financial forecasting teams

Abstract: Transformers have demonstrated strong performance in long-term time series forecasting (LTSF), yet modeling non-stationary temporal dependencies remains challenging. In this paper, we interpret self-attention as a Bayesian posterior over attended positions, combining a content-based prior induced by scaled dot-product similarity with a temporal-evidence likelihood induced by positional encoding. This formulation provides a probabilistic interpretation of how positional encoding shapes the temporal dependencies captured by self-attention. Building on this perspective, we derive a population-level evidence lower bound (ELBO) that characterizes the role of positional encoding in forecasting weakly stationary time series. Our analysis further highlights a limitation of static positional encoding: when temporal dependence structures vary across input windows, a fixed temporal bias must accommodate heterogeneous dynamics and can therefore be suboptimal for non-stationary forecasting. Motivated by this analysis, we propose Bayesian Time-aware Attention (BTA), which employs a mixture-of-experts (MoE) router to adaptively combine temporal kernels and generate input-conditioned, head-specific positional biases. Extensive experiments on standard LTSF benchmarks demonstrate that BTA consistently improves forecasting performance across multiple Transformer backbones and achieves competitive overall performance with modest computational overhead and stable training.

Abstract: Repeated event forecasting requires extracting predictive signals from noisy evidence and evaluating their value across successive decisions. We introduce JockeyBench, a benchmark and evaluation protocol that studies this problem through historical Japanese horse racing. The protocol combines time-gated evidence, priced tools, paired frozen-program controls, and two workflows: executing an LLM-written predictor or acquiring evidence for a fresh per-race LLM forecast. Evaluation separates forecast quality, benchmark-specific net utility, and retrospective betting returns and risk under fixed decision rules. Across 28 model--scaffold configurations on 324 races, paired tests identify seven revision gains and two declines after multiple-testing correction. Yet every configuration has negative mean profit under capped-Kelly settlement. In a four-model comparison, the reusable-program workflow has higher mean betting profit and lower research fees, although both workflows lose on average. Further diagnostics reveal that mean probability bias reverses on selected bets and that profitable individual runs can depend on concentrated returns. These findings motivate evaluating predictive competence, adaptation, resource use, and decision value separately when assessing agents for repeated event forecasting.

Abstract: Accurate uncertainty quantification is critical for many time series forecasting applications, and recent studies have increasingly adopted generative models to capture predictive uncertainty. Existing approaches often combine deterministic forecasting with generative modeling to improve predictive performance. However, their joint training is typically unstable because the deterministic model is embedded within the generative process, resulting in deep computational graphs and changing the probability transport path. In this work, we propose DV-Flow, a unified flow-matching formulation that incorporates the deterministic predictor as a parallel velocity component rather than as the endpoint of the transport path. This design enables stable end-to-end optimization while subsuming several existing formulations as special cases, allowing direct comparisons among them. Extensive experiments on six real-world datasets demonstrate that DV-Flow consistently improves probabilistic forecasting performance over strong baselines. Our code is available at https://github.com/tufts-ml/dv-flow-time-series.

Abstract: Despite the success of Time Series Foundation Models (TSFMs) on broad benchmarks, their ability to internalize basic temporal logic, especially in settings supported by exogenous covariates, remains under-examined. We introduce SimpleTimeBench, a diagnostic univariate and multivariate "unit test" suite for primitives such as monotonic trends, periodic signals and leading indicator covariates, scenarios where near-perfect forecasts should be trivial. Surprisingly, prominent multivariate TSFMs (Chronos-2, Moirai and Toto) frequently produce suboptimal zero-shot forecasts for these inputs. While fine-tuning Chronos-2 improves its behaviour on specific tasks, we show that this adaptation degrades performance on other fundamental patterns rather than enhancing its generalizable foundational capabilities. This reveals a gap between pre-training scale and basic temporal reasoning, suggesting that current TSFMs could potentially lack the inductive biases needed to capture simple predictable functions. We further demonstrate that these failures are not merely synthetic curiosities: they persist in real-world sensor forecasting, where TSFMs consistently underutilize leading indicators available in observed covariates. This inability to capture simple relationships limits the practical utility and reliability of current multivariate models.

Abstract: Time series foundation models (TSFMs) are pretrained on heterogeneous collections containing billions of observations, yet their training windows are typically sampled without estimating whether they provide useful learning signal. We introduce a static data-selection framework that scores each window with a reference forecaster and retains an intermediate interval within every source dataset. Specifically, we connect forecasting loss to optimization difficulty by showing that normalized squared loss controls the per-sample gradient norm under a local Jacobian condition. We then define a reference loss score and apply dataset-stratified selection to preserve the diversity of samples. Across various TSFM architectures, our method outperforms random selection by an absolute margin and even improves both relative MASE and CRPS over full-data pretraining by retaining fewer candidate pretraining windows. Further analyses show strong cross-scale and cross-architecture score correlations, indicating that a small reference model can often select data for larger targets, provided that the reference and target share compatible difficulty orderings.

Abstract: Time-series foundation models are evaluated almost exclusively on public archives that predate them, so a strong score cannot be separated from having seen the test set during pretraining. The obvious remedy is a hold-out that postdates the models. We build one: thirteen forecasters -- four classical, three trained per dataset, six pretrained -- on seven groups drawn from five domains, every observation published after the last model was released, and every dataset rebuildable without an API key. Under this protocol pretrained models win 5 of 7 groups, lose one to a Theta baseline, and on daily exchange rates are indistinguishable from a seasonal naive forecast, along with every other method tested. We then ask what separates the wins from the losses, and report a negative result: the two intrinsic properties one would reach for -- seasonal strength and spectral entropy, measured on the input window -- do not account for the pattern, and seasonal strength is if anything negatively associated with the advantage. What does track it is corpus familiarity. Our largest gain (28% lower MASE than the best classical method, on weekly Wikipedia pageviews) falls on Wikipedia pageviews, the domain TimesFM's authors describe as the bulk of its pretraining corpus, at the same granularities and differing only in time window. Within the pretrained family, where every model forecasts identical series so that series difficulty cancels, the TimesFM family outranks the Chronos family by -0.53 ranks on Wikipedia against -0.09 everywhere else (1,500 vs. 754 series, Mann-Whitney p < 1e-5). We conclude that a temporal hold-out removes memorisation of a window but not familiarity with a domain, that benchmarks therefore need domain hold-outs stated relative to disclosed corpora, and that the practitioner's question is less which model is better than whether their domain is one the model was raised on.