## 4 Conclusions  
This study outlines the process of creating a synthetic signal designed for evaluating the dynamic characteristics of directional connectivity techniques. The signal is generated by reconstructing data from real signals using coefficients from regression models. By employing the approach proposed in this article, the impact of source signals can be controlled through the incorporation of a variable temporal connectivity parameter \(K\), which adjusts dynamically over time, thereby defining the fluctuation in actual connectivity dynamics. This ensures that the generated synthetic signals closely mirror real-world scenarios. During the evaluation of dynamic connectivity methods, the connectivity between the generated signal \(R^{\prime}\) and the source signal \(S^{\prime}\) is assessed. These results are compared against the weighting parameter \(K\). This process was demonstrated through dynamic \(GC\) estimation using a sliding window approach. The challenge lies in selecting an appropriate window size: larger windows typically provide lower temporal resolution of dynamic connectivity estimates, while narrower windows can compromise the accuracy of autoregressive models, leading to increased variability in estimated dynamics. Identifying the optimal window size or comparing different methodologies requires knowledge of the genuine changes in connectivity, which are precisely known only in the case of synthetically generated signals. Hence, it is crucial that the generated signals accurately reflect properties obtained from real signals. The proposed methodology satisfies both criteria, ensuring that the synthetic test signals are realistic and suitable for validating and advancing dynamic connectivity techniques. Therefore, the proposed method for generating synthetic test signals is well suited for the development and evaluation of dynamic connectivity methods. Additionally, in this study, a comprehensive analysis was conducted of dynamic \(GC\) across varying window sizes and regression orders \(M_{GC}\). By evaluating the root mean square error between reference and estimated dynamic \(GC\) values, the optimum window size was identified. Our findings demonstrate that, in our case, the window size increases with order size; the minimum error is obtained for order 9, and it only slightly increases with further increase in the order. Furthermore, the transition time of \(GC\) change was analyzed by calculating rise and fall times between 10% and 90% of connectivity thresholds. The results show that the  
Figure 12: Optimum window size in terms of the minimization of the product \(TT\cdot\varepsilon_{RMS}\) with respect to selected regression order \(M_{GC}\) (blue asterisks) and corresponding minimal \(TT\cdot\varepsilon_{RMS}\) (red triangles). smallest \(TT\) value generally corresponds to higher \(\varepsilon_{RMS}\). Therefore, an optimal solution that minimizes the \(TT\) and \(\varepsilon_{RMS}\) product was further determined. These findings provide a detailed framework for selecting appropriate window sizes and regression orders in dynamic \(GC\) analysis, enhancing the reliability of connectivity studies. In addition, this methodology could be applied to applications in other domains where connectivity analysis of signals is relevant. Future work should focus on further refining these parameters and exploring their applicability in various experimental and real-world scenarios. For real-time applications, where responsiveness is critical, smaller windows can provide faster adaptation to abrupt changes, although with potentially increased noise in the estimates. Increased computational complexity and cost of methods based on varying window sizes should be analyzed in more detail for real-time applications.