Multivariate Time Series Forecasting needs Cross Variable Loss

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.

Persistent Structure Meets Dynamic Attention: Cross-Variable Priors for Multivariate Time Series Forecasting

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

It is argued 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.

Iterative ensemble forecasting with residual integration for complex and volatile demand time series

Accurate forecasting in volatile and structurally complex demand environments requires models capable of capturing evolving trends, seasonality, nonlinear behavior and externally driven fluctuations. This study aims to propose the iterative ensemble forecasting with residual integration (IEFRI) framework, a structured ensemble methodology that improves forecast accuracy by explicitly and iteratively learning from residual errors rather than treating them as random noise. Unlike conventional one-stage ensemble approaches, IEFRI uses a multistage refinement process in which forecasts from heterogeneous base models are progressively corrected through successive neural and regression-based residual-learning cycles, allowing both nonlinear and linear error structures to be captured systematically. The framework integrates Holt–Winters exponential smoothing, seasonal auto regressive integrated moving average (SARIMA), artificial neural networks (ANNs) and multiple linear regression (MLR) within a decomposition-driven architecture. IEFRI is empirically validated using 25 years of monthly demand data (April 1998–March 2024) covering all major petroleum products in India – petrol, diesel, Liquified Petroleum Gas (LPG), jet fuel and kerosene – each exhibiting strong seasonality, trend shifts, structural change and sensitivity to macroeconomic and policy factors. Comparative evaluation using standard accuracy measures shows that IEFRI consistently outperforms individual models and widely used ensemble techniques such as bagging, boosting, random forests and stacked regression. While demonstrated using petroleum demand, the framework is generalizable to other complex and uncertainty-prone time-series forecasting applications. This study develops and evaluates the IEFRI framework for complex demand time series. The approach combines heterogeneous base forecasting models – Holt–Winters exponential smoothing, SARIMA, ANNs and MLR – within a decomposition-driven ensemble structure. Initial forecasts are aggregated and subsequently refined through a multistage residual-learning process that integrates neural-network-based nonlinear correction and iterative regression-based linear adjustment. Model performance is assessed using rolling-origin out-of-sample evaluation and standard accuracy measures mean absolute percentatge error (MAPE), symmetric mean absolute percentage error (SMAPE), root mean square error (RMSE). The framework is empirically validated using 25 years of monthly demand data across five petroleum products, enabling robust comparison with conventional ensemble methods. The empirical results show that the proposed IEFRI framework consistently improves forecast accuracy across all five petroleum products – petrol, diesel, LPG, jet fuel and kerosene – each characterized by strong seasonality, structural change and nonlinear dynamics. Compared with individual base models and conventional ensemble techniques such as bagging, boosting, random forests and stacked regression, IEFRI achieves lower forecasting errors under rolling-origin evaluation. The iterative residual-learning mechanism is found to be effective in systematically reducing both nonlinear and linear forecast errors across successive refinement stages. Performance gains are stable across products with differing demand characteristics, demonstrating the robustness of the framework. These findings indicate that explicitly modeling and reintegrating residual information enhances ensemble forecasting accuracy in complex, volatile demand environments. Despite its strengths, this study has several limitations. First, the analysis relies on secondary data compiled from multiple sources, requiring interpolation and harmonization, which may introduce minor measurement bias. Second, the IEFRI framework is validated using historical monthly data from a single domain, and its generalizability to other sectors and higher-frequency data has not been empirically tested. Third, while the iterative residual-learning process improves accuracy, it increases computational complexity and may be sensitive to data quality and parameter settings. Finally, the study does not incorporate probabilistic or uncertainty forecasting, which could further enhance decision support in practice. The proposed IEFRI framework provides practitioners with a systematic and robust approach for improving forecast accuracy in environments characterized by volatility, nonlinearity and structural change. By explicitly learning from residual errors, the model supports more reliable demand forecasts that can enhance operational planning, capacity allocation, inventory management and medium-term strategic decision-making. The framework is flexible and can be integrated with existing forecasting systems that already use statistical or machine learning models, allowing organizations to improve performance without fully replacing current tools. For policymakers and managers, more accurate forecasts enable better resource planning, risk mitigation and policy evaluation in sectors where demand uncertainty has significant economic and operational consequences. This study is based on original research and contributes original value by introducing the IEFRI framework, which advances ensemble forecasting beyond conventional one-stage aggregation. Unlike standard ensemble methods that treat residuals as random noise, IEFRI explicitly and iteratively models residual errors through a structured combination of neural-network-based nonlinear learning and regression-based linear correction. This multistage residual integration provides a systematic mechanism for continuous forecast refinement. The study has been subjected to extensive empirical validation using the demand for various petroleum products which exhibit multiple, structurally diverse demand series. The framework offers a reusable, domain-agnostic methodology for improving forecast accuracy in complex, volatile time-series environments.

TRiP-Net: Risk-driven adaptive patching for financial time series forecasting.

Financial time series forecasting remains a challenging problem due to the clear non-stationarity of financial data, complex temporal dependencies, and frequent local fluctuations. Although Transformer-based models have achieved good performance in recent years, most methods still use fixed-length patch partitioning, which cannot adapt well to changing volatility patterns in financial sequences. To address this issue, this paper proposes a new forecasting framework named TRiP-Net. The model introduces TRiP, a risk-aware adaptive patching strategy that adjusts patch granularity based on local risk characteristics within the sequence. This allows the model to better capture local dynamic changes in financial time series. In addition, a DCN module is used to improve state-aware feature normalisation under different market regimes. Experimental results show that, under multiple forecasting horizons, TRiP-Net outperforms several mainstream baselines, including PatchTST, Pathformer, and iTransformer, in terms of MAE, RMSE, and MAPE. Ablation studies further confirm the effectiveness of the proposed modules and the adaptive patching strategy. Overall, the results show that TRiP-Net improves the accuracy of multi-step financial time series forecasting.

Decomposition-Enhanced Network for financial time series forecasting

The extreme non-stationarity, high noise levels, and multi-timescale coupling in financial futures markets pose major challenges for time series forecasting. Existing models often struggle to disentangle localized shocks from global trends due to incompatible inductive biases. To address this issue, we propose a Decomposition-Enhanced Network (DENet). Following a divide-and-conquer paradigm, DENet adopts a multi-stream architecture: the main path extracts stable trends via moving averages and dual-path linear projections, while Auxiliary Stream I captures seasonal and local cyclical patterns using depthwise separable convolutions, and Auxiliary Stream II models high-frequency dynamics through a nonlinear autoregressive-style mapping. These components are integrated via an adaptive fusion mechanism, balancing global robustness and local structural sensitivity. Experiments on real-world futures data demonstrate that DENet outperforms a wide range of state-of-the-art benchmarks. Compared with seven state-of-the-art baselines, DENet achieves an average reduction of 10.15% in RMSE for daily forecasting on iron ore futures, and an average reduction of 22.57% in MAE under the 5-min, 12-step forecasting horizon. Furthermore, we integrate DENet’s dual-scale predictions into the R-Breaker strategy with parameter switching and dynamic position sizing. Backtesting results reveal that the annualized return of iron ore futures outperforms the baseline strategy by an average of 7.6 percentage points across five backtesting windows. Ultimately, DENet effectively bridges advanced structural modeling and actionable algorithmic trading.