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

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

The literature is organized around five recurring difficulties: nonlinear and nonstationary behavior, contamination and structural breaks, uncertainty, long contexts and cross-variable dependence, and limited target-domain data.

Multivariate Time Series Forecasting needs Cross Variable Loss

This work proposes CvLoss, a plug-in structural regularizer that constrains forecast residuals on a cross-variable graph and shows that CvLoss consistently improves competitive forecasting models, outperforms representative learning objectives, and is compatible with a variety of forecasting backbones.

Volatility forecasting with econometric and machine learning models under capacity control

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.

FEDA: Fast Exponential Decay Approach for Multivariate Time Series Forecasting

Multivariate time series forecasting that uses past observations to predict future data has been widely used in various application. Numerous methods have been developed, including deep learning based approaches. One of the most successful models is Mamba, which is based the state space models (SSMs). However, Mamba and its variants still face the challenges of long training times owing to its nonlinear operations. In this paper, we proposed a Fast Exponential Decay Approach (FEDA) to improve the training efficiency of Mamba. We have observed that the hidden states in the model are linear combinations of past inputs. Therefore, we attempted to use a fully connected layer to generate all the hidden states. Although a fully connected layer does not have a recurrent structure, based on the intuitive idea in multivariate time series forecasting that the influence of observations diminishes over time, we multiplied the weights of the fully connected layer by a time-dependent coefficient to emulate a recurrence-like behavior. We evaluated our model on various datasets, and the results show that our model achieves the performance comparable to the state of the art models, while significantly improving their training efficiency. More specifically, it reduces training time by 20% to 80% depending on the channels of the dataset.

Conditional projection methods for large-scale Bayesian VARs

We develop fast methods for conditional forecasting and structural scenario analysis with high-dimensional Bayesian vector autoregressions (VARs). Our general framework features a factor structure on the reduced-form errors, which enables fast and order-invariant equation-by-equation estimation; suitably identified factors admit a structural interpretation. The scenarios are defined through separate distributional restrictions on observables, structural shocks and idiosyncratic components. The computational cost of our proposed algorithm is cubic only in the number of restrictions, while the dimension of the forecasted system enters linearly. In our application with $33$ macroeconomic and financial variables and ten set-identified structural shocks for the US, we compute counterfactual predictions for oil price scenarios in the context of the 2026 closure of the Strait of Hormuz. The same oil price path is consistent with outcomes ranging from a mostly benign episode to pronounced stagflation, depending on which structural and idiosyncratic shocks are allowed to deliver it.