Synthetic time series generation has gained significant attention in finance as it may enable the augmentation of limited data and preserves data privacy, thereby unlocking the full potential of data-intensive machine learning algorithms. However, generating high-fidelity time series using generative adversarial networks (GANs) remains challenging. In this talk, I will introduce PCF-GAN, a novel GAN that incorporates the path characteristic function (PCF) into the discriminator, enhancing generative performance. We further enhance complex time series generation by integrating an auto-encoder structure via sequential embedding into PCF-GAN, which provides additional reconstruction functionality.. Extensive experiments on various datasets (e.g., rough volatility and empirical stock data) show consistently superior performance over state-of-the-art baselines in generation and reconstruction quality. Joint work with Dr. Siran Li (Shanghai Jiao Tong Uni) and Hang Lou (UCL). Paper: [https://arxiv.org/pdf/2305.12511.pdf].