diff --git a/src/connectedness/mhar.py b/src/connectedness/mhar.py
index 01b3afc..095350c 100644
--- a/src/connectedness/mhar.py
+++ b/src/connectedness/mhar.py
@@ -152,7 +152,7 @@ def fit_mhar_fixed_alpha(
     bd, bw, bm = np.split(model.coef_, 3, axis=1)
     phi1 = bd + bw / cfg.weekly_window + bm / cfg.monthly_window
     residuals = Y - (X @ model.coef_.T + model.intercept_)
-    sigma = np.cov(residuals.T)
+    sigma = residuals.T @ residuals / residuals.shape[0]
     return MHARFit(
         phi1=phi1,
         coef=model.coef_,
diff --git a/src/connectedness/pipeline.py b/src/connectedness/pipeline.py
index 68d68ca..4f6bb01 100644
--- a/src/connectedness/pipeline.py
+++ b/src/connectedness/pipeline.py
@@ -42,11 +42,16 @@ class SpilloverPipeline:
     ...     SpilloverPipeline(prices)
     ...     .compute_returns()
     ...     .compute_realized_measures()
-    ...     .auto_pit()
+    ...     .force_pit()
     ...     .fit_static()
     ...     .fit_rolling(window=365)
     ...     .run()
     ... )
+
+    If no PIT method is called before ``fit_static``/``run``, the pipeline
+    applies :meth:`force_pit` automatically. This matches Chanatásig-Niza,
+    Ciarreta and Zárraga (2022), who PIT every realized series. Use
+    :meth:`auto_pit` to opt in to the selective variant.
     """
 
     def __init__(
@@ -104,6 +109,8 @@ def force_pit(self) -> SpilloverPipeline:
         return self
 
     def fit_static(self) -> SpilloverPipeline:
+        if not self._transformed:
+            self.force_pit()
         for name in self._measure_names:
             df = self._transformed.get(name, self._measure(name))
             self._static[name] = static_spillover(df, self._config)
@@ -122,6 +129,8 @@ def fit_rolling(
     def run(self) -> PipelineResult:
         if self._realized is None:
             self.compute_realized_measures()
+        if not self._transformed:
+            self.force_pit()
         if not self._static:
             self.fit_static()
         if self._rolling_kwargs is not None and not self._rolling: