BUG: ARIMA fit with trend and constant exog

statsmodels/tsa/arima_model.py

@@ -404,7 +404,7 @@ def _make_arma_exog(endog, exog, trend):
     if exog is None and trend == 'c':   # constant only
         exog = np.ones((len(endog), 1))
     elif exog is not None and trend == 'c':  # constant plus exogenous
-        exog = add_trend(exog, trend='c', prepend=True)
+        exog = add_trend(exog, trend='c', prepend=True, has_constant='raise')
     elif exog is not None and trend == 'nc':
         # make sure it's not holding constant from last run
         if exog.var() == 0:

statsmodels/tsa/tests/test_arima.py

@@ -2465,3 +2465,20 @@ def test_arima_no_full_output():
     mod = ARIMA(endog, (1, 0, 1))
     res = mod.fit(trend="c", disp=-1, full_output=False)
     assert res.mle_retvals is None
+
+
+def test_constant_column_trend():
+    # GH#3343 analogous to GH#5258 for AR, when the user passes a constant exog
+    #  and also passes trend="c", raise instead _make_arma_exog used to
+    #  silently drop a column and return an inconsistenct k_trend value.
+
+    exog = np.array([0.5, 0.5, 0.5, 0.5, 0.5])
+    endog =  np.array([-0.011866, 0.003380, 0.015357, 0.004451, -0.020889])
+
+    model = ARIMA(endog=endog, order=(1, 1, 0), exog=exog)
+
+    # Fitting with a constant and constant exog raises because of colinearity
+    with pytest.raises(ValueError, match="already contains"):
+        model.fit(trend="c")
+
+    # FIXME: calling model.fit(trend="nc") raises for orthogonal reasons