This paper presents a path signature-based XAI-enabled network time series (NTS) classification model called RecurSig. NTS classification is crucial for network automation and cybersecurity, enabling anomaly detection, attack identification, and performance monitoring. However, modern communication networks pose challenges for NTS classification, including handling large-scale and complex data, feature extraction, and explainability. These challenges are particularly significant for 5G networks, where explainability is essential for widespread deployment of network automation. To address these challenges, RecurSig is proposed, which combines deep learning (DL) techniques with an explainable classification approach. The model includes two main components: Verbe, a data augmentation module using 1D convolutional neural networks (1D-CNN), and SigRNN, a feature-extraction module with XAI-enabled properties. Verbe enhances data while preserving its intrinsic flow properties, while SigRNN converts time series into multidimensional paths and computes interpretable signature features. Extensive experiments on six public datasets show that RecurSig outperforms existing models in accuracy and explainability. The results indicate its potential for application in cyberspace security and automated network management, offering an explainable solution for network protection and optimization. The paper also discusses the importance of accurate NTS classification for network automation, emphasizing the need for reliable, efficient, and explainable methods. The proposed model addresses the challenges of time-consuming feature extraction and black-box issues in DL, providing a robust solution for NTS classification. The paper concludes with a discussion of future research directions.This paper presents a path signature-based XAI-enabled network time series (NTS) classification model called RecurSig. NTS classification is crucial for network automation and cybersecurity, enabling anomaly detection, attack identification, and performance monitoring. However, modern communication networks pose challenges for NTS classification, including handling large-scale and complex data, feature extraction, and explainability. These challenges are particularly significant for 5G networks, where explainability is essential for widespread deployment of network automation. To address these challenges, RecurSig is proposed, which combines deep learning (DL) techniques with an explainable classification approach. The model includes two main components: Verbe, a data augmentation module using 1D convolutional neural networks (1D-CNN), and SigRNN, a feature-extraction module with XAI-enabled properties. Verbe enhances data while preserving its intrinsic flow properties, while SigRNN converts time series into multidimensional paths and computes interpretable signature features. Extensive experiments on six public datasets show that RecurSig outperforms existing models in accuracy and explainability. The results indicate its potential for application in cyberspace security and automated network management, offering an explainable solution for network protection and optimization. The paper also discusses the importance of accurate NTS classification for network automation, emphasizing the need for reliable, efficient, and explainable methods. The proposed model addresses the challenges of time-consuming feature extraction and black-box issues in DL, providing a robust solution for NTS classification. The paper concludes with a discussion of future research directions.