diff --git a/pymc_extras/statespace/utils/data_tools.py b/pymc_extras/statespace/utils/data_tools.py
index 5119726e..8c8284c5 100644
--- a/pymc_extras/statespace/utils/data_tools.py
+++ b/pymc_extras/statespace/utils/data_tools.py
@@ -87,12 +87,7 @@ def preprocess_pandas_data(data, n_obs, obs_coords=None, check_column_names=Fals
     col_names = data.columns
     _validate_data_shape(data.shape, n_obs, obs_coords, check_column_names, col_names)
 
-    if isinstance(data.index, pd.RangeIndex):
-        if obs_coords is not None:
-            warnings.warn(NO_TIME_INDEX_WARNING)
-        return preprocess_numpy_data(data.values, n_obs, obs_coords)
-
-    elif isinstance(data.index, pd.DatetimeIndex):
+    if isinstance(data.index, pd.DatetimeIndex):
         if data.index.freq is None:
             warnings.warn(NO_FREQ_INFO_WARNING)
             data.index.freq = data.index.inferred_freq
@@ -100,10 +95,30 @@ def preprocess_pandas_data(data, n_obs, obs_coords=None, check_column_names=Fals
         index = data.index
         return data.values, index
 
+    elif isinstance(data.index, pd.RangeIndex):
+        if obs_coords is not None:
+            warnings.warn(NO_TIME_INDEX_WARNING)
+        return preprocess_numpy_data(data.values, n_obs, obs_coords)
+
+    elif isinstance(data.index, pd.MultiIndex):
+        if obs_coords is not None:
+            warnings.warn(NO_TIME_INDEX_WARNING)
+
+        raise NotImplementedError("MultiIndex panel data is not currently supported.")
+
     else:
-        raise IndexError(
-            f"Expected pd.DatetimeIndex or pd.RangeIndex on data, found {type(data.index)}"
-        )
+        if obs_coords is not None:
+            warnings.warn(NO_TIME_INDEX_WARNING)
+
+        index = data.index
+        if not np.issubdtype(index.dtype, np.integer):
+            raise IndexError("Provided index is not an integer index.")
+
+        index_diff = index.to_series().diff().dropna().values
+        if not (index_diff == 1).all():
+            raise IndexError("Provided index is not monotonic increasing.")
+
+        return preprocess_numpy_data(data.values, n_obs, obs_coords)
 
 
 def add_data_to_active_model(values, index, data_dims=None):
diff --git a/tests/statespace/test_coord_assignment.py b/tests/statespace/test_coord_assignment.py
index 8e2fea58..40aaec12 100644
--- a/tests/statespace/test_coord_assignment.py
+++ b/tests/statespace/test_coord_assignment.py
@@ -8,6 +8,7 @@
 import pytest
 
 from pymc_extras.statespace.models import structural
+from pymc_extras.statespace.models.structural import LevelTrendComponent
 from pymc_extras.statespace.utils.constants import (
     FILTER_OUTPUT_DIMS,
     FILTER_OUTPUT_NAMES,
@@ -114,3 +115,67 @@ def test_data_index_is_coord(f, warning, create_model):
     with warning:
         pymc_model = create_model(f)
     assert TIME_DIM in pymc_model.coords
+
+
+def make_model(index):
+    n = len(index)
+    a = pd.DataFrame(index=index, columns=["A", "B", "C", "D"], data=np.arange(n * 4).reshape(n, 4))
+
+    mod = LevelTrendComponent(order=2, innovations_order=[0, 1])
+    ss_mod = mod.build(name="a", verbose=False)
+
+    initial_trend_dims, sigma_trend_dims, P0_dims = ss_mod.param_dims.values()
+    coords = ss_mod.coords
+
+    with pm.Model(coords=coords) as model:
+        P0_diag = pm.Gamma("P0_diag", alpha=5, beta=5)
+        P0 = pm.Deterministic("P0", pt.eye(ss_mod.k_states) * P0_diag, dims=P0_dims)
+
+        initial_trend = pm.Normal("initial_trend", dims=initial_trend_dims)
+        sigma_trend = pm.Gamma("sigma_trend", alpha=2, beta=50, dims=sigma_trend_dims)
+
+        with pytest.warns(UserWarning, match="No time index found on the supplied data"):
+            ss_mod.build_statespace_graph(
+                a["A"],
+                mode="JAX",
+            )
+    return model
+
+
+def test_integer_index():
+    index = np.arange(8).astype(int)
+    model = make_model(index)
+    assert TIME_DIM in model.coords
+    np.testing.assert_allclose(model.coords[TIME_DIM], index)
+
+
+def test_float_index_raises():
+    index = np.linspace(0, 1, 8)
+
+    with pytest.raises(IndexError, match="Provided index is not an integer index"):
+        make_model(index)
+
+
+def test_non_strictly_monotone_index_raises():
+    # Decreases
+    index = [0, 1, 2, 1, 2, 3]
+    with pytest.raises(IndexError, match="Provided index is not monotonic increasing"):
+        make_model(index)
+
+    # Has gaps
+    index = [0, 1, 2, 3, 5, 6]
+    with pytest.raises(IndexError, match="Provided index is not monotonic increasing"):
+        make_model(index)
+
+    # Has duplicates
+    index = [0, 1, 1, 2, 3, 4]
+    with pytest.raises(IndexError, match="Provided index is not monotonic increasing"):
+        make_model(index)
+
+
+def test_multiindex_raises():
+    index = pd.MultiIndex.from_tuples([(0, 0), (1, 1), (2, 2), (3, 3)])
+    with pytest.raises(
+        NotImplementedError, match="MultiIndex panel data is not currently supported"
+    ):
+        make_model(index)