Repository: statsmodels/statsmodels

Issue:
BUG: Typo - b0 = fixed.get("initial_trend", l0)
#### Describe the bug

Seems you may have a Typo in the - models.py file on line - 668 
File Path >> python3.9/site-packages/statsmodels/tsa/holtwinters/model.py

#### Code Sample, a copy-pastable example if possible


```python
b0 = fixed.get("initial_trend", l0)
```
<details>

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</details>


If the issue has not been resolved, please file it in the issue tracker.

#### Expected Output

```python
#probable correction - though im obviously not sure 
l0 = fixed.get("initial_trend", l0)
```


#### Output of ``import statsmodels.api as sm; sm.show_versions()``

<details>

[paste the output of ``import statsmodels.api as sm; sm.show_versions()`` here below this line]

</details>



Discussion:
Should be ` b0 = fixed.get("initial_trend", b0)`

Resolving patch:
diff --git a/statsmodels/tsa/holtwinters/model.py b/statsmodels/tsa/holtwinters/model.py
--- a/statsmodels/tsa/holtwinters/model.py
+++ b/statsmodels/tsa/holtwinters/model.py
@@ -659,7 +659,7 @@ def _update_for_fixed(self, sel, alpha, beta, gamma, phi, l0, b0, s0):
             gamma = fixed.get("smoothing_seasonal", gamma)
             phi = fixed.get("damping_trend", phi)
             l0 = fixed.get("initial_level", l0)
-            b0 = fixed.get("initial_trend", l0)
+            b0 = fixed.get("initial_trend", b0)
             for i in range(self.seasonal_periods):
                 s0[i] = fixed.get(f"initial_seasonal.{i}", s0[i])
         return sel, alpha, beta, gamma, phi, l0, b0, s0


Test patch:
diff --git a/statsmodels/tsa/holtwinters/tests/test_holtwinters.py b/statsmodels/tsa/holtwinters/tests/test_holtwinters.py
--- a/statsmodels/tsa/holtwinters/tests/test_holtwinters.py
+++ b/statsmodels/tsa/holtwinters/tests/test_holtwinters.py
@@ -14,10 +14,7 @@
 import pytest
 import scipy.stats
 
-from statsmodels.tools.sm_exceptions import (
-    ConvergenceWarning,
-    ValueWarning,
-)
+from statsmodels.tools.sm_exceptions import ConvergenceWarning, ValueWarning
 from statsmodels.tsa.holtwinters import (
     PY_SMOOTHERS,
     SMOOTHERS,
@@ -537,6 +534,16 @@ def test_holt_damp_r(self):
         for key in params.keys():
             assert_allclose(fit.params[key], params[key])
 
+        with mod.fix_params(params):
+            opt_fit = mod.fit(optimized=True)
+        assert_allclose(fit.sse, opt_fit.sse)
+        assert_allclose(
+            opt_fit.params["initial_trend"], params["initial_trend"]
+        )
+        alt_params = {k: v for k, v in params.items() if "level" not in k}
+        with mod.fix_params(alt_params):
+            alt_fit = mod.fit(optimized=True)
+        assert not np.allclose(alt_fit.trend[0], opt_fit.trend[0])
         # Summary output
         # print(res$mse)
         assert_allclose(fit.sse / mod.nobs, 195.4397924865488, atol=1e-3)
@@ -1028,11 +1035,15 @@ def test_damping_trend_zero():
 
 def test_different_inputs():
     array_input_add = [10, 20, 30, 40, 50]
-    series_index_add = pd.date_range(start="2000-1-1", periods=len(array_input_add))
+    series_index_add = pd.date_range(
+        start="2000-1-1", periods=len(array_input_add)
+    )
     series_input_add = pd.Series(array_input_add, series_index_add)
 
     array_input_mul = [2, 4, 8, 16, 32]
-    series_index_mul = pd.date_range(start="2000-1-1", periods=len(array_input_mul))
+    series_index_mul = pd.date_range(
+        start="2000-1-1", periods=len(array_input_mul)
+    )
     series_input_mul = pd.Series(array_input_mul, series_index_mul)
 
     fit1 = ExponentialSmoothing(array_input_add, trend="add").fit()
@@ -1040,22 +1051,18 @@ def test_different_inputs():
     fit3 = ExponentialSmoothing(array_input_mul, trend="mul").fit()
     fit4 = ExponentialSmoothing(series_input_mul, trend="mul").fit()
 
-    assert_almost_equal(fit1.predict(),
-                        [60], 1)
-    assert_almost_equal(fit1.predict(start=5, end=7),
-                        [60, 70, 80], 1)
-    assert_almost_equal(fit2.predict(),
-                        [60], 1)
-    assert_almost_equal(fit2.predict(start="2000-1-6", end="2000-1-8"),
-                        [60, 70, 80], 1)
-    assert_almost_equal(fit3.predict(),
-                        [64], 1)
-    assert_almost_equal(fit3.predict(start=5, end=7),
-                        [64, 128, 256], 1)
-    assert_almost_equal(fit4.predict(),
-                        [64], 1)
-    assert_almost_equal(fit4.predict(start="2000-1-6", end="2000-1-8"),
-                        [64, 128, 256], 1)
+    assert_almost_equal(fit1.predict(), [60], 1)
+    assert_almost_equal(fit1.predict(start=5, end=7), [60, 70, 80], 1)
+    assert_almost_equal(fit2.predict(), [60], 1)
+    assert_almost_equal(
+        fit2.predict(start="2000-1-6", end="2000-1-8"), [60, 70, 80], 1
+    )
+    assert_almost_equal(fit3.predict(), [64], 1)
+    assert_almost_equal(fit3.predict(start=5, end=7), [64, 128, 256], 1)
+    assert_almost_equal(fit4.predict(), [64], 1)
+    assert_almost_equal(
+        fit4.predict(start="2000-1-6", end="2000-1-8"), [64, 128, 256], 1
+    )
 
 
 @pytest.fixture