diff --git a/.github/workflows/tests.yml b/.github/workflows/tests.yml
index b954f22..8af2c7c 100644
--- a/.github/workflows/tests.yml
+++ b/.github/workflows/tests.yml
@@ -10,7 +10,7 @@ jobs:
     runs-on: ubuntu-latest
     strategy:
       matrix:
-        python-version: ["3.9", "3.10", "3.11", "3.12"]
+        python-version: ["3.10", "3.11", "3.12"]
 
     steps:
       - uses: actions/checkout@v4
@@ -43,7 +43,7 @@ jobs:
     runs-on: ubuntu-latest
     strategy:
       matrix:
-        python-version: ["3.9", "3.10", "3.11", "3.12"]
+        python-version: ["3.10", "3.11", "3.12"]
 
     steps:
       - uses: actions/checkout@v4
diff --git a/lingam/longitudinal_lingam.py b/lingam/longitudinal_lingam.py
index 8a697c9..7a91da3 100644
--- a/lingam/longitudinal_lingam.py
+++ b/lingam/longitudinal_lingam.py
@@ -191,7 +191,7 @@ def fit(self, X_list):
 
         return self
 
-    def bootstrap(self, X_list, n_sampling, start_from_t=1):
+    def bootstrap(self, X_list, n_sampling, start_from_t=None):
         """Evaluate the statistical reliability of DAG based on the bootstrapping.
 
         Parameters
@@ -202,6 +202,8 @@ def bootstrap(self, X_list, n_sampling, start_from_t=1):
             where ``n_samples`` is the number of samples and ``n_features`` is the number of features.
         n_sampling : int
             Number of bootstrapping samples.
+        start_from_t : int, optional
+            The time step to calculate total effects from. If None, defaults to the number of lags.
 
         Returns
         -------
@@ -225,6 +227,13 @@ def bootstrap(self, X_list, n_sampling, start_from_t=1):
                 raise ValueError("X_list must be a list with the same shape")
             X_t.append(X)
 
+        # Check and set start_from_t
+        if start_from_t is None:
+            start_from_t = self._n_lags
+        else:
+            if start_from_t < self._n_lags:
+                raise ValueError(f"start_from_t must be greater than or equal to n_lags ({self._n_lags})")
+
         # Bootstrapping
         adjacency_matrices = np.zeros(
             (n_sampling, self._T, 1 + self._n_lags, self._p, self._p)
diff --git a/pyproject.toml b/pyproject.toml
index ac1ad15..f67d672 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -17,11 +17,11 @@ authors = [
     { name = "Shohei Shimizu" }
 ]
 license = { file = "LICENSE" }
-requires-python = ">=3.9"
+requires-python = ">=3.10"
 dependencies = [
     "numpy",
-    "scipy",
-    "scikit-learn",
+    "scipy<=1.13.1",
+    "scikit-learn>=1.6",
     "graphviz",
     "statsmodels",
     "networkx",
diff --git a/requirements.txt b/requirements.txt
index d3cd678..2f2d4cc 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -1,6 +1,6 @@
 numpy
-scipy<=1.13.1
-scikit-learn>=1.2
+scipy<=1.13.1 # Scipy version limitation due to semopy using the deprecated scipy.stats.mvn.
+scikit-learn>=1.6 # sklearn.utils.check_array with the ensure_all_finite argument.
 graphviz
 statsmodels
 networkx
diff --git a/tests/test_longitudinal_lingam.py b/tests/test_longitudinal_lingam.py
index be16cfe..c363508 100644
--- a/tests/test_longitudinal_lingam.py
+++ b/tests/test_longitudinal_lingam.py
@@ -289,7 +289,7 @@ def test_bootstrap_success():
     # fit by list
     X_list = [X1, X2, X3]
     model = LongitudinalLiNGAM()
-    result = model.bootstrap(X_list, n_sampling=3)
+    result = model.bootstrap(X_list, n_sampling=3, start_from_t=1)
 
     result.adjacency_matrices_
     result.total_effects_
@@ -532,6 +532,15 @@ def test_bootstrap_invalid_data():
     else:
         raise AssertionError
 
+    # Invalid argument: start_from_t must be greater than or equal to n_lags
+    model = LongitudinalLiNGAM(n_lags=2)
+    try:
+        result = model.bootstrap(X_list, n_sampling=3, start_from_t=1)
+    except ValueError:
+        pass
+    else:
+        raise AssertionError
+
     # Invalid argument: get_causal_direction_counts(n_directions=-1)
     model = LongitudinalLiNGAM()
     result = model.bootstrap(X_list, n_sampling=5)