diff --git a/feature_engine/selection/drop_psi_features.py b/feature_engine/selection/drop_psi_features.py
index 9dab10bc8..8b5cdcbd7 100644
--- a/feature_engine/selection/drop_psi_features.py
+++ b/feature_engine/selection/drop_psi_features.py
@@ -214,7 +214,7 @@ class DropHighPSIFeatures(BaseSelector):
 
     def __init__(
         self,
-        split_col: str = None,
+        split_col: Union[str, None] = None,
         split_frac: float = 0.5,
         split_distinct: bool = False,
         cut_off: Union[None, int, float, datetime.date, List] = None,
diff --git a/feature_engine/selection/shuffle_features.py b/feature_engine/selection/shuffle_features.py
index b0053aa02..7ea906716 100644
--- a/feature_engine/selection/shuffle_features.py
+++ b/feature_engine/selection/shuffle_features.py
@@ -138,9 +138,9 @@ def __init__(
         estimator,
         scoring: str = "roc_auc",
         cv=3,
-        threshold: Union[float, int] = None,
+        threshold: Union[float, int, None] = None,
         variables: Variables = None,
-        random_state: int = None,
+        random_state: Union[int, None] = None,
         confirm_variables: bool = False,
     ):
 
diff --git a/feature_engine/selection/single_feature_performance.py b/feature_engine/selection/single_feature_performance.py
index da5308853..d084df1c6 100644
--- a/feature_engine/selection/single_feature_performance.py
+++ b/feature_engine/selection/single_feature_performance.py
@@ -119,7 +119,7 @@ def __init__(
         estimator,
         scoring: str = "roc_auc",
         cv=3,
-        threshold: Union[int, float] = None,
+        threshold: Union[int, float, None] = None,
         variables: Variables = None,
         confirm_variables: bool = False,
     ):
diff --git a/feature_engine/selection/target_mean_selection.py b/feature_engine/selection/target_mean_selection.py
index e90d013ca..7ded0a620 100644
--- a/feature_engine/selection/target_mean_selection.py
+++ b/feature_engine/selection/target_mean_selection.py
@@ -175,7 +175,7 @@ def __init__(
         strategy: str = "equal_width",
         scoring: str = "roc_auc",
         cv=3,
-        threshold: Union[int, float] = None,
+        threshold: Union[int, float, None] = None,
         regression: bool = False,
         confirm_variables: bool = False,
     ):
diff --git a/feature_engine/timeseries/forecasting/expanding_window_features.py b/feature_engine/timeseries/forecasting/expanding_window_features.py
index 2da549191..26c005e19 100644
--- a/feature_engine/timeseries/forecasting/expanding_window_features.py
+++ b/feature_engine/timeseries/forecasting/expanding_window_features.py
@@ -124,7 +124,7 @@ def __init__(
         min_periods: int | None = None,
         functions: str | list[str] = "mean",
         periods: int = 1,
-        freq: str = None,
+        freq: str | None = None,
         sort_index: bool = True,
         missing_values: str = "raise",
         drop_original: bool = False,
diff --git a/feature_engine/timeseries/forecasting/lag_features.py b/feature_engine/timeseries/forecasting/lag_features.py
index 10f633424..7a871dafd 100644
--- a/feature_engine/timeseries/forecasting/lag_features.py
+++ b/feature_engine/timeseries/forecasting/lag_features.py
@@ -101,7 +101,7 @@ def __init__(
         self,
         variables: Union[None, int, str, List[Union[str, int]]] = None,
         periods: Union[int, List[int]] = 1,
-        freq: Union[str, List[str]] = None,
+        freq: Union[str, List[str], None] = None,
         sort_index: bool = True,
         missing_values: str = "raise",
         drop_original: bool = False,
diff --git a/feature_engine/timeseries/forecasting/window_features.py b/feature_engine/timeseries/forecasting/window_features.py
index b5e5fed06..9207e15a8 100644
--- a/feature_engine/timeseries/forecasting/window_features.py
+++ b/feature_engine/timeseries/forecasting/window_features.py
@@ -127,10 +127,10 @@ def __init__(
         self,
         variables: Union[None, int, str, List[Union[str, int]]] = None,
         window: Union[str, int, Callable, List[int], List[str]] = 3,
-        min_periods: int = None,
+        min_periods: Union[int, None] = None,
         functions: Union[str, List[str]] = "mean",
         periods: int = 1,
-        freq: str = None,
+        freq: Union[str, None] = None,
         sort_index: bool = True,
         missing_values: str = "raise",
         drop_original: bool = False,