Add exogenous forecasting models (ARIMAX, SARIMAX, and linear regression)

[Irozuku]

Summary

ExogenousForecastingTask had no models to run. ForecastingModel now reads the numeric columns beside the date as explanatory variables when the model declares SUPPORTS_EXOGENOUS.

Three models serve the new task, and the split between them is the point:

Model	Reads a date alone	Needs variables	Tasks
ARIMA	yes	no	both
SARIMAX (new)	yes	no	both
ExogenousLinearRegression (new)	no	yes	exogenous only
NaiveForecaster, SeasonalNaiveForecaster, ExponentialSmoothing	yes	cannot use them	plain only

ARIMA gains an exog term, so with a date alone it is the plain ARIMA it was, and with variables beside it an ARIMA with regressors. SARIMAX adds the seasonal orders ARIMA does not expose, and is likewise optional in both. ExogenousLinearRegression fits the series as a straight line in the variables with no memory of its own history, which is what makes it worth comparing against the other two: a large gap between their scores says whether the series is driven by its own momentum or by something outside it.

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Type of Change

Check all that apply like this [x]:

• Backend change
• Frontend change
• CI / Workflow change
• Build / Packaging change
• Bug fix
• Documentation

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Changes (by file)

• DashAI/back/models/forecasting/base_forecasting_model.py: added SUPPORTS_EXOGENOUS, _remember_exogenous, _exogenous_of and _exogenous_over. _forecast_at no longer takes a callable and passes the exogenous matrix when the model was fitted with variables. _forecast gained an optional exog argument. COMPATIBLE_COMPONENTS was removed from this class, see Notes.
• DashAI/back/models/forecasting/arima.py: fits and forecasts with exog. Declares both tasks and SUPPORTS_EXOGENOUS.
• DashAI/back/models/forecasting/sarimax.py: new. Seven orders (p, d, q, P, D, Q, season length), the seasonal part disabled at a season length below 2. Refuses a season the series is too short to show twice. Declares both tasks.
• DashAI/back/models/forecasting/exogenous_linear_regression.py: new. Ridge on the variables, with an optional period number trend so a drift the variables do not account for can still be fitted. Refuses a date column with nothing beside it. Declares the exogenous task alone.
• DashAI/back/models/forecasting/naive.py, seasonal_naive.py, exponential_smoothing.py: each now declares COMPATIBLE_COMPONENTS = ["ForecastingTask"] for itself.
• DashAI/back/initial_components.py: registers SARIMAX and ExogenousLinearRegression.
• tests/back/models/test_exogenous_forecasting_models.py: new. Covers which tasks each model declares, one value per requested row, the variables actually changing the forecast, a forecast far past the training data, a missing variable being refused, save/load round trips, the dual models still working from a date alone, the linear model recovering a known linear relationship, and the SARIMAX seasonal guards.

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Testing

• Plain forecasting regression: Train ARIMA, Naive, Seasonal Naive and Exponential Smoothing on Forecasting using only date as input. ARIMA scores should match develop, and all models should train successfully.

• Task/model compatibility: Verify Forecasting offers ARIMA, SARIMAX, Naive, Seasonal Naive and Exponential Smoothing, but not Exogenous Linear Regression. Verify Forecasting with Exogenous Variables offers only ARIMA, SARIMAX and Exogenous Linear Regression.

• Input validation: On Forecasting with Exogenous Variables, verify date + exg_1 is accepted, date alone and exg_1 alone are rejected, multiple date columns are rejected, and column order does not matter.

• Training and prediction: Train ARIMA, SARIMAX and Exogenous Linear Regression with date + exg_1 + exg_2. Verify Temporal Holdout/Rolling Origin are the only available splitters, metrics produce values, and future predictions respond to changes in the exogenous variables. Missing variables and dates inside the training window must be rejected.

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Notes

Exogenous variables are used contemporaneously:

y[t] = b * x[t] + n[t]

The models do not automatically use x[t-1], x[t-2], etc. Future forecasts therefore require the exogenous values for the requested forecast rows.

Intermediate exogenous rows may be interpolated when the forecast horizon contains gaps. These values do not affect the requested forecast rows, as verified by regression tests.

Lagged exogenous variables are out of scope and would require extending the time series windowing/conversion pipeline.