Exogenous-Only Temperature Forecasting

Updated 18 December 2025

Exogenous-only temperature forecasting is a method that predicts future temperatures solely by leveraging external meteorological and environmental variables.
It employs techniques such as linear regression, nonparametric analogs, CNNs, and probabilistic postprocessing while excluding past target values during training and inference.
The approach enhances operational robustness by exploiting teleconnections and high-fidelity weather model outputs, despite modest hit rates for extreme events.

Exogenous-only temperature forecasting refers to quantitative prediction of future air or surface temperatures using only external (exogenous) variables—excluding any direct autoregressive (past value) information from the target temperature series. All relevant exogenous-only approaches strictly prohibit the algorithm from “seeing” or conditioning on past temperatures of the location being forecast, either during training or inference. This field has gained increasing attention due to operational constraints (e.g., absence of reliable on-site past temperature data, need for robustness in nonstationary or regime-shifting settings), the desire to avoid artificial self-persistence, and the opportunity to exploit teleconnections and high-fidelity weather and climate model outputs.

1. Fundamental Principles of Exogenous-Only Temperature Forecasting

The defining characteristic of exogenous-only forecasting is the strict partition of model inputs into:

Exogenous variables: meteorological or environmental covariates (e.g., ensemble NWP or reanalysis fields, observed weather variables at other locations, climate indices, etc.).
Target: the temperature series to be forecast, which is inaccessible at inference except for historical “ground truth” labels.

Exogenous-only approaches are pursued either for scientific purposes (causal analysis, teleconnection modeling) or necessitated by data availability. By construction, they avoid recursiveness: there are no lagged observations of the predictand in the predictor set. This rules out any ARIMA or classic autoregressive DL sequence models in their vanilla form. The result is models that can only exploit the information content present in the selected exogenous variables.

Non-parametric analog methods, linear regression, regularized ensemble postprocessors, convolutional neural networks, and transformer-free deep architectures have been investigated, all subject to this constraint (Zubov et al., 2015, Orlova et al., 2022, Lopez-Gomez et al., 2022, Landry et al., 4 Jun 2024, 2505.23116, Gokhman, 11 Dec 2025).

2. Exogenous Predictors and Feature Engineering

Exogenous-only frameworks rely on an expanded set of external covariates:

Synoptic and climate-scale predictors: surface and upper-air fields from NWP/reanalysis (T2m, Z500, SST, soil moisture), indices such as ENSO, SOI, multivariate MEI, Darwin/Tahiti sea level pressure, etc. (Zubov et al., 2015, Orlova et al., 2022, Lopez-Gomez et al., 2022).
NWP or weather model outputs: deterministic or ensemble model forecasts for temperature (at any grid, not the target location), dew point, humidity, wind, precipitation, geopotential, etc. (Orlova et al., 2022, Landry et al., 4 Jun 2024).
Local environmental exogenous inputs: observations at remote sites and physical covariates (e.g., relative humidity, barometric pressure, radiation, precipitation, cloud cover, wind), but not the history of the target temperature (2505.23116, Gokhman, 11 Dec 2025).
Positional and static features: latitude, longitude, elevation, station/category embeddings to encode location-specific priors; time-of-day, day-of-year, lead time conditioning (Landry et al., 4 Jun 2024).

Principal component or patch-based representations are used for high-dimensional global predictors such as SST (Orlova et al., 2022). Feature preprocessing includes z-score standardization or instance normalization per channel, log-transformation of certain physical variables, and bias correction for NWP gridpoint forecasts (Landry et al., 4 Jun 2024, 2505.23116, Gokhman, 11 Dec 2025).

3. Model Architectures and Algorithmic Strategies

A wide spectrum of architectures has been deployed, reflecting the absence of autoregressive target information.

a. Linear and Generalized Linear Models

Pure one-shot linear regression on windowed exogenous histories (Gokhman, 11 Dec 2025).
Bias-corrected, trend/seasonal-decomposed linear projections (NLinear, DLinear) to mitigate nonstationarity and capture additive structure (Gokhman, 11 Dec 2025).
Linear regression per-location or as a global estimator, sometimes with ensemble-member expansion (Orlova et al., 2022, Landry et al., 4 Jun 2024).

b. Nonparametric Analog and Rule-Based Methods

Predictor-sum statistics for pairs of exogenous variables (analog approach): compute weighted sums of standardized anomalies at remote sites over a lead time and summation window, select those that historically maximized anticipation of target extremes (Zubov et al., 2015).
Teleconnection mining via a data-driven analog-configuration search, bypassing classical parametric fit to extremes (Zubov et al., 2015).

c. Deep Learning Architectures

CNN/U-Net architectures for spatial map-to-map regression from exogenous field tensors at initialization to temperature anomalies at horizon, trained via MSE or super-quadratic losses targeting extreme temperature events (Lopez-Gomez et al., 2022).
Multi-layer perceptrons (MLP) with station and lead-time embeddings, trained for parameter prediction (e.g., to output location/time-dependent parameters of probabilistic distributions) (Landry et al., 4 Jun 2024).
Cross-correlation embedding models that couple exogenous features in a time-invariant, linear fashion using shared 1D convolutions, followed by patch embedding and global linear heads for both short-term and long-term exogenous-only forecasting. Residual endogenous channels can be removed entirely in strict exogenous-only regimes (2505.23116).

d. Ensemble and Probabilistic Postprocessing

Quantile regression forests, Bernstein polynomial quantile networks, normal-parametric NNs for full-distribution prediction from raw deterministic or ensemble NWP outputs, with or without explicit model spread information (Landry et al., 4 Jun 2024, Orlova et al., 2022).
Stacked models blending predictions from linear, RF, and CNN architectures as base learners and meta-learners for ensembling (Orlova et al., 2022).

e. Transformer-type vs. Linear Models

Standard and enhanced Transformer architectures (Informer, Autoformer) compared to linear baselines for exogenous-only indoor temperature forecasting, with empirical findings that linear architectures (NLinear, DLinear) are substantially more robust and accurate in these scenarios (Gokhman, 11 Dec 2025).

4. Training, Validation, and Loss Functions

Exogenous-only models are trained exclusively on historical exogenous/target pairs, never feeding back predictions. Key regimes:

Strict temporal splits, blocking all future-leaking variables and avoiding cross-talk with target temperature sequences (Zubov et al., 2015, Gokhman, 11 Dec 2025).
Windowing: Input look-back of length L in exogenous features, forecast horizon H, building non-overlapping [L→H] training blocks (Gokhman, 11 Dec 2025).
Bias correction, outlier removal (>15 K), z-score or min-max scaling restricted to training data for robust normalization (Landry et al., 4 Jun 2024, 2505.23116).

Losses are selected based on the output endpoint:

L2 (MSE) for mean prediction.
Symmetric exponential or "pinball" (quantile) loss for extreme-value targeting (Lopez-Gomez et al., 2022, Orlova et al., 2022).
Continuous Ranked Probability Score (CRPS) for probabilistic output calibration (Landry et al., 4 Jun 2024). For analog methods, combinatorial search is guided by rule quality criteria based on frequency and sharpness of predictor-exceedance during true extremes (Zubov et al., 2015).

Early stopping, batch normalization, regularization (e.g., weight decay), and ensembling over model seeds are applied as needed. Station and lead-time embeddings are learned via additive parametric vectors (Landry et al., 4 Jun 2024).

5. Performance Benchmarks and Empirical Insights

Across operational, climate, and energy/building datasets, exogenous-only methods exhibit several robust findings.

Approach	Domain/Horizon	Key Metrics / Results	Reference
Nonanticipative Analog	Daily/annual, US, extremes	Hit rate for hot-waves up to 18.2%, 100% sign accuracy	(Zubov et al., 2015)
Neural Weather Models	Global, 1-28 days	ACC at 14d=0.68 (vs persist 0.30, ECMWF 0.62); HR≈0.55	(Lopez-Gomez et al., 2022)
Deterministic-to-Prob. NN	In-situ, 10-day, N. America	CRPS reduced by 15.6% vs. naive; best with BQN/DRN	(Landry et al., 4 Jun 2024)
CrossLinear (pure exo)	Real-world, var. term	Consistent improvements over neural/attention models	(2505.23116)
LTSF-Linear/Transformer	Indoor, 4-day	NLinear MAE=0.2461, DLinear=0.2811 outperforms Transformer (MAE>0.8)	(Gokhman, 11 Dec 2025)
ML postprocessed ensembles	CONUS, subseasonal	Stacked (full ensemble) R² ≈ 0.18, RMSE=1.77°C	(Orlova et al., 2022)

A consistent pattern emerges: well-designed linear and convolutional models often outperform deeper attention-based architectures under pure exogenous-only restrictions, due to their regularization and tendency to avoid overparameterization and overfitting (Gokhman, 11 Dec 2025). Use of full ensemble vectors as exogenous features systematically outperforms summarization (e.g., ensemble mean), with statistically significant skill improvements (Orlova et al., 2022).

For extremes, analog and exponential-loss-trained CNNs yield meaningful hit rates, but challenges in recall and smoothing remain, especially at long leads (Zubov et al., 2015, Lopez-Gomez et al., 2022). Probabilistic postprocessing of deterministic forecasts via NNs, MLPs, or ensemble methods can recover sharp, calibrated predictive distributions without costly ensemble simulation (Landry et al., 4 Jun 2024).

6. Operational Implications, Strengths, and Limitations

Exogenous-only approaches exhibit several distinctive operational and scientific properties:

No artificial self-persistence: Models avoid overfitting to slow-moving internal dynamics or persistent anomalies in the target, as only exogenous drivers are used (Zubov et al., 2015).
Robustness to out-of-distribution and nonstationary changes, assuming exogenous predictors contain up-to-date causal or correlational information (Gokhman, 11 Dec 2025).
Low computational cost for probabilistic prediction: Single deterministic NWP or ML-based forecasts can be efficiently postprocessed into full probabilistic distributions (Landry et al., 4 Jun 2024).
Teleconnection and remote driver identification, particularly in analog and rule-mining methods, which automatically discover historical precedents without forced parametric form (Zubov et al., 2015).
Limitations include reduced “upper bound” on forecast skill (modest hit rates for extremes, e.g. 10–20%), susceptibility to loss in long-term state memory (soil moisture feedback, persistent local anomalies), and, for DL models, the risk of over-smoothing or amplitude underestimation at long leads (Lopez-Gomez et al., 2022, Landry et al., 4 Jun 2024).

Empirical findings underscore the perils of high-capacity models (e.g., Transformer-family) in overfitting or collapsing on purely exogenous input, whereas explicit linear decomposition or convolutional inductive biases yield more consistent performance (2505.23116, Gokhman, 11 Dec 2025).

7. Research Developments and Directions

Recent developments have advanced exogenous-only temperature forecasting in several respects:

Plug-and-play cross-correlation embedding approaches for modular integration of exogenous-only forecasting into broader time series pipelines, with explicit removal of shallow autoregressive dynamics (2505.23116).
Evaluation frameworks and community benchmarks (“UrbanAI 2025 Challenge”) enforcing strict exogenous-only constraints for energy/building and indoor-outdoor forecasting, revealing the practical supremacy of normalized and decomposed linear models (Gokhman, 11 Dec 2025).
Comprehensive postprocessing frameworks capable of upgrading deterministic NWP and ML forecasts to well-calibrated probabilistic outputs—spanning static (EMOS), quantile-based (BQN), and neural density methods (Landry et al., 4 Jun 2024).
Exploitation of the full ensemble-member structure in subseasonal and seasonal climate prediction tasks, yielding skill advances attributable to high-dimensional exogenous signals and auxiliary variables (Orlova et al., 2022).
Persistent open problems include scaling hit rates for extreme events, reducing computational search burden (in analog/rule-based systems), adaptively expanding exogenous pools (via feature selection, clustering, or representation learning), and understanding limits of predictability in the absence of endogenous data.

Together, the exogenous-only paradigm, as developed and validated in these studies, provides a rigorous discipline for the design, evaluation, and interpretation of temperature forecasts—a framework that, while sometimes sacrificing maximum recall, offers critical benefits in transparency, transferability, and real-world operational reliability.