Neural Time Series Forecasting: A Problem-Driven Survey from Data Challenges to Model Choice

From Vector Autoregressions to AI-based Time Series Forecasting: A Review

Forecasting is a central goal of time-series analysis. This review centers on three major developments in recent AI-based time-series forecasting: transformers, large pretrained models for zero-shot forecasting, and diffusion-based generative forecasters. We connect these methods to the econometric tradition built around the vector autoregression (VAR) through a common object: the conditional distribution of the future given the past. The review is organized around three long-standing challenges: \emph{high dimensionality}, \emph{nonstationarity}, and \emph{nonlinearity}. We argue that modern methods make progress by expanding the classical forecasting template: they allow more flexible dynamics, use larger information sets and training corpora, and represent richer predictive distributions. Yet they often lack the inferential and structural tools that make classical models useful for testing, explanation, and policy analysis. We close by outlining open problems where econometric tools remain important.

Multivariate Time Series Forecasting needs Cross Variable Loss

Multivariate time series forecasting presents unique challenges because future variables often co-evolve under shared system dynamics. While existing studies mainly focus on cross-variable dependencies in historical observations, dependencies among future values are much less explored. Specifically, modern forecasting models largely follow the Direct Forecasting (DF) paradigm, generating multi-step forecasts with point-wise objectives that do not explicitly constrain cross-variable structure. In this work, we show that the DF objective is mismatched in the presence of cross-variable and lagged dependencies, revealing an objective gap. To address this issue, we propose \textbf{C}ross-\textbf{V}ariable \textbf{Loss} (CvLoss), a plug-in structural regularizer that constrains forecast residuals on a cross-variable graph. CvLoss penalizes inconsistent edge-wise residual differences over forecast patches, encouraging consistency across both synchronous and asynchronous interactions. Our experiments show that CvLoss consistently improves competitive forecasting models, outperforms representative learning objectives, and is compatible with a variety of forecasting backbones.

Forecasting Multivariate Time Series: A Comparison of Machine Learning, Statistical and Deep Learning Models

This study develops a rigorous, leakage-free forecasting framework for monthly Robusta coffee prices using historical observations from January 1975 to December 2025. A comprehensive set of explanatory variables is constructed from lagged coffee prices, moving averages, logarithmic returns, rolling volatility, and exogenous variables such as the Oceanic Niño Index (ONI), the U.S. Dollar Index, and Brent crude oil prices. To ensure methodological fairness, all predictors are generated exclusively from information available at the forecast origin, and all competing models are evaluated under a unified expanding-window walk-forward validation framework. Seven forecasting models are compared: Naïve, Exponential Smoothing (ETS), ARIMA, ARIMAX, Extreme Gradient Boosting (XGBoost), Long Short-Term Memory (LSTM), and Gated Recurrent Unit (GRU). Forecasting performance is evaluated using R2, RMSE, MAE, and MAPE, while Taylor diagrams and the Diebold–Mariano test are employed to assess model agreement and differences in predictive accuracy. The results show that XGBoost achieves the highest forecasting accuracy (R2 = 0.956, RMSE = 0.264), followed closely by the Naïve (R2 = 0.954, RMSE = 0.271) and ARIMA (R2 = 0.954, RMSE = 0.270) benchmarks, whereas ARIMAX and ETS provide comparable performance and the deep learning models (LSTM and GRU) produce substantially larger prediction errors. Feature importance analysis further indicates that the first lag of coffee price is the dominant predictor, accounting for approximately 94% of the predictive gain in XGBoost. Overall, the findings demonstrate that rigorous leakage-free validation is essential for reliable forecasting research and that, for monthly Robusta coffee prices, increased model complexity does not necessarily yield superior predictive performance.

Efficient and explainable multivariate time series forecasting: a survey of architectures, taxonomies, and open challenges

The rapid expansion of multivariate time series (MTS) data has made deep learning a central tool for forecasting across industrial and scientific domains. As these architectures move into settings such as clinical decision support, industrial monitoring, and financial risk management, researchers need to examine not only predictive accuracy but also computational cost and the kinds of explanations that a model can support. This survey re-examines deep learning models for MTS forecasting through the requirements of efficiency and explainability. Our contributions are threefold: (1) We synthesize the literature through a dual-axis scalability view over sequence length L and variate dimension N , together with a three-question explainability taxonomy covering temporal importance, variate importance, and pattern decomposition. (2) We review dominant architectural families, including Transformer variants, frequency-domain methods, linear and channel-independent backbones, state space models, and foundation-style forecasters, to describe how different designs occupy different efficiency–explainability profiles under specific data and deployment assumptions. (3) Building on this synthesis, we identify key open challenges—including the absence of standardized explainability benchmarks for time series, the interpretability gap in state space models, and the need to advance from correlational to causal explanations—and offer reporting considerations to guide more comparable future research.

NeuroFlexMLP: A Low Complexity MLP Architecture for Long-Term Time Series Forecasting

Forecasting time series over long horizons is essential for proactive decision-making in many systems. Recent research has focused on transformer-based architectures, which capture long-range dependencies in sequential data. However, several studies show that simpler linear models can outperform transformers by avoiding overfitting during training. In this context, we present NeuroFlexMLP, a deep learning model for multivariate time series forecasting tasks. NeuroFlexMLP's key distinct feature is the adaptability to the diverse complexity of real-world time series, which is achieved, from the architecture standpoint, by adding non-linear residual blocks to a first linear block. This architectural design simplifies hyperparameter optimization, leading to accurate forecasts for various time series data types regardless of the lookback or prediction horizons, outperforming state-of-the-art (SOTA) models on challenging real-world datasets. Its Multi-Layer Perceptron (MLP) design ensures high computational efficiency, making it scalable for longer input sequences than transformer-based models. We validate NeuroFlexMLP for the LEO satellite beam hopping use case, where its lightweight design enables on-board deployment, and on state-of-the art AI datasets. Across all these benchmarks, NeuroFlexMLP achieves competitive accuracy over state-of-the-art models while providing an adaptive architecture that significantly reduces computational overhead. On the LEO beam hopping task, it achieves up to 35.9% MSE reduction over Informer, which translates into up to 28% lower provisioning cost under asymmetric cost models that penalize under-allocation more heavily than over-allocation.

Volatility forecasting with econometric and machine learning models under capacity control