Modern time series forecasting is evaluated almost entirely through passive observation of single historical trajectories, rendering claims about a model's robustness to non-stationarity fundamentally unfalsifiable. We propose a paradigm shift toward interventionist, exact-statistical benchmarking. By systematically titrating calibrated Gaussian observation noise into known chaotic and stochastic dynamical systems, we transform forecasting from a black-box sequence matching game into an exact distributional inference task. Because the underlying data-generating process and noise variance are mathematically explicit, evaluation can rely on exact negative log-likelihoods and calibrated distributional tests rather than heuristic approximations. To fully leverage this framework, we extend the Fern architecture into a probabilistic generative model that natively parameterizes the Symmetric Positive Definite (SPD) cone, outputting calibrated joint covariance structures without the computational bottleneck of generic Jacobian modeling. Under this rigorous evaluation, we find that state-of-the-art zero-shot foundation models behave consistently with the context-parroting mechanism, failing systematically under non-stationary regime shifts and elevated noise. In contrast, Fern explicitly captures the invariant measure and multivariate geometry of the underlying dynamics, maintaining structural fidelity and statistically sharp calibration precisely where massive sequence-matching models collapse.

Autocorrelation is a defining characteristic of time-series data, where each observation is statistically dependent on its predecessors. In the context of deep time-series forecasting, autocorrelation arises in both the input history and the label sequences, presenting two central research challenges: (1) designing neural architectures that model autocorrelation in history sequences, and (2) devising learning objectives that model autocorrelation in label sequences. Recent studies have made strides in tackling these challenges, but a systematic survey examining both aspects remains lacking. To bridge this gap, this paper provides a comprehensive review of deep time-series forecasting from the perspective of autocorrelation modeling. In contrast to existing surveys, this work makes two distinctive contributions. First, it proposes a novel taxonomy that encompasses recent literature on both model architectures and learning objectives -- whereas prior surveys neglect or inadequately discuss the latter aspect. Second, it offers a thorough analysis of the motivations, insights, and progression of the surveyed literature from a unified, autocorrelation-centric perspective, providing a holistic overview of the evolution of deep time-series forecasting. The full list of papers and resources is available at https://github.com/Master-PLC/Awesome-TSF-Papers.

Functional magnetic resonance imaging (fMRI) enables noninvasive investigation of brain function, while short clinical scan durations, arising from human and non-human factors, usually lead to reduced data quality and limited statistical power for neuroimaging research. In this paper, we propose BrainCast, a novel spatio-temporal forecasting framework specifically tailored for whole-brain fMRI time series forecasting, to extend informative fMRI time series without additional data acquisition. It formulates fMRI time series forecasting as a multivariate time series prediction task and jointly models temporal dynamics within regions of interest (ROIs) and spatial interactions across ROIs. Specifically, BrainCast integrates a Spatial Interaction Awareness module to characterize inter-ROI dependencies via embedding every ROI time series as a token, a Temporal Feature Refinement module to capture intrinsic neural dynamics within each ROI by enhancing both low- and high-energy temporal components of fMRI time series at the ROI level, and a Spatio-temporal Pattern Alignment module to combine spatial and temporal representations for producing informative whole-brain features. Experimental results on resting-state and task fMRI datasets from the Human Connectome Project demonstrate the superiority of BrainCast over state-of-the-art time series forecasting baselines. Moreover, fMRI time series extended by BrainCast improve downstream cognitive ability prediction, highlighting the clinical and neuroscientific impact brought by whole-brain fMRI time series forecasting in scenarios with restricted scan durations.

Specifically, we summarize our contributions into the following points.

By introducing LLM-embedded textual timestamps, Auto-Times can utilize chronological information to align multivariate time series. Empirically, AutoTimes achieves state-of-the-art with 0.1% trainable parameters and