###### Abstract  
This study presents a method for generating synthetic electroencephalography (\(EEG\)) signals to test dynamic directed brain connectivity estimation methods. Current methods for evaluating dynamic brain connectivity estimation techniques face challenges due to the lack of ground truth in real \(EEG\) signals. To address this, we propose a framework for generating synthetic \(EEG\) signals with predefined dynamic connectivity changes. Our approach allows for evaluating and optimizing dynamic connectivity estimation methods, particularly Granger causality (\(GC\)). We demonstrate the framework's utility by identifying optimal window sizes and regression orders for \(GC\) analysis. The findings could guide the development of more accurate dynamic connectivity techniques. elecroencephalography; granger causality; synthetic signals; dynamic connectivity +
Footnote †: This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ([[https://creativecommons.org/licenses/by/4.0/](https://creativecommons.org/licenses/by/4.0/)]([https://creativecommons.org/licenses/by/4.0/](https://creativecommons.org/licenses/by/4.0/))). Footnote †: This article is a revised and expanded version of a paper entitled Generation of Synthetic EEG Signals for Resting Dynamic Brain Connectivity Estimation Methods, which was presented at 6 th International Conference on Advances in Signal Processing and Artificial Intelligence (ASPAI' 2024), Funchal, Portugal, 17-19 April 2024. In this study, connectivity is defined as the directional relationship between two time-series signals, quantified using _GC_. _GC_ assesses whether past values of one signal improve the prediction of another signal's future values, beyond what could be predicted using its own past values. The assumption of _GC_ is that the system is stationary and that a sufficient number of samples can be acquired to ensure reliable estimation. An autoregressive model was also used in [20], where a novel bivariate irregular autoregressive (_BIAR_) model was proposed. The _BIAR_ model assumes an autoregressive structure on each time series, it is stationary, and it allows the autocorrelation to be estimated, i.e., the cross-correlation and the contemporary correlation between two unequally spaced time series. It was shown that if the two signals are highly correlated, the model provides more accurate forecasts and predictions using the bivariate model compared to similar methods that use only univariate information. This feature could enable future application of the _BIAR_ model in connectivity analyses of _EEG_ signals, similar to _GC_. However, the problem of generating synthetic _EEG_ signals with known connectivity remains unresolved in this case as well. To facilitate the evaluation of connectivity methods for assessing dynamic connectivity [21; 22], and specifically the capability of measuring changes in connectivity over time, a method for generating synthetic _EEG_ signals is proposed. Synthetic signals can provide known reference values for directed connectivity, enabling the validation and improvement of dynamic connectivity estimation methods. Numerous methods exist for generating synthetic _EEG_ signals, each with its own strengths and limitations. Sinusoidal models generate signals using sine and cosine functions to mimic the rhythmic activity of brain waves. This approach is straightforward and computationally efficient, making it a popular choice for basic simulations. However, these models often lack the complexity of real _EEG_ signals, such as non-stationarities and noise characteristics. Consequently, they may not adequately represent the true dynamics of brain connectivity. Studies indicate that while sinusoidal models can capture the basic oscillatory nature of _EEG_, they fail to reproduce the intricate signal characteristics observed in empirical data [23; 24].