diff --git a/pandas/_typing.py b/pandas/_typing.py
index 074b57054c0d1..c50d532f40dd7 100644
--- a/pandas/_typing.py
+++ b/pandas/_typing.py
@@ -64,6 +64,7 @@
     from pandas.core.window.rolling import BaseWindow
 
     from pandas.io.formats.format import EngFormatter
+    from pandas.tseries.offsets import DateOffset
 else:
     # typing.final does not exist until py38
     final = lambda x: x
@@ -110,6 +111,7 @@
 Suffixes = Tuple[str, str]
 Ordered = Optional[bool]
 JSONSerializable = Optional[Union[PythonScalar, List, Dict]]
+Frequency = Union[str, "DateOffset"]
 Axes = Collection[Any]
 
 # dtypes
diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index 3fe330f659513..3c872bdedbc02 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -63,6 +63,7 @@
     FloatFormatType,
     FormattersType,
     FrameOrSeriesUnion,
+    Frequency,
     IndexKeyFunc,
     IndexLabel,
     Level,
@@ -4678,7 +4679,11 @@ def _replace_columnwise(
 
     @doc(NDFrame.shift, klass=_shared_doc_kwargs["klass"])
     def shift(
-        self, periods=1, freq=None, axis: Axis = 0, fill_value=lib.no_default
+        self,
+        periods=1,
+        freq: Optional[Frequency] = None,
+        axis: Axis = 0,
+        fill_value=lib.no_default,
     ) -> DataFrame:
         axis = self._get_axis_number(axis)
 
@@ -9499,7 +9504,7 @@ def quantile(
     @doc(NDFrame.asfreq, **_shared_doc_kwargs)
     def asfreq(
         self,
-        freq,
+        freq: Frequency,
         method=None,
         how: Optional[str] = None,
         normalize: bool = False,
@@ -9545,7 +9550,11 @@ def resample(
         )
 
     def to_timestamp(
-        self, freq=None, how: str = "start", axis: Axis = 0, copy: bool = True
+        self,
+        freq: Optional[Frequency] = None,
+        how: str = "start",
+        axis: Axis = 0,
+        copy: bool = True,
     ) -> DataFrame:
         """
         Cast to DatetimeIndex of timestamps, at *beginning* of period.
@@ -9578,7 +9587,9 @@ def to_timestamp(
         setattr(new_obj, axis_name, new_ax)
         return new_obj
 
-    def to_period(self, freq=None, axis: Axis = 0, copy: bool = True) -> DataFrame:
+    def to_period(
+        self, freq: Optional[Frequency] = None, axis: Axis = 0, copy: bool = True
+    ) -> DataFrame:
         """
         Convert DataFrame from DatetimeIndex to PeriodIndex.