[ENH] cleaned up probabilistic forecasting tests for quantile and interval predictions

[fkiraly]

This PR cleans up probabilistic forecasting tests for quantile and interval predictions, i.e., test_predict_interval and test_predict_quantiles.

It makes the two tests consistent, and ensures both check the expected index and columns, which they previously did not.

Minor additions in this PR connected to the tests:

• adds a probabilistic test case to ForecastX, which would surface the bug [BUG] ForecastX does not pass parameters to proba prediction methods #4386 (and covers its fix)
• BaggingForecaster and DynamicFactor have a broken predict_interval, this is a known issue, see [BUG] DynamicFactor returns incorrect index for probabilistic forecasts #4362 and [BUG] BaggingForecaster returns incorrect index for probabilistic forecasts #4363. They also need to be excepted from the updated test_predict_interval which also would surface the same bug now.

Depends on #4399, as fixes of bugs detected through this are in #4399

[yarnabrina]

Continuing what I said here, does it make sense to change from this:

sktime/sktime/forecasting/tests/test_all_forecasters.py

Lines 406 to 410 in e75cfc4

	if isinstance(y_train, pd.Series):
	expected = pd.MultiIndex.from_product([["Quantiles"], [alpha]])
	else:
	# multiply variables with all alpha values
	expected = pd.MultiIndex.from_product([y_train.columns, [alpha]])

to the effect of this?

expected_columns = ["Quantiles"] if isinstance(y_train, pd.Series) else y_train.columns
expected_quantiles = [alpha] if isinstance(alpha, float) else alpha
expected = pd.MultiIndex.from_product([expected_columns, expected_quantiles])

And then add at least a list element in here:

sktime/sktime/forecasting/tests/_config.py

Line 92 in e75cfc4

TEST_ALPHAS = [0.05, 0.1]

For example:

TEST_ALPHAS = [0.05, 0.1, [0.25, 0.75]]

Please let me know what you think.

[fkiraly]

yes, that's better! Much clearer, and adds a test case with multiple alphas.

I'd be happy if you branch off this PR and make the change. Or, suggest the change (using the GitHub graphical web interface) and I'll accept it.

[yarnabrina]

I'd be happy if you branch off this PR and make the change. Or, suggest the change (using the GitHub graphical web interface) and I'll accept it.

Done. See #4394.

[fkiraly]

Great, thanks!

I will merge in this sequence:

• [BUG] pass user passed parameters to ForecastX to underlying estimators #4391
• this
• [ENH] cover list input case for test_predict_interval/coverage and test_predict_quantiles/alpha in forecaster contract tests #4394

First I'll update from main and ensure the tests pass here.
They have already failed with ForecastX, so I'd expect they now run after the fix #4391 is merged.

If that is the case, we merge to main and update #4394 from main and check whether the extended tests still run.