Generating high-fidelity time series data using generative adversarial
networks (GANs) remains a challenging task, as it is difficult to capture the
temporal dependence of joint probability distributions induced by time-series
data. Towards this goal, a key step is the development of an effective
discriminator to distinguish between time series distributions. We propose the
so-called PCF-GAN, a novel GAN that incorporates the path characteristic
function (PCF) as the principled representation of time series distribution
into the discriminator to enhance its generative performance. On the one hand,
we establish theoretical foundations of the PCF distance by proving its
characteristicity, boundedness, differentiability with respect to generator
parameters, and weak continuity, which ensure the stability and feasibility of
training the PCF-GAN. On the other hand, we design efficient initialisation and
optimisation schemes for PCFs to strengthen the discriminative power and
accelerate training efficiency. To further boost the capabilities of complex
time series generation, we integrate the auto-encoder structure via sequential
embedding into the PCF-GAN, which provides additional reconstruction
functionality. Extensive numerical experiments on various datasets demonstrate
the consistently superior performance of PCF-GAN over state-of-the-art
baselines, in both generation and reconstruction quality. Code is available at
this https URL

本文提出了一种名为 PCF-GAN 的新型生成对抗网络，将路径特征函数（PCF）作为时间序列分布的原则表示，并将其并入鉴别器以增强其生成性能，同时通过序列嵌入将自编码器结构集成到模型中，实现了复杂时间序列数据的生成和重构。实验证明，PCF-GAN 在生成和重构质量上始终优于现有技术。