diff --git a/pymc_extras/statespace/models/structural.py b/pymc_extras/statespace/models/structural.py
index bc61eab98..40d1dedff 100644
--- a/pymc_extras/statespace/models/structural.py
+++ b/pymc_extras/statespace/models/structural.py
@@ -1071,6 +1071,12 @@ class TimeSeasonality(Component):
 
         If None, states will be numbered ``[State_0, ..., State_s]``
 
+    remove_first_state: bool, default True
+        If True, the first state will be removed from the model. This is done because there are only n-1 degrees of
+        freedom in the seasonal component, and one state is not identified. If False, the first state will be
+        included in the model, but it will not be identified -- you will need to handle this in the priors (e.g. with
+        ZeroSumNormal).
+
     Notes
     -----
     A seasonal effect is any pattern that repeats every fixed interval. Although there are many possible ways to
@@ -1163,7 +1169,7 @@ def __init__(
         innovations: bool = True,
         name: str | None = None,
         state_names: list | None = None,
-        pop_state: bool = True,
+        remove_first_state: bool = True,
     ):
         if name is None:
             name = f"Seasonal[s={season_length}]"
@@ -1176,14 +1182,15 @@ def __init__(
                 )
             state_names = state_names.copy()
         self.innovations = innovations
-        self.pop_state = pop_state
+        self.remove_first_state = remove_first_state
 
-        if self.pop_state:
+        if self.remove_first_state:
             # In traditional models, the first state isn't identified, so we can help out the user by automatically
             # discarding it.
             # TODO: Can this be stashed and reconstructed automatically somehow?
             state_names.pop(0)
-            k_states = season_length - 1
+
+        k_states = season_length - int(self.remove_first_state)
 
         super().__init__(
             name=name,
@@ -1218,8 +1225,16 @@ def populate_component_properties(self):
             self.shock_names = [f"{self.name}"]
 
     def make_symbolic_graph(self) -> None:
-        T = np.eye(self.k_states, k=-1)
-        T[0, :] = -1
+        if self.remove_first_state:
+            # In this case, parameters are normalized to sum to zero, so the current state is the negative sum of
+            # all previous states.
+            T = np.eye(self.k_states, k=-1)
+            T[0, :] = -1
+        else:
+            # In this case we assume the user to be responsible for ensuring the states sum to zero, so T is just a
+            # circulant matrix that cycles between the states.
+            T = np.eye(self.k_states, k=1)
+            T[-1, 0] = 1
 
         self.ssm["transition", :, :] = T
         self.ssm["design", 0, 0] = 1
diff --git a/tests/statespace/test_structural.py b/tests/statespace/test_structural.py
index 858efadfb..c398c723e 100644
--- a/tests/statespace/test_structural.py
+++ b/tests/statespace/test_structural.py
@@ -2,6 +2,7 @@
 import warnings
 
 from collections import defaultdict
+from copyreg import remove_extension
 from typing import Optional
 
 import numpy as np
@@ -592,13 +593,18 @@ def test_autoregressive_model(order, rng):
 
 @pytest.mark.parametrize("s", [10, 25, 50])
 @pytest.mark.parametrize("innovations", [True, False])
-def test_time_seasonality(s, innovations, rng):
+@pytest.mark.parametrize("remove_first_state", [True, False])
+def test_time_seasonality(s, innovations, remove_first_state, rng):
     def random_word(rng):
         return "".join(rng.choice(list("abcdefghijklmnopqrstuvwxyz")) for _ in range(5))
 
     state_names = [random_word(rng) for _ in range(s)]
     mod = st.TimeSeasonality(
-        season_length=s, innovations=innovations, name="season", state_names=state_names
+        season_length=s,
+        innovations=innovations,
+        name="season",
+        state_names=state_names,
+        remove_first_state=remove_first_state,
     )
     x0 = np.zeros(mod.k_states, dtype=floatX)
     x0[0] = 1
@@ -615,7 +621,8 @@ def random_word(rng):
     # Check coords
     mod.build(verbose=False)
     _assert_basic_coords_correct(mod)
-    assert mod.coords["season_state"] == state_names[1:]
+    test_slice = slice(1, None) if remove_first_state else slice(None)
+    assert mod.coords["season_state"] == state_names[test_slice]
 
 
 def get_shift_factor(s):