Synthetic time series are often used in practical applications to augment the
historical time series dataset for better performance of machine learning
algorithms, amplify the occurrence of rare events, and also create
counterfactual scenarios described by the time series.
Distributional-similarity (which we refer to as realism) as well as the
satisfaction of certain numerical constraints are common requirements in
counterfactual time series scenario generation requests. For instance, the US
Federal Reserve publishes synthetic market stress scenarios given by the
constrained time series for financial institutions to assess their performance
in hypothetical recessions. Existing approaches for generating constrained time
series usually penalize training loss to enforce constraints, and reject
non-conforming samples. However, these approaches would require re-training if
we change constraints, and rejection sampling can be computationally expensive,
or impractical for complex constraints. In this paper, we propose a novel set
of methods to tackle the constrained time series generation problem and provide
efficient sampling while ensuring the realism of generated time series. In
particular, we frame the problem using a constrained optimization framework and
then we propose a set of generative methods including ``GuidedDiffTime'', a
guided diffusion model to generate realistic time series. Empirically, we
evaluate our work on several datasets for financial and energy data, where
incorporating constraints is critical. We show that our approaches outperform
existing work both qualitatively and quantitatively. Most importantly, we show
that our ``GuidedDiffTime'' model is the only solution where re-training is not
necessary for new constraints, resulting in a significant carbon footprint
reduction.

本文利用一个带限制的优化框架，提出了一套生成方法，包括 “GuidedDiffTime”，用于生成合成的具有现实性的时间序列，相比现有方法更加高效，且无需重新训练，取得了显著的性能提升，并大幅降低了碳足迹。

关于有限时间序列生成问题的研究

On the Constrained Time-Series Generation Problem

A framework is proposed for the unconditional generation of synthetic time
series based on learning from a single sample in low-data regime case. The
framework aims at capturing the distribution of patches in wavelet scalogram of
time series using single image generative models and producing realistic
wavelet coefficients for the generation of synthetic time series. It is
demonstrated that the framework is effective with respect to fidelity and
diversity for time series with insignificant to no trends. Also, the
performance is more promising for generating samples with the same duration
(reshuffling) rather than longer ones (retargeting).

本研究提出了一种从单一样本中学习生成低数据制度下合成时间序列的框架，它利用单个图像生成模型捕捉时间序列波小波形成对数分布，为生成合成时间序列绘制逼真的波小波系数。结果显示这个框架对于在无趋势的时间序列中保证了逼真度和多样性，而且生成的样本时长相同时（重新混洗），其性能更加优秀。