[ENH] ARIMA support for exogenous variables

[JoaquinAmatRodrigo]

Describe the feature or idea you want to propose

Hi,

First, thank you for the great work on implementing a Python-native and efficient version of ARIMA.

It would be very helpful if ARIMA could support the use of exogenous variables (exog). This would enable users to incorporate additional predictors into their time series models, making the implementation more flexible and powerful.

Thanks again for your efforts on this project!

Describe your proposed solution

I don’t have a concrete implementation proposal at the moment. My request is mainly for adding support for exogenous variables (exog) within the ARIMA implementation, similar to what is available in libraries like statsmodels. I’d be happy to test or provide feedback once a design or prototype is available.

Describe alternatives you've considered, if relevant

No response

Additional context

No response

[TonyBagnall]

thanks @JoaquinAmatRodrigo its a good idea

[satwiksps]

Hi! @TonyBagnall and @JoaquinAmatRodrigo

I've opened a PR that adds full support for exogenous variables (exog) to ARIMA and AutoARIMA:
[ENH] Add exogenous variable support to ARIMA (#3116).

The implementation includes:

• OLS regression of y on exog during fitting
• ARIMA applied to the residual series
• Regression contribution added back during prediction
• Support for multi-step iterative forecasting with future exogenous values
• Backward-compatible behaviour when no exog is provided
• Comprehensive tests covering fit/predict, shape validation, iterative forecasting, and no-exog paths

Feedback or suggestions are very welcome!

[JoaquinAmatRodrigo]

Hi @satwiksps
I am happy to try it :)
The code merge must be reviwed by the aeon team, so I think @TonyBagnall is the right person to talk with.