The human brain is a complex and dynamic physiological system that can be considered as a network of reciprocally interconnected systems localized in different brain regions. To fully characterize the brain's complex dynamics, it is essential to investigate temporal and spatial dimensions jointly. Much of the efforts to quantify the complexity of time series, such as electroencephalogram (EEG) signals, focused on either the temporal dimension or the spatial dimension. However, very few studies explored the complex dynamics in both dimensions simultaneously. In this work, we propose a method to quantify the spatiotemporal complexity of the multivariate time series and test it on the EEG sleep state dataset and EEG seizure dataset. The experimental results demonstrate that the proposed method effectively discriminates between different sleep stages and between seizure and non-seizure states. The achieved area under the Receiver Operating Characteristic curve is 1.8 for the sleep data (a 5-class problem) and 0.7 for the seizure data (a binary classification problem) compared to the human annotation of the datasets. The proposed method shows potential for improving our understanding of the complex dynamics of the human brain system.