Trajectory Generator Matching for Time Series
This work addresses a significant problem in time series analysis for researchers and practitioners dealing with irregularly sampled data, representing a novel method rather than an incremental improvement.
The paper tackles the challenge of modeling time-continuous stochastic processes from irregular observations by introducing new generators for SDEs and jump processes, achieving accurate time series generation with the ability to handle discontinuities and irregular sampling.
Accurately modeling time-continuous stochastic processes from irregular observations remains a significant challenge. In this paper, we leverage ideas from generative modeling of image data to push the boundary of time series generation. For this, we find new generators of SDEs and jump processes, inspired by trajectory flow matching, that have the marginal distributions of the time series of interest. Specifically, we can handle discontinuities of the underlying processes by parameterizing the jump kernel densities by scaled Gaussians that allow for closed form formulas of the corresponding Kullback-Leibler divergence in the loss. Unlike most other approaches, we are able to handle irregularly sampled time series.