[ENH] Chen & Yang (2004) forecast accuracy metrics (#8681) - #9364

Reference Issues/PRs

Fixes #8681

What does this implement/fix? Explain your changes.

Adds 7 forecast accuracy metrics from Section 4 of Chen & Yang (2004) "Assessing Forecast Accuracy Measures":

• NormalizedMeanSquaredError (NMSE) — RMSE normalized by standard deviation of actuals
• InterQuartileRangeError (IQR Error) — RMSE normalized by interquartile range of actuals
• KLDivergenceNormal (KL-N) — KL-divergence assuming normal errors, with optional windowed variants (KL-N1 window=5, KL-N2 window=10)
• KLDivergenceSingleExponential (KL-DE1) — KL-divergence assuming Laplace errors, rolling std scale
• KLDivergenceDoubleExponential (KL-DE2) — KL-divergence assuming Laplace errors, rolling MAD scale
• MeanAbsolutePercentageErrorStabilized (msMAPE) — symmetric MAPE stabilized by rolling MAD
• TheilU2 — Theil's U2 statistic (forecast MSE relative to naive seasonal walk)

All metrics support multioutput, evaluate, and evaluate_by_index. Metrics with non-linear aggregation (NMSE, IQR, KL-N, TheilU2) use jackknife leave-one-out pseudo-values for evaluate_by_index. Linear-mean metrics (KL-DE1, KL-DE2, msMAPE) return per-index values directly.

Files added/changed:

• _nmse.py, _iqre.py, _kln.py, _klde_base.py, _klde1.py, _klde2.py, _mapes.py, _theilu2.py
• init.py — registered all 7 classes
• docs/source/api_reference/performance_metrics.rst — added to API reference
• sktime/tests/_config.py — added doctest exclusions for np.float64() formatting
• tests/test_metrics.py — added unit tests for all 7 metrics + evaluate_by_index index correctness test

Does your contribution introduce a new dependency? If yes, which one?

No.

What should a reviewer concentrate their feedback on?

• Rolling scale estimators: population variance in KL-N/KL-DE1, MAD in KL-DE2/msMAPE
• Jackknife leave-one-out logic in _evaluate_by_index for NMSE, IQR, KL-N, and TheilU2
• get_test_params coverage for each metric class

Did you add any tests for the change?

Yes:

• Individual class tests for all 7 metrics (test_msmape_class, test_nmse_class, test_iqre_class, test_kln_class, test_klde1_class, test_klde2_class, test_theilu2_class)
• test_evaluate_by_index_returns_correct_index covering all 4 jackknife metrics
• All 112 framework tests in test_all_metrics_forecasting.py pass

Any other comments?

No.

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