diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index 61715397e8e0b..8fe3a32fe3d39 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -94,10 +94,8 @@
 )
 from pandas.core.dtypes.generic import (
     ABCDataFrame,
-    ABCDatetimeIndex,
     ABCIndexClass,
     ABCMultiIndex,
-    ABCPeriodIndex,
     ABCSeries,
 )
 from pandas.core.dtypes.missing import isna, notna
@@ -8245,7 +8243,9 @@ def quantile(self, q=0.5, axis=0, numeric_only=True, interpolation="linear"):
 
         return result
 
-    def to_timestamp(self, freq=None, how="start", axis=0, copy=True) -> "DataFrame":
+    def to_timestamp(
+        self, freq=None, how: str = "start", axis: Axis = 0, copy: bool = True
+    ) -> "DataFrame":
         """
         Cast to DatetimeIndex of timestamps, at *beginning* of period.
 
@@ -8265,23 +8265,16 @@ def to_timestamp(self, freq=None, how="start", axis=0, copy=True) -> "DataFrame"
         -------
         DataFrame with DatetimeIndex
         """
-        new_data = self._data
-        if copy:
-            new_data = new_data.copy()
+        new_obj = self.copy(deep=copy)
 
-        axis = self._get_axis_number(axis)
-        if axis == 0:
-            assert isinstance(self.index, (ABCDatetimeIndex, ABCPeriodIndex))
-            new_data.set_axis(1, self.index.to_timestamp(freq=freq, how=how))
-        elif axis == 1:
-            assert isinstance(self.columns, (ABCDatetimeIndex, ABCPeriodIndex))
-            new_data.set_axis(0, self.columns.to_timestamp(freq=freq, how=how))
-        else:  # pragma: no cover
-            raise AssertionError(f"Axis must be 0 or 1. Got {axis}")
+        axis_name = self._get_axis_name(axis)
+        old_ax = getattr(self, axis_name)
+        new_ax = old_ax.to_timestamp(freq=freq, how=how)
 
-        return self._constructor(new_data)
+        setattr(new_obj, axis_name, new_ax)
+        return new_obj
 
-    def to_period(self, freq=None, axis=0, copy=True) -> "DataFrame":
+    def to_period(self, freq=None, axis: Axis = 0, copy: bool = True) -> "DataFrame":
         """
         Convert DataFrame from DatetimeIndex to PeriodIndex.
 
@@ -8299,23 +8292,16 @@ def to_period(self, freq=None, axis=0, copy=True) -> "DataFrame":
 
         Returns
         -------
-        TimeSeries with PeriodIndex
+        DataFrame with PeriodIndex
         """
-        new_data = self._data
-        if copy:
-            new_data = new_data.copy()
+        new_obj = self.copy(deep=copy)
 
-        axis = self._get_axis_number(axis)
-        if axis == 0:
-            assert isinstance(self.index, ABCDatetimeIndex)
-            new_data.set_axis(1, self.index.to_period(freq=freq))
-        elif axis == 1:
-            assert isinstance(self.columns, ABCDatetimeIndex)
-            new_data.set_axis(0, self.columns.to_period(freq=freq))
-        else:  # pragma: no cover
-            raise AssertionError(f"Axis must be 0 or 1. Got {axis}")
+        axis_name = self._get_axis_name(axis)
+        old_ax = getattr(self, axis_name)
+        new_ax = old_ax.to_period(freq=freq)
 
-        return self._constructor(new_data)
+        setattr(new_obj, axis_name, new_ax)
+        return new_obj
 
     def isin(self, values) -> "DataFrame":
         """