diff --git a/src/rtctools/data/timeseries.py b/src/rtctools/data/timeseries.py
index a6cbc4c..4d1bd0a 100644
--- a/src/rtctools/data/timeseries.py
+++ b/src/rtctools/data/timeseries.py
@@ -82,5 +82,7 @@ def fill_nan_in_timeseries(times: List[datetime], values: np.ndarray, interp_arg
         interp_args = {}
     times_sec = np.array([(t - times[0]).total_seconds() for t in times])
     nans = np.isnan(values)
+    if all(nans):
+        return values
     result = np.interp(times_sec, times_sec[~nans], values[~nans], **interp_args)
     return result
diff --git a/tests/data/test_timeseries.py b/tests/data/test_timeseries.py
index 54047b6..82308e3 100644
--- a/tests/data/test_timeseries.py
+++ b/tests/data/test_timeseries.py
@@ -65,3 +65,10 @@ def test_fill_nan_in_timeseries(self):
         result = fill_nan_in_timeseries(times, values)
         ref_result = np.array([1.0, 1.0, 2.0, 3.0, 3.0])
         np.testing.assert_almost_equal(result, ref_result)
+        values = np.array([np.nan, 1.0, np.nan, np.nan, np.nan])
+        result = fill_nan_in_timeseries(times, values)
+        ref_result = np.array([1.0, 1.0, 1.0, 1.0, 1.0])
+        np.testing.assert_almost_equal(result, ref_result)
+        values = np.array([np.nan, np.nan, np.nan, np.nan, np.nan])
+        result = fill_nan_in_timeseries(times, values)
+        assert all(np.isnan(result))