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Generating high-fidelity time series data using generative adversarialnetworks (GANs) remains a challenging task, as it is difficult to capture thetemporal dependence of joint probability distributions induced by time-seriesdata. Towards this goal, a key step is the development of an effectivediscriminator to distinguish between time series distributions. We propose theso-called PCF-GAN, a novel GAN that incorporates the path characteristicfunction (PCF) as the principled representation of time series distributioninto the discriminator to enhance its generative performance. On the one hand,we establish theoretical foundations of the PCF distance by proving itscharacteristicity, boundedness, differentiability with respect to generatorparameters, and weak continuity, which ensure the stability and feasibility oftraining the PCF-GAN. On the other hand, we design efficient initialisation andoptimisation schemes for PCFs to strengthen the discriminative power andaccelerate training efficiency. To further boost the capabilities of complextime series generation, we integrate the auto-encoder structure via sequentialembedding into the PCF-GAN, which provides additional reconstructionfunctionality. Extensive numerical experiments on various datasets demonstratethe consistently superior performance of PCF-GAN over state-of-the-artbaselines, in both generation and reconstruction quality. Code is available athttps://github.com/DeepIntoStreams/PCF-GAN.

PCF-GAN: generating sequential data via the characteristic function of measures on the path space