diff --git a/doc/source/whatsnew/v0.20.2.txt b/doc/source/whatsnew/v0.20.2.txt
index e0857019d2fd4..03afc11156cc2 100644
--- a/doc/source/whatsnew/v0.20.2.txt
+++ b/doc/source/whatsnew/v0.20.2.txt
@@ -38,6 +38,7 @@ Bug Fixes
 
 - Bug in using ``pathlib.Path`` or ``py.path.local`` objects with io functions (:issue:`16291`)
 
+
 Conversion
 ^^^^^^^^^^
 
@@ -68,7 +69,7 @@ Plotting
 Groupby/Resample/Rolling
 ^^^^^^^^^^^^^^^^^^^^^^^^
 
-
+- Bug creating datetime rolling window on an empty DataFrame (:issue:`15819`)
 
 
 Sparse
diff --git a/pandas/core/window.py b/pandas/core/window.py
index df8e0c05009f4..cf1bad706ae1d 100644
--- a/pandas/core/window.py
+++ b/pandas/core/window.py
@@ -1074,7 +1074,7 @@ def validate(self):
         super(Rolling, self).validate()
 
         # we allow rolling on a datetimelike index
-        if (self.is_datetimelike and
+        if ((self.obj.empty or self.is_datetimelike) and
                 isinstance(self.window, (compat.string_types, DateOffset,
                                          timedelta))):
 
diff --git a/pandas/tests/test_window.py b/pandas/tests/test_window.py
index 634cd5fe2586b..6a640d62108b3 100644
--- a/pandas/tests/test_window.py
+++ b/pandas/tests/test_window.py
@@ -441,6 +441,20 @@ def test_closed(self):
         with pytest.raises(ValueError):
             df.rolling(window=3, closed='neither')
 
+    @pytest.mark.parametrize('roller', ['1s', 1])
+    def tests_empty_df_rolling(self, roller):
+        # GH 15819 Verifies that datetime and integer rolling windows can be
+        # applied to empty DataFrames
+        expected = DataFrame()
+        result = DataFrame().rolling(roller).sum()
+        tm.assert_frame_equal(result, expected)
+
+        # Verifies that datetime and integer rolling windows can be applied to
+        # empty DataFrames with datetime index
+        expected = DataFrame(index=pd.DatetimeIndex([]))
+        result = DataFrame(index=pd.DatetimeIndex([])).rolling(roller).sum()
+        tm.assert_frame_equal(result, expected)
+
 
 class TestExpanding(Base):
 
@@ -483,6 +497,24 @@ def test_numpy_compat(self):
             tm.assert_raises_regex(UnsupportedFunctionCall, msg,
                                    getattr(e, func), dtype=np.float64)
 
+    @pytest.mark.parametrize(
+        'expander',
+        [1, pytest.mark.xfail(
+            reason='GH 16425 expanding with offset not supported')('1s')])
+    def tests_empty_df_expanding(self, expander):
+        # GH 15819 Verifies that datetime and integer expanding windows can be
+        # applied to empty DataFrames
+        expected = DataFrame()
+        result = DataFrame().expanding(expander).sum()
+        tm.assert_frame_equal(result, expected)
+
+        # Verifies that datetime and integer expanding windows can be applied
+        # to empty DataFrames with datetime index
+        expected = DataFrame(index=pd.DatetimeIndex([]))
+        result = DataFrame(
+            index=pd.DatetimeIndex([])).expanding(expander).sum()
+        tm.assert_frame_equal(result, expected)
+
 
 class TestEWM(Base):