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Synthetic time series are often used in practical applications to augment thehistorical time series dataset for better performance of machine learningalgorithms, amplify the occurrence of rare events, and also createcounterfactual scenarios described by the time series.Distributional-similarity (which we refer to as realism) as well as thesatisfaction of certain numerical constraints are common requirements incounterfactual time series scenario generation requests. For instance, the USFederal Reserve publishes synthetic market stress scenarios given by theconstrained time series for financial institutions to assess their performancein hypothetical recessions. Existing approaches for generating constrained timeseries usually penalize training loss to enforce constraints, and rejectnon-conforming samples. However, these approaches would require re-training ifwe change constraints, and rejection sampling can be computationally expensive,or impractical for complex constraints. In this paper, we propose a novel setof methods to tackle the constrained time series generation problem and provideefficient sampling while ensuring the realism of generated time series. Inparticular, we frame the problem using a constrained optimization framework andthen we propose a set of generative methods including "GuidedDiffTime", aguided diffusion model to generate realistic time series. Empirically, weevaluate our work on several datasets for financial and energy data, whereincorporating constraints is critical. We show that our approaches outperformexisting work both qualitatively and quantitatively. Most importantly, we showthat our "GuidedDiffTime" model is the only solution where re-training is notnecessary for new constraints, resulting in a significant carbon footprintreduction, up to 92% w.r.t. existing deep learning methods.

On the Constrained Time-Series Generation Problem