Some hypotheses relate oscillations of EEG band power with autonomic processes derived from homeostatic control modulated by structures like the Central Autonomic Network and the Autonomic Nervous System. This research project studies the causal relationships between fluctuations of an autonomic process marker like the Heart Rate Variability (HRV) and the proposed EEG band power time series (BPts). To verify the existence of directional causal relationships, using Granger Causality (GC) test between HRV and BPts. Analyses were performed using two databases, of 9 and 14 subjects respectively. Experiments consisted of spontaneous breathing and a controlled breathing task (CBT). GC was tested over Intrinsinc Mode Functions of HRV derived from Empirical Mode Decomposition and BPts computed over alpha, beta and gamma bands. Positive GC tests were observed through each experimental task, channels, IMFs, EEG band, and direction. The largest number of positive GC relationships were found from BPts to HRV when testing, higher EEG band and IMF with lower spectral content. Opposite direction achieves lower total counts, but more related with IMFs of higher spectral content. Its presence also suggests that some homeostatic condition alters the BPts course given its increment under the CBT. It is important to notice that in both cases gamma band achieves larger values for almost all of the studied conditions. Suggesting that such band has an important influence over HRV, but alterations on breathing condition also produce changes on BPts evolution, suggesting that the closed loop for homeostatic control alters neural dynamics at cortical level.