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Preprint
Sep 2026
Exponential Smoothing for Time Series of Random Objects
Time series of random objects, such as covariance matrices, probability distributions, and functional data, call for forecasting methods that do not rely on standard arithmetic operations. We introduce geodesic exponential smoothing, a generalization of exponential smoothing to time series in Hadamard spaces: the forec...
Takuo Matsubara, Pei-Wen Jiang, W. Y. Chen et al.
· 0 citations
Preprint
Aug 2026
StocBench: A Benchmark for Generative Modeling of Stochastic Dynamics
While stochastic diffusion samplers such as DDPM better preserve the enstrophy spectrum during rollouts in the stochastic setting, deterministic samplers such as DDIM and DPM-2 show better spectral preservation in the deterministic setting.
S. Pfister, Benjamin J. Holzschuh, Nils Thuerey
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TimeES: Probabilistic and Deterministic Time Series Forecasting via Evolutionary Spectra
Real-world time series are inherently non-stationary, with trends, periodic patterns, and uncertainty evolving over time. While the Fourier domain offers a natural lens to model time series, current deep learning approaches do not explicitly model evolution and randomness in the Fourier spectra, which limits their abil...
Wei-Wei Ye, Ren-He Jiang, Hang-Chen Liu et al.
· 0 citations
Preprint
Sep 2026
A Dirichlet-Quantile Bootstrap approach for the probabilistic resampling of time series
The results indicate that incorporating DPQBootstrap can improve point forecast accuracy and the quality of predictive intervals, particularly when combined with appropriately specified ARMA models.
Ahmed Hamimes, Abdennour Boulesnane
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DiffPTS: Rethinking Diffusion ELBO for Probabilistic Time Series Forecasting
This work rethink the ELBO under the Location-Scale Noise Model and finds that it naturally induces a Gaussian negative log likelihood objective for the estimators and inherently defines a joint training objective that unifies recent diffusion paradigms for probabilistic forecasting.
Wei-Wei Ye, Dong-Yuan Li, Hang-Chen Liu et al.
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Open access
Aug 2026
On the Background Driving Lévy Density Associated with the General Tempered Stable Distribution: Theoretical Properties and Financial Applications
This paper identifies and characterizes the background driving Lévy process (BDLP) associated with the Generalized Tempered Stable (GTS) distribution, a flexible seven-parameter family of infinitely divisible distributions with applications in physics and quantitative finance. We show that the corresponding BDLP is a f...
A. Nzokem, D. Maposa
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