[ENH] Add prediction intervals to ARIMA iterative_forecast (#3100)

[satwiksps]

[ENH] Add prediction intervals to ARIMA iterative_forecast (#3100)

Reference Issues/PRs

• Fixes #3100.

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What does this implement/fix?

This PR adds optional prediction interval support to the ARIMA.iterative_forecast method in aeon.forecasting.stats._arima.

Key features:

• Adds a new optional parameter:
  alpha (default: None)
• Backward compatible:
  • If alpha=None → returns the same np.ndarray as before.
  • If alpha is provided → returns a pandas.DataFrame with columns:
    • "mean" - point forecasts
    • "lower" - lower prediction interval
    • "upper" - upper prediction interval
• Prediction intervals are computed using:
  • Empirical residual standard deviation
  • Normal quantiles via scipy.stats.norm.ppf
  • Standard error scaling with sqrt(horizon)

Additional updates:

• AutoARIMA.iterative_forecast now forwards the alpha argument to the wrapped ARIMA model.
• Added new unit tests covering prediction intervals.
• All existing tests pass with no modification.

This enhancement provides users with basic forecast uncertainty estimates while keeping the ARIMA implementation lightweight and backward compatible.

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Does this contribution introduce a new dependency?

No.
Uses existing NumPy, SciPy, and pandas packages already in the project.

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Any other comments?

• All pre-commit hooks pass (ruff, flake8, isort, black, etc.).
• Tests pass locally, including new interval tests.
• Changes are intentionally minimal to avoid regressions.

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PR checklist

For all contributions

• [ ] I've added myself to the list of contributors (after merge).
• [x] The PR title starts with [ENH].

For new estimators/functions

• [ ] Not applicable - this PR modifies an existing estimator.

For developers with write access

• [ ] Not applicable.

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I have added the following labels to this PR based on the title: [ enhancement ]. I have added the following labels to this PR based on the changes made: [ forecasting ]. Feel free to change these if they do not properly represent the PR.

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[MatthewMiddlehurst]

Hi, a fix for this has been merged.