1 Problem formulation and forecast horizons
Multi-step forecasting aims to predict the future values of a time-dependent variable at several time points beyond the observation window. Given historical data, the objective is not only to estimate the next value, but to produce a trajectory (or a set of future snapshots) over a specified horizon. The defining distinction from one-step forecasting is that errors can accumulate as predictions move further into the future, making horizon-aware strategies and evaluation necessary.
1.1 Time series setting and notation
A common formulation considers a sequence of observations \(\{y_t\}_{t=1}^T\). Multi-step forecasting specifies a forecast start time \(t_0\) (often the end of the training window) and predicts future values at time points \(t_0+1, \dots, t_0+H\), where \(H\) is the maximum forecast horizon. Inputs may include only past values of \(y_t\) or may also incorporate exogenous covariates \(\{x_t\}\) and/or additional related variables.
Formally, a model learns a mapping from observed history (and possibly covariates) to a vector-valued target: \[ \hat{\mathbf{y}}_{t_0} = [\hat{y}_{t_0+1}, \dots, \hat{y}_{t_0+H}]. \] Depending on the modeling approach, this vector may be produced all at once (many-to-many) or step by step (recursive, direct per-step).
1.2 Forecast horizons (short-, medium-, long-term)
Forecast horizons are often grouped by how far into the future they extend and how quickly the dynamics typically change. Short-term horizons tend to be closer to the current system state, where past patterns remain informative. Medium-term horizons reflect a balance between persistence and drift, where uncertainty grows and seasonal or regime effects may start to matter more. Long-term horizons require the model to extrapolate over periods where direct dependence on recent history weakens, increasing the importance of robust modeling assumptions and uncertainty quantification.
Although the exact boundaries vary by domain, the conceptual difference is consistent: longer horizons raise the likelihood of compounding error and reduce the predictability of fine-grained fluctuations.
1.3 Single target vs multivariate forecasting
Single-target forecasting predicts one variable across future time points. Multivariate forecasting extends the target to a vector \(\mathbf{y}_t \in \mathbb{R}^K\), requiring the model to generate multiple correlated series simultaneously. This can improve accuracy when variables interact, but it increases complexity because correlations may change over time and because cross-series errors can propagate.
In practice, multivariate setups can be treated as separate univariate models (simpler but less expressive) or as joint models that explicitly represent dependencies among variables.
1.4 Deterministic vs probabilistic forecasting
Deterministic forecasting outputs a single predicted value for each future time point (and possibly for each output variable). Probabilistic forecasting aims to characterize uncertainty by producing either distributional parameters (e.g., mean and variance) or predictive distributions (e.g., quantiles or mixtures).
The distinction affects both training and evaluation. Deterministic methods are typically trained with pointwise losses, while probabilistic methods require objective functions aligned with the intended uncertainty representation and metrics that reflect distributional correctness.
2 Modeling strategies for multi-step forecasts
Several families of strategies exist for producing multi-horizon predictions. The core design question is how future values are generated: whether each step depends on its own predicted predecessors, whether each horizon has a dedicated model, or whether all horizons are produced jointly.
2.1 Recursive (autoregressive) forecasting
Recursive forecasting generates future steps sequentially. The model is trained to predict the next value given past observations and/or past predictions. At inference time, once \(\hat{y}_{t_0+1}\) is produced, it is fed back as an input to predict \(\hat{y}_{t_0+2}\), and so on until step \(H\).
2.1.1 Error propagation mechanisms
The defining limitation of recursive approaches is that prediction errors can feed into subsequent inputs. If the model underestimates or overestimates early steps, those deviations influence later steps, potentially amplifying bias and altering temporal patterns. The magnitude of error growth depends on how sensitive the system is to input perturbations and on the model’s ability to correct deviations during rollout.
In many cases, the error propagation resembles a cascade: small inaccuracies at early horizons can become structured discrepancies at longer horizons, especially when the model uses predicted values as strong regressors.
2.1.1.1 Mitigation via scheduled sampling
Scheduled sampling addresses mismatch between training and inference. During training, the model sometimes receives ground-truth past values and sometimes receives its own predictions as inputs. A schedule controls how frequently predictions are used, gradually shifting toward the inference-like regime. This reduces the gap between how the model learns conditional dependencies and how it must operate during rollout.
The approach can be implemented without changing the model architecture, but it requires careful tuning to avoid destabilizing learning.
2.1.2 Practical implementation considerations
Implementation choices include whether to roll out on normalized vs raw values, whether to include covariates available in the future, and how to handle exogenous inputs when those are themselves forecasted. Recursive methods also require efficient batch generation for long horizons and careful attention to numerical stability when iterative feedback is used.
In neural implementations, the same network may be reused for every step, while in statistical implementations, recursive forecasts may rely on explicit autoregressive structures.
2.2 Direct forecasting (one model per step)
Direct forecasting trains a model specifically for each horizon step. Instead of using the same predictor repeatedly, one trains \(H\) predictors, where the \(h\)-th predictor targets \(\,y_{t_0+h}\,\).
2.2.1 Horizon-specific model training
In horizon-specific training, each model learns a relationship between past history (and covariates) and the value at a particular forecast lead time. This can reduce compounding effects associated with recursive feedback, because the model does not depend on its own earlier predictions during inference.
However, horizon-specific modeling can result in large training effort, particularly for long horizons, and different horizons may require different effective features or different model sensitivities.
2.2.2 Trade-offs in scalability and accuracy
The key trade-off is between accuracy and scalability. Direct methods can be more accurate at longer horizons when tuned appropriately, but they scale linearly with the number of horizons if separate models are trained. A related consideration is that direct models may not enforce consistency across horizons (e.g., smoothness or monotonic relationships), which can lead to unrealistic forecast trajectories.
Some implementations share parameters across horizons or use multi-output heads to partially alleviate the scalability burden.
2.3 Many-to-many (direct joint) forecasting
Many-to-many forecasting produces multiple future steps jointly in a single forward pass. This approach can be seen as a direct multi-output prediction problem where the model outputs \(\hat{y}_{t_0+1:t_0+H}\) at once.
2.3.1 Sequence-to-sequence formulations
Sequence-to-sequence architectures map an input sequence to an output sequence of equal or different length. In time series, the encoder ingests past observations (and covariates), and the decoder outputs future values across the horizon. The decoder may use attention to focus on relevant portions of the past, and it may be configured to output all future points either autoregressively or with a fully parallel decoding strategy.
Joint decoding can capture cross-horizon dependencies by learning patterns that span the entire forecast trajectory.
2.3.2 Learning cross-horizon dependencies
Because the model outputs a horizon vector simultaneously, it can learn how errors at one step relate to errors at others and can impose implicit structure, such as smooth evolution or recurring patterns. This capability is especially useful when future values are strongly correlated across time.
The degree to which the model captures such dependencies depends on architecture, training objectives, and how horizons are represented (e.g., fixed-length vectors vs irregular lead times).
2.4 Hybrid approaches
Hybrid methods combine characteristics of recursive and direct strategies to balance error control and computational efficiency. A common motivation is to reduce compounding effects without fully training separate models for every horizon.
2.4.1 Combining recursive and direct methods
One hybrid approach uses direct prediction for some initial horizon steps and recursive rollout beyond that point, effectively shortening the feedback chain. Another uses a direct multi-output head for subsets of horizons while using recursion for intermediate states or for latent variables.
These designs can reduce training overhead while still benefiting from horizon-specific learning for the most sensitive parts of the trajectory.
2.4.2 Teacher forcing and curriculum strategies
Teacher forcing is closely related to scheduled sampling and refers to providing ground-truth context during training for sequence generation. Curriculum strategies can gradually increase the difficulty of prediction by expanding the effective horizon or by transitioning from easy (more ground-truth-provided) to harder (more model-generated) inputs. The goal is to stabilize training and improve performance during deployment rollouts.
In time series settings, curriculum schedules may also be adjusted based on observed stability or measured error growth over different lead times.
3 Data preparation and feature engineering
Model performance in multi-step forecasting depends heavily on data handling, because horizon modeling requires consistent alignment of inputs and targets and careful treatment of missingness, irregular sampling, and seasonality.
3.1 Windowing and lag selection
Windowing converts a long time series into supervised training examples. A sliding window selects past observations over a lookback length \(L\), forming inputs like \([y_{t-L+1}, \dots, y_t]\), while targets are the future steps \([y_{t+1}, \dots, y_{t+H}]\). The choice of lookback length influences which temporal dependencies are available to the model.
Lag selection or feature selection may focus on specific autoregressive orders, periodic lags, or statistically motivated transforms. Too-short windows can limit predictive power, while overly long windows can increase noise and computational cost.
3.2 Handling missing values and irregular sampling
Real-world data may have gaps, inconsistent sampling intervals, or sensor downtime. Regular-window multi-step forecasting often assumes consistent time steps; when that assumption fails, preprocessing is required. Common strategies include interpolation, resampling to a common grid, or using time-gap features to inform the model about irregular spacing.
Missing values can also be handled by masking mechanisms in neural networks or by imputation methods that preserve temporal structure. For multi-step targets, it is especially important to decide whether to discard samples with missing future labels or to partially train on available steps using masks.
3.3 Exogenous variables and covariate design
Covariates \(x_t\) may include calendar indicators, known-in-advance information (e.g., planned events), or measurements from related processes. In multi-step forecasting, some covariates are available only up to the present, while others may be projected or known ahead. Covariate design therefore must align with the forecast horizon: only information available at or before each predicted time point can be used in a strictly causal setup.
Good covariate engineering also involves selecting features that vary predictably at the horizon scale, such as seasonal factors, holiday effects, or lagged versions of external signals.
3.4 Normalization, detrending, and seasonality
Time series often exhibit nonstationarity, scaling differences, and periodic structure. Normalization (e.g., standardization or robust scaling) helps stabilize training. Detrending and seasonal decomposition can separate slowly varying baselines from recurring cycles, which can improve both statistical and neural models.
Seasonality can be represented via engineered features (sine/cosine encodings of periodic indices), via differencing, or via model architectures that incorporate seasonal components. The chosen transformation should be applied consistently across training, validation, and inference, with inverse transformations applied to convert predictions back to the original scale.
4 Model families and architectures
Multi-step forecasting spans statistical and modern machine learning approaches, from interpretable autoregressive models to complex deep architectures. Selection depends on data size, horizon length, required latency, and desired uncertainty outputs.
4.1 Statistical models
Statistical models often encode explicit temporal dynamics and can be efficient, particularly for shorter horizons or when strong assumptions about structure are appropriate.
4.1.1 ARIMA-style multi-horizon adaptations
Classic ARIMA frameworks can be extended to multi-step outputs either by iterating one-step forecasts recursively or by producing horizon-specific forecasts with model-implied dynamics. Seasonal ARIMA variants incorporate periodic components and can improve accuracy when repeating cycles exist.
Multi-horizon performance depends on how well the model structure matches the data-generating process, and long-horizon forecasts may drift toward unconditional means.
4.1.2 State space and smoothing-based methods
State space models represent the system state as a latent process that evolves over time, with observations providing noisy evidence. Smoothing methods can estimate latent trajectories and support multi-step forecasting by propagating the state forward. These models can be particularly useful when measurement noise and time-varying behavior are prominent.
Multi-step forecasts from state space models naturally align with probabilistic output, since uncertainty can be tracked through the state transition and observation equations.
4.2 Machine learning models
Machine learning methods often treat forecasting as supervised learning: features derived from past history predict targets at one or more future lead times.
4.2.1 Gradient boosting for horizon targets
Gradient boosting regression can be adapted to multi-step forecasting by predicting horizon-specific targets (direct) or by training a multi-output regressor. Feature sets may include lagged values, rolling statistics, calendar variables, and interactions. Gradient boosting can handle nonlinearities and heterogeneous relationships without requiring sequence-specific architectures.
Its performance depends on the adequacy of feature engineering and on careful regularization to prevent overfitting to particular temporal patterns.
4.2.2 Regression trees and feature-based learners
Decision tree-based models, including random forests and other regressors, can also be used for multi-step prediction. These methods can capture nonlinear effects and provide relative robustness when relationships are stable. However, they may require more informative features to represent temporal structure effectively.
When multi-horizon outputs are modeled jointly, care is needed to ensure that learned relationships do not produce inconsistent trajectories across steps.
4.3 Deep learning models
Deep learning architectures can learn temporal representations directly from data and can support complex dependencies across horizons.
4.3.1 Recurrent networks and temporal dependencies
Recurrent neural networks (RNNs), including variants such as LSTMs and GRUs, process sequences iteratively and maintain a hidden state summarizing the past. For multi-step forecasting, the network can output a horizon vector via a feedforward head or decode step-by-step depending on the design. RNN-based systems can model long-range dependencies, though they may struggle with very long horizons without architectural enhancements.
Training stability and gradient flow are central concerns, especially when horizons are long and targets have noisy dynamics.
4.3.2 Temporal convolutional networks
Temporal convolutional networks (TCNs) use causal convolutions and dilations to expand the receptive field over time. This can make it easier to capture long contexts while maintaining parallel computation. Multi-step heads can output multiple future steps, often with straightforward training objectives.
TCNs are frequently valued for their efficiency and for avoiding some recurrence-related training difficulties.
4.3.3 Attention mechanisms and transformers
Attention-based models can weigh different parts of the past when generating future predictions. Transformers have become prominent for time series tasks because they can represent dependencies without relying solely on sequential recurrence. Multi-step outputs can be produced via decoder-only, encoder-decoder, or fully parallel decoding variants.
For long horizons, attention mechanisms may require efficiency techniques or careful design to avoid excessive memory and computation.
4.4 Graph and spatial-temporal models
When time series are related across space or network structure, graph-based approaches can exploit topology and interdependence.
4.4.1 Multistation forecasting setups
In multistation forecasting, multiple locations or sensors produce correlated signals. The model may predict values at each station for future steps, leveraging both temporal history and spatial relationships. This often improves performance when stations influence one another or share external drivers.
4.4.2 Message passing for temporal signals
Graph neural networks use message passing to aggregate information from neighboring nodes. For forecasting, temporal dynamics can be combined with graph operations, producing architectures that alternate or integrate temporal modeling with spatial aggregation. Multi-step forecasting is then realized by producing horizon outputs per node, potentially with shared or node-specific parameters.
Such models must handle missing sensors and nonstationary coupling between locations.
5 Uncertainty quantification and reliability
Uncertainty quantification (UQ) aims to represent predictive uncertainty rather than only point estimates. In multi-step forecasting, uncertainty typically increases with horizon, and reliable uncertainty estimates are essential for decision-making.
5.1 Probabilistic output parameterizations
Probabilistic methods can output uncertainty using explicit distribution parameters or using nonparametric approaches such as quantiles.
5.1.1 Quantile regression approaches
Quantile regression trains models to predict specified quantiles (e.g., 10th, 50th, 90th percentiles) of the future distribution. This produces prediction intervals that can widen with horizon. Training often uses a pinball loss tailored to quantile estimation.
Quantile-based forecasts are practical because they do not require a specific distributional assumption, though they may produce quantile crossing unless constrained.
5.1.2 Distributional forecasting (e.g., mixture models)
Distributional forecasting models the entire predictive distribution. Mixture models, such as mixtures of Gaussians, can represent multimodality and non-Gaussian tails. Other parameterizations may output mean and variance for assumed families (e.g., Gaussian, Student-t) or use learned transformations to approximate more complex shapes.
Distributional UQ can be powerful but requires selecting families that are flexible enough while remaining stable to train.
5.2 Conformal prediction for time series
Conformal prediction provides distribution-free uncertainty quantification by calibrating prediction intervals using held-out data. For time series, calibration must respect temporal order; methods often use rolling or blocked calibration windows to preserve dependence structure.
When applied to multi-step forecasting, conformal techniques produce intervals for each horizon step, sometimes requiring separate calibration per lead time to maintain validity.
5.3 Calibration and prediction interval evaluation
Reliability refers to whether nominal coverage probabilities match observed coverage frequencies. Calibration is assessed by checking whether, for example, a 90% interval contains the true value about 90% of the time across a dataset. Evaluation can also consider interval width: overly wide intervals may be calibrated but uninformative.
For multi-step forecasts, calibration should be checked across horizons since coverage and sharpness vary with lead time.
6 Training procedures and optimization
Training multi-step models requires objectives that align with horizon structure and with the output type (point or distributional). Optimization must balance accuracy across steps and stability during training.
6.1 Loss functions for multi-step objectives
Loss functions aggregate errors across forecast steps and, in multivariate cases, across variables.
6.1.1 Horizon-weighted losses
Horizon-weighted losses assign different importance to errors at different lead times. For instance, a model might weight early steps more heavily when near-term accuracy is crucial, or weight longer steps more if strategic planning depends on them. Weights can also be learned or adapted based on error statistics.
Proper weighting can reduce the tendency to overfit to short-horizon patterns at the expense of useful long-horizon behavior.
6.1.2 Masked losses for variable-length targets
When some targets are missing or when horizons differ between samples, masked losses allow training on available steps without forcing imputation. A mask indicates which horizon indices have valid labels, and the loss is computed only for those entries. This is common in irregular datasets and in scenarios where not all future measurements are observed.
6.2 Regularization and early stopping
Regularization controls model complexity to avoid overfitting. Because multi-step targets provide many supervised signals, models can inadvertently fit idiosyncrasies in particular horizons or in seasonal segments.
Early stopping monitors validation performance, ideally using a metric that reflects horizon goals rather than only aggregated error.
6.2.1 Preventing overfitting across horizons
Overfitting can manifest as excellent performance on some steps and poor generalization on others, especially near the ends of the horizon range. Techniques include sharing parameters across horizons, using dropout or weight decay, and selecting training objectives that penalize inconsistent horizon behavior.
In some setups, validation uses horizon-stratified metrics to identify when certain steps degrade.
6.3 Curriculum and horizon scheduling
Curriculum learning structures training to progressively increase the prediction difficulty. For example, training may start with shorter horizons or with simpler decoders, then expand to longer horizons. Horizon scheduling can also adjust the effective weighting of steps over time.
This can be particularly helpful for autoregressive or sequence-to-sequence systems where long rollouts are harder to learn from scratch.
7 Evaluation and benchmarking
Evaluation measures whether a forecasting model produces accurate, robust, and well-calibrated predictions over different lead times. Because multi-step forecasts include multiple future points, metrics must respect the horizon dimension.
7.1 Horizon-aware metrics
Horizon-aware metrics compute errors separately for each forecast step (or grouped bins), then summarize or visualize performance across the horizon.
7.1.1 MAE/RMSE across steps
Mean absolute error (MAE) and root mean squared error (RMSE) can be computed at each lead time \(h\). Reporting a curve of error vs. horizon reveals how quickly performance degrades and helps compare models with different trade-offs. RMSE penalizes larger errors more strongly, which can be relevant if extreme deviations matter.
7.1.2 MASE and scale-free comparisons
Mean absolute scaled error (MASE) normalizes errors relative to a baseline, enabling comparison across time series with different scales or variability. This is useful in benchmarking collections of datasets and for ensuring that performance differences are not driven solely by amplitude.
Scale-free comparisons can also be aggregated across horizons to yield interpretable overall rankings.
7.2 Distributional metrics
For probabilistic forecasts, evaluation requires metrics that compare predicted uncertainty to observed outcomes.
7.2.1 Pinball loss and quantile accuracy
Pinball loss assesses accuracy for quantile forecasts by penalizing under- and over-predictions differently depending on the quantile level. Averaging pinball loss over quantiles provides a summary that reflects the full set of predicted intervals.
Quantile accuracy can be further inspected by checking empirical coverage of each quantile-to-interval mapping.
7.2.2 CRPS-style measures
Continuous ranked probability score (CRPS) aggregates discrepancies between the predicted distribution and the realized outcome. It encourages both sharpness and calibration. CRPS-like measures are commonly used when models output distributions directly or can be converted to distribution functions.
In multi-step settings, CRPS can be computed per horizon and then aggregated with appropriate weighting.
7.3 Backtesting and cross-validation schemes
Time series evaluation typically uses backtesting, where the model is trained on a rolling or expanding window and tested on subsequent time periods. Cross-validation must preserve temporal order to avoid leakage. Schemes such as rolling-origin evaluation produce multiple forecasts from different historical points, improving robustness of conclusions.
For multi-step tasks, backtesting should ensure that each test instance includes the full target horizon (or uses masking consistent with training).
7.4 Robustness checks
Robustness testing examines how performance changes under conditions that differ from those seen during training.
7.4.1 Stress tests under distribution shift
A distribution shift may arise from changes in seasonality strength, altered noise levels, or changes in underlying dynamics. Stress tests can include evaluating on earlier vs later periods, testing different seasonal subsets, or using synthetic perturbations. Robust models should degrade gracefully and maintain reasonable uncertainty behavior.
8 Practical deployment considerations
Deploying multi-step forecasters introduces engineering constraints that differ from offline evaluation, including latency, updating strategies, and handling changing patterns.
8.1 Real-time inference and latency constraints
Real-time systems may require forecasts at frequent intervals with strict latency budgets. Recursive methods can be slower due to iterative rollouts, while many-to-many and parallel decoding can be faster when computation permits. Batch inference and model compression may be used to meet performance targets.
Additionally, deployment should account for the cost of feature computation and for retrieving exogenous inputs needed by each horizon step.
8.2 Model updating and drift monitoring
Time series often evolve, causing model parameters or learned relationships to degrade. Model updating strategies include periodic retraining, incremental learning (where supported), or adaptive recalibration of uncertainty estimates. Drift monitoring can rely on input distribution changes, residual behavior, or forecast calibration metrics.
In multi-step settings, drift should be assessed across horizons, since some lead times may degrade earlier than others.
8.3 Forecast serving formats and interfaces
Forecast services typically expose predictions as arrays or time-indexed tables. For probabilistic outputs, serving interfaces must also represent distributional objects such as quantiles, samples, or parametric distributions. Consistency of time indexing, horizon definitions, and time zone handling is crucial to prevent off-by-one errors and misalignment between prediction requests and returned forecasts.
Versioning is commonly used so downstream consumers can track changes in model behavior.
8.4 Managing changing seasonal patterns
Seasonal effects may weaken, shift phase, or change amplitude over time. Practical mitigation includes using dynamic seasonal features, employing models that can represent time-varying patterns, or retraining more frequently around seasonal transitions. For systems with known periodic drivers, periodic re-estimation of baseline components can improve stability.
Horizon-aware monitoring can also detect when seasonality contributes most to error for specific lead times.
9 Common challenges and mitigation strategies
Multi-step forecasting faces challenges that arise from both modeling and data limitations. Many issues are connected to horizon length and to mismatch between training conditions and rollout behavior.
9.1 Compounding errors in long horizons
As horizon increases, predictive dependence on earlier estimates can amplify errors, particularly for recursive strategies. Even direct or joint models may produce unrealistic long-range trajectories if the training data does not cover similar future conditions.
Mitigation includes switching to many-to-many or hybrid strategies, improving uncertainty quantification, and using training methods that better match inference-time conditions.
9.2 Nonstationarity and structural breaks
Nonstationarity refers to changes in statistical properties over time, while structural breaks involve abrupt changes in dynamics. Models trained on historical patterns can fail when underlying processes shift. Feature updates, frequent retraining, and robust architectures that incorporate time-varying representations can help.
Evaluation under distribution shift is important to detect these limitations early.
9.3 Sparse/noisy observations
When observations are sparse or measurement noise is high, multi-step targets can become harder to learn because the model must infer both temporal structure and signal reliability. Noise-aware losses, better imputation, and architectures that incorporate uncertainty can improve resilience.
In some cases, it is beneficial to focus on robust central tendencies rather than trying to perfectly capture noisy fluctuations at every horizon.
9.4 Multicollinearity in exogenous features
Exogenous variables can be correlated, which may cause instability in linear or feature-weighted models. Tree-based methods can be more tolerant, while gradient-based models may require regularization or careful feature selection. Dimensionality reduction techniques or grouping of related covariates can also help.
Proper validation should verify that including additional covariates improves multi-step performance rather than only fitting short-horizon patterns.
10 Research directions
Active research explores architectures and evaluation frameworks that improve efficiency, reliability, and generality of multi-step forecasting systems.
10.1 Foundation models for time series
Foundation models aim to learn general representations from large collections of time series, enabling transfer to new tasks with limited data. For multi-step forecasting, such models may support improved horizon generalization by capturing diverse temporal patterns and shared structures. Key challenges include scaling training, managing varying dataset characteristics, and ensuring that probabilistic outputs remain calibrated.
10.2 Efficient long-horizon inference
Long horizons can make inference expensive, especially for autoregressive decoding and for models with attention over long contexts. Research focuses on reducing computational complexity via efficient attention, caching mechanisms, distillation, and parallel decoding strategies. Approaches that can generate far-ahead predictions with fewer iterative steps are particularly valuable.
10.3 Causal and counterfactual forecasting
Beyond predictive accuracy, researchers study interventions and counterfactual scenarios: how forecasts change under hypothetical changes to inputs. While strictly causal modeling introduces additional assumptions, the objective aligns with decision support. Methods explore causal representation learning, structural modeling, and hybrid causal-probabilistic forecasting.
10.4 Benchmarking standards and reproducibility
Benchmarking multi-step forecasts requires consistent definitions of horizons, dataset splits, metrics, and uncertainty evaluation procedures. Reproducibility efforts include standardized data preprocessing, publicly available implementations, and well-documented evaluation protocols. Horizon-aware comparisons and calibration-focused reporting are increasingly emphasized to avoid misleading performance summaries.