Unsupervised Anomaly Detection Using Flow Matching on Tabular Data

Financial anomaly detection often relies on large unlabeled transaction logs, where anomalous samples may already be present during training. Such training-set contamination violates the clean-normal data assumption underlying many anomaly detection methods. Although flow matching has demonstrated strong performance in generative modeling, its robustness in unsupervised tabular anomaly detection remains underexplored. In this work, we study flow-matching-based anomaly detection under contaminated training data by comparing Time-Conditioned Contraction Matching (TCCM) with Forest-Flow and evaluating multiple anomaly scoring functions. Our results show that the choice of anomaly score is critical. The original single-step Decision score used by TCCM is sensitive to contamination, whereas trajectory-based Deviation and Reconstruction scores provide more stable anomaly signals. With these scores, Forest-Flow becomes competitive with, and in some cases outperforms, TCCM. These findings highlight the importance of anomaly scoring for flow-matching methods in financial anomaly detection under severe class imbalance.

Forecast Collapse in Time-Series Foundation Models

When forecasting hourly returns for 1,000 US equities, we observe an unexpected phenomenon: predictions become nearly flat and show poor stock ranking, as measured by cross-sectional correlation. We call this forecast collapse. Surprisingly, the phenomenon largely disappears when forecasting trading volume under the same setting. We investigate forecast collapse across time-series foundation models (TSFMs), twelve deep-learning forecasting models, and 97 public benchmark configurations, and find that it is closely tied to target predictability. We identify two distinct reasons behind it: low predictability limits the amplitude of calibrated point forecasts, while per-series objectives leave cross-series structure unidentified. These findings reveal a calibration-ranking tradeoff: optimizing squared error leads to flat predictions, whereas directly optimizing cross-sectional correlation improves ranking but can inflate forecast amplitude by more than an order of magnitude. To address this tradeoff, we introduce CalibRank, a simple objective that balances calibration and ranking. On Finance1K, CalibRank nearly triples cross-sectional correlation while keeping amplitude close to the target, and improves correlation on all tested models. Our results reveal a blind spot in conventional time-series evaluation: per-series metrics can hide failures in cross-series structure needed by downstream decisions.

Probabilistic Signature Inversion: Learning Conditional Distributions from Truncated Signatures

The signature transform is a principled feature map for continuous-time paths, valued for its uniqueness and universality. Recovering a path from its truncated signature is, however, structurally ill-posed because the truncated signature map is not injective. We therefore reframe truncated signature inversion as a probabilistic problem -- learning the conditional distribution of a path given its truncated signature -- and adopt a signature-conditioned flow matching model as a practical estimator. This probabilistic formulation elucidates the fundamental difficulty of inversion: Bayes reconstruction error quantifies the irreducible uncertainty remaining after conditioning on a statistic. We derive the Bayes-optimal error under linear statistics, obtaining a closed form for log-GBM and numerically tractable formulas for log-fBM and OU, yielding a concrete theoretical baseline for model validation. This baseline upper-bounds the Bayes error under truncated-signature conditioning, since truncated signatures provide richer information than linear statistics. Experiments show that empirical reconstruction errors under linear-statistics conditioning faithfully align with the theory-derived baseline, while errors decrease when the statistic is replaced with truncated signatures. Moreover, generated paths faithfully recover the conditioning signature while preserving key distributional and temporal structures, indicating that the estimator is well-calibrated to the target conditional distribution. Together, these results establish a well-posed probabilistic framework for truncated-signature inversion, with applicability demonstrated on real financial data beyond the parametric process families covered by theory.

Generating Financial Time Series by Matching Random Convolutional Features

Generating realistic financial time series is challenging as training data is often limited to a single historical path. With such scarce data, overfitting is hard to avoid, especially under adversarial training where a trained discriminator can memorize the training samples. To mitigate this, recent approaches train generators to minimize the discrepancy between untrained feature representations of real and generated time series. In these works, the feature maps are based on path signatures, which can fail to capture relevant time series properties at tractable truncation depths. In this work, we instead train generators by matching random convolutional features of real and generated time series. Existing random convolutional feature maps, such as Rocket and Hydra, have been shown to provide informative representations of real-world time series, but cannot supervise generative models because they are non-differentiable. We introduce SOCK (SOft Competing Kernels), a fully differentiable random convolutional feature map, suited to train generative time series models. We show that generators trained by matching random SOCK features consistently outperform signature and diffusion baselines across a wide range of small-sample financial datasets. We further demonstrate SOCK's expressiveness on two-sample hypothesis testing and time series classification tasks, where SOCK matches or outperforms existing unsupervised feature maps.

FinStressTS: A Parametric Synthetic Benchmark for Time-Series Forecasting in Finance

Financial forecasting is difficult due to low signal-to-noise ratios, latent factors, heavy tails, regime shifts, and jumps. Real-world benchmarks offer limited failure attribution: researchers can observe underperformance, but often cannot isolate why because mechanisms are unobservable and entangled. Real financial data reveal only one realized path, making it difficult to assess tail-risk calibration or data efficiency. We introduce FinStressTS, a mechanism-aware synthetic benchmark that links model behavior to controlled structural causes. FinStressTS comprises 30 diagnostic environments around six mechanism families: volatility clustering, multi-scale persistence, heavy-tailed shocks, regime switching, self-exciting jumps, and zero-inflated processes. We evaluate two tasks: point forecasting, using NMAE across five settings, and probabilistic forecasting, using CRPS under known data-generating mechanisms. We benchmark 15 models, from classical methods (HAR, VAR) to Transformer forecasters (PatchTST, iTransformer) and deep probabilistic architectures (DeepAR, TSFlow), and use learning curves to measure sample efficiency. Our evaluation reveals three insights. First, performance is mechanism-dependent: autoregressive and linear models are highly competitive, and often outperform Transformer-based models, in several volatility-, tail-, and jump-driven environments. Second, distributional alignment matters: parametric probabilistic models such as DeepAR calibrate well in stationary settings, while flexible models can help when distributions become multimodal or sparse. Third, neural models often require more data to match simple baselines, with larger gains mainly when learning latent regimes or complex distributions. FinStressTS provides an open framework for diagnosing failure modes and advancing risk-aware forecasting.

Learning Time-Inhomogeneous Markov Dynamics in Financial Time Series via Neural Parameterization

Modeling the dynamics of non-stationary stochastic systems requires balancing the representational power of deep learning with the mathematical transparency of classical models. While classical Markov transition operators provide explicit, theoretically grounded rules for system evolution, their empirical estimation collapses due to severe data sparsity when applied to high-resolution, high-noise environments. We explore this statistical barrier using financial time series as a canonical, real-world testbed. To overcome the degeneracy of empirical counting, we introduce a framework that utilizes neural networks strictly as parameterization engines to generate explicit, time-varying Markov transition matrices. By constraining the neural network to output its predictions as a formal stochastic operator, we maintain complete structural interpretability. We demonstrate that these learned operators successfully capture complex regime shifts: the state-conditioned model achieves mean row heterogeneity $\barρ = 0.0073$ while the state-free ablation collapses to exactly zero, and operator row entropy correlates with realized variance at $r = -0.62$ ($p \approx 10^{-251}$), revealing that high-volatility regimes homogenize transition dynamics rather than diversify them. Furthermore, rather than enforcing the Chapman-Kolmogorov equations as a rigid structural requirement, we repurpose them as a localized diagnostic tool to pinpoint specific temporal windows where first-order memory assumptions break down. Ultimately, this framework demonstrates how neural networks can be constrained to make rigorous, classical operator analysis viable for complex real-world time series.