Transformer-based architectures dominate time series modeling by enabling global attention over all timestamps, yet their rigid 'one-size-fits-all' context aggregation fails to address two critical challenges in real-world data: (1) inherent lag effects, where the relevance of historical timestamps to a query varies dynamically; (2) anomalous segments, which introduce noisy signals that degrade forecasting accuracy. To resolve these problems, we propose the Temporal Mix of Experts (TMOE), a novel attention-level mechanism that reimagines key-value (K-V) pairs as local experts (each specialized in a distinct temporal context) and performs adaptive expert selection for each query via localized filtering of irrelevant timestamps. Complementing this local adaptation, a shared global expert preserves the Transformer's strength in capturing long-range dependencies. We then replace the vanilla attention mechanism in popular time-series Transformer frameworks (i.e., PatchTST and Timer) with TMOE, without extra structural modifications, yielding our specific version TimeExpert and general version TimeExpert-G. Extensive experiments on seven real-world long-term forecasting benchmarks demonstrate that TimeExpert and TimeExpert-G outperform state-of-the-art methods. Code is available at https://github.com/xwmaxwma/TimeExpert.

Children's health studies support an association between maternal environmental exposures and children's birth and health outcomes. A common goal in such studies is to identify critical windows of susceptibility -- periods during gestation with increased association between maternal exposures and a future outcome. The associations and timings of critical windows are likely heterogeneous across different levels of individual, family, and neighborhood characteristics. However, the few studies that have considered effect modification were limited to a few pre-specified subgroups. We propose a statistical learning method to estimate critical windows at the individual level and identify important characteristics that induce heterogeneity. The proposed approach uses distributed lag models (DLMs) modified by Bayesian additive regression trees to account for effect heterogeneity based on a potentially high-dimensional set of modifying factors. We show in a simulation study that our model can identify both critical windows and modifiers responsible for DLM heterogeneity. We estimate the relationship between weekly exposures to fine particulate matter during gestation and birth weight in an administrative Colorado birth cohort. We identify maternal body mass index (BMI), age, Hispanic designation, and education as modifiers of the distributed lag effects and find non-Hispanics with increased BMI to be a susceptible population.