From d2e8cb1fd4760373f688cc570b5f97652d13e536 Mon Sep 17 00:00:00 2001
From: Kevin Sheppard <kevin.k.sheppard@gmail.com>
Date: Fri, 5 Jan 2024 12:40:15 +0000
Subject: [PATCH] MAINT: Make case less extreme

---
 arch/tests/univariate/test_volatility.py |  4 ++--
 arch/univariate/volatility.py            | 16 ++++++++++++++--
 arch/utility/exceptions.py               |  4 ++++
 3 files changed, 20 insertions(+), 4 deletions(-)

diff --git a/arch/tests/univariate/test_volatility.py b/arch/tests/univariate/test_volatility.py
index b313652c42..2ddc61e77a 100644
--- a/arch/tests/univariate/test_volatility.py
+++ b/arch/tests/univariate/test_volatility.py
@@ -1431,9 +1431,9 @@ def test_figarch(setup, initial_value):
     assert_equal(figarch.num_params, 4)
     assert_equal(figarch.truncation, trunc_lag)
 
-    params = np.array([0.1, 0.2, 0.4, 1.1])
+    params = np.array([0.1, 1.01, 0.4, 1.005])
     with pytest.warns(InitialValueWarning):
-        figarch.simulate(params, 1000, rng.simulate([]))
+        figarch.simulate(params, 20, rng.simulate([]))
 
 
 def test_figarch_no_phi(setup):
diff --git a/arch/univariate/volatility.py b/arch/univariate/volatility.py
index 68a59b66ce..2738301bb5 100644
--- a/arch/univariate/volatility.py
+++ b/arch/univariate/volatility.py
@@ -25,7 +25,11 @@
 )
 from arch.univariate.distribution import Normal
 from arch.utility.array import AbstractDocStringInheritor, ensure1d
-from arch.utility.exceptions import InitialValueWarning, initial_value_warning
+from arch.utility.exceptions import (
+    InitialValueWarning,
+    ValueWarning,
+    initial_value_warning,
+)
 
 if TYPE_CHECKING:
     from arch.univariate import recursions_python as rec
@@ -3143,7 +3147,15 @@ def simulate(
         fdata[:truncation] = abs(data[:truncation]) ** power
         omega = parameters[0]
         beta = parameters[-1] if q else 0
-        omega_tilde = omega / (1 - beta)
+        if beta < 1:
+            omega_tilde = omega / (1 - beta)
+        else:
+            warn(
+                "beta >= 1.0, using omega as intercept since long-run variance "
+                "is ill-defined.",
+                ValueWarning,
+            )
+            omega_tilde = omega
         for t in range(truncation, truncation + nobs + burn):
             fsigma[t] = omega_tilde + lam_rev.dot(fdata[t - truncation : t])
             sigma2[t] = fsigma[t] ** (2.0 / power)
diff --git a/arch/utility/exceptions.py b/arch/utility/exceptions.py
index 3d10c04950..e279b970b1 100644
--- a/arch/utility/exceptions.py
+++ b/arch/utility/exceptions.py
@@ -88,3 +88,7 @@ class InfeasibleTestException(RuntimeError):
 
 class PerformanceWarning(UserWarning):
     """Warning issued if recursions are run in CPython"""
+
+
+class ValueWarning(UserWarning):
+    """Warning issued if value is problematic but no fatal."""