[BUG] Fix predict_residuals internal data type conversion

sktime/forecasting/base/_base.py

@@ -1129,10 +1129,7 @@ def predict_residuals(self, y=None, X=None):
         y_pred = self.predict(fh=fh, X=X)
 
         if not type(y_pred) == type(y):
-            raise TypeError(
-                "y must have same type, dims, index as expected predict return. "
-                f"expected type {type(y_pred)}, but found {type(y)}"
-            )
+            y = convert_to(y, self._y_mtype_last_seen)
 
         y_res = y - y_pred
 

sktime/forecasting/base/tests/test_base_bugs.py

@@ -10,8 +10,10 @@
     ForecastingGridSearchCV,
 )
 from sktime.forecasting.reconcile import ReconcilerForecaster
+from sktime.forecasting.sarimax import SARIMAX
 from sktime.forecasting.trend import PolynomialTrendForecaster
 from sktime.transformations.hierarchical.aggregate import Aggregator
+from sktime.transformations.series.difference import Differencer
 from sktime.utils._testing.hierarchical import _make_hierarchical
 from sktime.utils.validation._dependencies import _check_estimator_deps
 
@@ -58,3 +60,21 @@ def test_heterogeneous_get_fitted_params():
 
     reconciler.fit(y_agg)
     reconciler.get_fitted_params()  # triggers an error pre-fix
+
+
+@pytest.mark.skipif(
+    not _check_estimator_deps(SARIMAX, severity="none"),
+    reason="skip test if required soft dependency not available",
+)
+def test_predict_residuals_conversion():
+    """Regression test for bugfix #4766, related to predict_residuals internal type."""
+    from sktime.datasets import load_longley
+    from sktime.forecasting.model_selection import temporal_train_test_split
+
+    y, X = load_longley()
+    y_train, y_test, X_train, X_test = temporal_train_test_split(y, X)
+    pipe = Differencer() * SARIMAX()
+    pipe.fit(y=y_train, X=X_train, fh=[1, 2, 3, 4])
+    result = pipe.predict_residuals()
+
+    assert type(result) == type(y_train)