Merge pull request #3 from RichardMM/cgarch

Cgarch

.gitignore

@@ -13,10 +13,12 @@ README.rst
 /totestimports.py
 *.user
 /.vs/config/applicationhost.config
-/examples/.ipynb_checkpoints/univariate_volatility_modeling-checkpoint.ipynb
 /local_cythonrecursion.py
 /.vs/arch/v14/.suo
 *.pyproj
 *.sln
 
 /.vs/config/applicationhost.config
+.vscode/settings.json
+**/*.ipynb_checkpoints/
+

arch/tests/univariate/test_volatility.py

@@ -100,8 +100,8 @@ def test_cgarch(self):
         bounds = cgarch.bounds(self.resids)
         assert_equal(bounds[0], (0, 1))
         assert_equal(bounds[1], (0, 1))
-        assert_equal(bounds[2], (-1, 1))
-        assert_equal(bounds[3], (0, 1))
+        assert_equal(bounds[2], (0, 1))
+        assert_equal(bounds[3], (0.79, 1))
         assert_equal(bounds[4], (0, 1))
         backcast = cgarch.backcast(self.resids)
         w = 0.94 ** np.arange(75)

arch/univariate/base.py

@@ -1262,7 +1262,7 @@ class ARCHModelResult(ARCHModelFixedResult):
     volatility : array
         Conditional volatility from model
     longterm_var : array
-        Longterm variance from model
+        Longterm variance from model if the volatility process outputs it
     cov_type : str
         String describing the covariance estimator used
     dep_var: Series
@@ -1328,7 +1328,7 @@ class ARCHModelResult(ARCHModelFixedResult):
     resid : {array, Series}
         nobs element array containing model residuals
     model : ARCHModel
-        Model instance used to produce the fit
+        Model instance used to produce the fit.
     """
 
     def __init__(self, params, param_cov, r2, resid, volatility, longterm_var,

arch/univariate/mean.py

@@ -1054,7 +1054,7 @@ class LS(HARX):
 
     Notes
     -----
-    The AR-X model is described by
+    The LS model is described by
 
     .. math::
 

arch/univariate/volatility.py

@@ -435,6 +435,11 @@ def compute_variance(self, parameters, resids, sigma2, backcast,
             Value to use when initializing ARCH recursion
         var_bounds : array
             Array containing columns of lower and upper bounds
+
+        Returns
+        -------
+        sigma : array
+            array of computed variances.
         """
         raise NotImplementedError('Must be overridden')  # pragma: no cover
 
@@ -2006,27 +2011,29 @@ def _simulation_forecast(self, parameters, resids, backcast, var_bounds, start,
 
 class CGARCH(GARCH):
     r"""
-    Component GARCH model. A restricted version of GARCH(2,2) by Engle and Lee
-
-    Parameters
-    ----------
-    All parameters are estimated
+    Component GARCH model. A restricted version of GARCH(2,2) by Engle and Lee.
+    Decomposes volatility into its long term and short term components.
+    No parameters needed
 
     Attributes
     ----------
     num_params : int
-    The number of parameters in the model
+        The number of parameters in the model
+
+    Examples
+    --------
+    >>> from arch.univariate import CGARCH
+    >>> cgarch = CGARCH()
 
     Notes
     -----
     In this class of processes, the variance dynamics are
 
     .. math::
 
-        \sigma^{2}_{t}=q_{t}+g_{t}
-        q_{t}=\omega + \rho q_{t-1} + \phi(r^{2}_{t-1}-\sigma^{2}_{t-1})
-        g_{t} = \alpha(r^{2}_{t-1}-q_{t-1})+\beta g_{t-1}
-
+        \sigma^{2}_{t}=q_{t}+g_{t}\\
+        q_{t}=\omega + \rho q_{t-1} + \phi(r^{2}_{t-1}-\sigma^{2}_{t-1})\\
+        g_{t} = \alpha(r^{2}_{t-1}-q_{t-1})+\beta g_{t-1}\\.
     """
 
     def __init__(self):
@@ -2054,14 +2061,47 @@ def backcast(self, resids):
         return super(CGARCH, self).backcast(resids)
 
     def bounds(self, resids):
-        return [(0, 1), (0, 1), (-1, 1), (0, 1), (0, 1)]
+        return [(0, 1), (0, 1), (0, 1), (0.79, 1), (0, 1)]
 
     def starting_values(self, resids):
-        return np.array([0.1, 0.4, np.var(resids)/2, 0.8, 0.2])
+        alphas = [0.08, 0.2]
+        betas = [0.6, 0.3, 0.01]
+        omegas = [np.var(resids), 0.1]
+        rhos = [0.98, 0.8, 0.7]
+        phis = [0.01, 0.2]
+        combos = list(itertools.product(*[alphas, betas, omegas, rhos, phis]))
+        llfs = np.ndarray(len(combos))
+
+        for i, values in enumerate(combos):
+            llfs[i] = self._gaussian_loglikelihood(np.array(values), resids,
+                                                   self.backcast(resids),
+                                                   self.variance_bounds(resids))
+
+        return np.array(combos[np.argmax(llfs)])
 
     def compute_variance(self, parameters, resids, sigma2, backcast,
                          var_bounds):
-        # this returns both sigma and long term variance
+        """
+        Compute the variance for the ARCH model
+
+        Parameters
+        ----------
+        resids : array
+            Vector of mean zero residuals
+        sigma2 : array
+            Array with same size as resids to store the conditional variance
+        backcast : float
+            Value to use when initializing ARCH recursion
+        var_bounds : array
+            Array containing columns of lower and upper bounds
+
+        Returns
+        -------
+        sigma : array
+            array of computed variances.
+        q2 : array
+            array of computed longterm variances.
+        """
         fresids = resids**2
         nobs = len(fresids)
         g2, q2 = np.ndarray(nobs*2).reshape(2, nobs)

doc/source/changes/4.0.txt

@@ -8,3 +8,5 @@ Changes since 4.0
   a ``ZeroMean`` variance process.
 - Fixed a bug that prevented ``fix`` from being used with a new model (:issue:`156`)
 - Added ``first_obs`` and ``last_obs`` parameters to ``fix`` to mimic ``fit``
+- Added Component GARCH process which decomposes volatility into long run and short run components.
+  The model comes with an extra ``longterm_var`` attribute when fit.

doc/source/univariate/forecasting.rst

@@ -178,13 +178,16 @@ Any call to :py:meth:`~arch.univariate.base.ARCHModelResult.forecast` returns a
 attributes and 1 which may be useful when using simulation- or bootstrap-based
 forecasts.
 
-The three core attributes are
+The four core attributes are
 
 * ``mean`` - The forecast conditional mean.
 * ``variance`` - The forecast conditional variance.
 * ``residual_variance`` - The forecast conditional variance of residuals.
   This will differ from ``variance`` whenever the model has dynamics
   (e.g. an AR model) for horizons larger than 1.
+* ``longterm_component`` - The forecast longterm conditional variance of residuals.
+  This is present only if the volatility process supports it
+  (e.g. ``CGARCH process``)
 
 Each attribute contains a ``DataFrame`` with a common structure.
 

doc/source/univariate/univariate.rst

@@ -12,6 +12,7 @@ Univariate Volatility Models
     Forecasting Examples <univariate_volatility_forecasting>
     Mean Models <mean>
     Volatility Processes <volatility>
+    CGARCH Model <CGARCH modelling>
     Using the Fixed Variance Process <univariate_using_fixed_variance>
     Distributions <distribution>
     Background and References <background>

doc/source/univariate/volatility.rst

@@ -36,6 +36,12 @@ ARCH
 .. autoclass:: ARCH
     :members: starting_values, backcast, compute_variance, bounds, constraints, simulate
 
+CGARCH
+------
+
+.. autoclass:: CGARCH
+    :members: starting_values, backcast, compute_variance, bounds, constraints, simulate
+
 Parameterless Variance Processes
 --------------------------------
 Some volatility processes use fixed parameters and so have no parameters that