diff --git a/delaynet/detrending_methods/delta.py b/delaynet/detrending_methods/delta.py
index 947b955..2009556 100644
--- a/delaynet/detrending_methods/delta.py
+++ b/delaynet/detrending_methods/delta.py
@@ -1,6 +1,6 @@
 """Delta detrending."""
 
-from numpy import copy, size, mean, integer
+from numpy import empty, empty_like, integer, cumsum
 
 from ..decorators import detrending_method
 
@@ -27,12 +27,15 @@ def delta(ts, window_size: int = 10):
     if not isinstance(window_size, (int, integer)) or window_size <= 0:
         raise ValueError(f"window_size must be a positive integer, not {window_size}.")
 
-    ts2 = copy(ts)
-    for k in range(size(ts)):
-        off1 = k - window_size
-        off1 = max(off1, 0)
-        sub_ts = ts[off1 : (k + window_size)]
+    n = ts.shape[0]
+    c = empty(n + 1, dtype=ts.dtype)
+    c[0] = 0
+    c[1:] = cumsum(ts)
 
-        ts2[k] = ts[k] - mean(sub_ts)
+    ts2 = empty_like(ts)
+    for k in range(n):
+        left = max(0, k - window_size)
+        right = min(n, k + window_size)
+        ts2[k] = ts[k] - (c[right] - c[left]) / (right - left)
 
     return ts2
diff --git a/tests/detrending_methods/test_delta.py b/tests/detrending_methods/test_delta.py
index c24aeac..67c3f1b 100644
--- a/tests/detrending_methods/test_delta.py
+++ b/tests/detrending_methods/test_delta.py
@@ -46,6 +46,69 @@ def test_invalid_window_size(window_size):
         detrend(ts, method="delta", window_size=window_size)
 
 
+@pytest.mark.parametrize(
+    "ts,window_size,expected",
+    [
+        (
+            arange(20, dtype=float),
+            3,
+            [
+                -1.0,
+                -0.5,
+                0.0,
+                0.5,
+                0.5,
+                0.5,
+                0.5,
+                0.5,
+                0.5,
+                0.5,
+                0.5,
+                0.5,
+                0.5,
+                0.5,
+                0.5,
+                0.5,
+                0.5,
+                0.5,
+                1.0,
+                1.5,
+            ],
+        ),
+        (
+            arange(20, dtype=float),
+            10,
+            [
+                -4.5,
+                -4.0,
+                -3.5,
+                -3.0,
+                -2.5,
+                -2.0,
+                -1.5,
+                -1.0,
+                -0.5,
+                0.0,
+                0.5,
+                1.0,
+                1.5,
+                2.0,
+                2.5,
+                3.0,
+                3.5,
+                4.0,
+                4.5,
+                5.0,
+            ],
+        ),
+    ],
+)
+def test_delta_linear_20(ts, window_size, expected):
+    """Delta detrending of length-20 linear series."""
+    result = detrend(ts, method="delta", window_size=window_size)
+    assert_allclose(result, array(expected), atol=1e-10)
+
+
 def test_window_larger_than_series():
     """Test Delta detrending with window size larger than time series."""
     ts = array([1, 2, 3, 4, 5])
@@ -113,3 +176,37 @@ def test_delta_with_seasonal_data():
     # Check that the seasonal pattern is removed
     # The detrended series should have mean close to 0
     assert -0.2 < mean(ts_detrended) < 0.2
+
+
+@pytest.mark.parametrize(
+    "length,window_size",
+    [
+        (10, 3),
+        (50, 5),
+        (50, 25),
+        (100, 10),
+        (100, 40),
+    ],
+)
+def test_delta_matches_naive_reference(length, window_size):
+    """Compare optimized delta against naive local-mean reference."""
+    rng = default_rng(152)
+    ts = rng.normal(0, 1, length) + arange(length, dtype=float) * 0.1
+
+    result = detrend(ts, method="delta", window_size=window_size)
+
+    expected = ts.copy()
+    for k in range(length):
+        left = max(0, k - window_size)
+        right = min(length, k + window_size)
+        expected[k] = ts[k] - ts[left:right].mean()
+
+    assert_allclose(result, expected, atol=1e-10)
+
+
+@pytest.mark.parametrize("window_size", [1, 2, 5])
+def test_delta_symmetry_constant_series(window_size):
+    """Delta detrending of constant series should yield zero."""
+    ts = array([5.0] * 20)
+    result = detrend(ts, method="delta", window_size=window_size)
+    assert_allclose(result, 0.0, atol=1e-10)