datasets instructions.txt. In LowLatencyEEGFiltering.zip one can find a code for the models used in our paper for low-latency filtering with this data. NOTE: Code is also published in the following GitHub repository: https://github.com/ivsemenkov/LowLatencyEEGFiltering If you use our data or code please cite: https://www.doi.org/10.1088/1741-2552/acf7f3