diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index d2b63c42d777b..67533259ae0c2 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -11014,7 +11014,9 @@ def ewm(
         times: Optional[Union[str, np.ndarray, FrameOrSeries]] = None,
     ) -> ExponentialMovingWindow:
         axis = self._get_axis_number(axis)
-        return ExponentialMovingWindow(
+        # error: Value of type variable "FrameOrSeries" of "ExponentialMovingWindow"
+        # cannot be "object"
+        return ExponentialMovingWindow(  # type: ignore[type-var]
             self,
             com=com,
             span=span,
diff --git a/pandas/core/window/expanding.py b/pandas/core/window/expanding.py
index 8b7182458dd1f..77f8486522626 100644
--- a/pandas/core/window/expanding.py
+++ b/pandas/core/window/expanding.py
@@ -5,11 +5,8 @@
     Dict,
     Optional,
     Tuple,
-    Union,
 )
 
-import numpy as np
-
 from pandas._typing import (
     Axis,
     FrameOrSeries,
@@ -589,7 +586,7 @@ def quantile(
     )
     def cov(
         self,
-        other: Optional[Union[np.ndarray, FrameOrSeriesUnion]] = None,
+        other: Optional[FrameOrSeriesUnion] = None,
         pairwise: Optional[bool] = None,
         ddof: int = 1,
         **kwargs,
@@ -654,7 +651,7 @@ def cov(
     )
     def corr(
         self,
-        other: Optional[Union[np.ndarray, FrameOrSeriesUnion]] = None,
+        other: Optional[FrameOrSeriesUnion] = None,
         pairwise: Optional[bool] = None,
         ddof: int = 1,
         **kwargs,
diff --git a/pandas/core/window/rolling.py b/pandas/core/window/rolling.py
index 37b043137858c..84c05a0563f04 100644
--- a/pandas/core/window/rolling.py
+++ b/pandas/core/window/rolling.py
@@ -1354,7 +1354,7 @@ def quantile(self, quantile: float, interpolation: str = "linear", **kwargs):
 
     def cov(
         self,
-        other: Optional[Union[np.ndarray, FrameOrSeriesUnion]] = None,
+        other: Optional[FrameOrSeriesUnion] = None,
         pairwise: Optional[bool] = None,
         ddof: int = 1,
         **kwargs,
@@ -1392,7 +1392,7 @@ def cov_func(x, y):
 
     def corr(
         self,
-        other: Optional[Union[np.ndarray, FrameOrSeriesUnion]] = None,
+        other: Optional[FrameOrSeriesUnion] = None,
         pairwise: Optional[bool] = None,
         ddof: int = 1,
         **kwargs,
@@ -2137,7 +2137,7 @@ def quantile(self, quantile: float, interpolation: str = "linear", **kwargs):
     )
     def cov(
         self,
-        other: Optional[Union[np.ndarray, FrameOrSeriesUnion]] = None,
+        other: Optional[FrameOrSeriesUnion] = None,
         pairwise: Optional[bool] = None,
         ddof: int = 1,
         **kwargs,
@@ -2262,7 +2262,7 @@ def cov(
     )
     def corr(
         self,
-        other: Optional[Union[np.ndarray, FrameOrSeriesUnion]] = None,
+        other: Optional[FrameOrSeriesUnion] = None,
         pairwise: Optional[bool] = None,
         ddof: int = 1,
         **kwargs,