The log-signature-based time series Wasserstein generative adversarial network
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- We introduce the Log-Signature Wasserstein GAN, combining log-signature features with a learnable 1-Lipschitz neural critic.
- Log-signatures provide a compact, numerically stable path representation, reducing target dimension while preserving the compression and invariance benefits of signature-based methods.
- The adaptive critic provides richer feedback than the static linear functional in Sig-WGAN, improving generator performance and the modeling of complex, non-Markovian temporal dependence.
- Experiments on synthetic and real-world financial data show improved marginal fit and temporal and spatial dependence, with only a moderate increase in training time; the discriminator also shows promise as a standalone classification model.
The signature Wasserstein generative adversarial network (SigWGAN) developed by Ni et al in 2021 achieved great results in time series generation using a recurrent neural network in combination with log signatures as the generator, trained to maximize the similarity between signatures given a static loss function. As an alternative to the static loss function on signatures, we propose using neural networks to minimize the Wasserstein distance between log signatures to reduce the target dimension of the generator and increase performance by introducing a learnable discriminator. We validate our proposed model on synthetic and real-world data across several performance evaluation metrics, showcasing its effectiveness for financial time series generation.
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