ENH: Add VAR-HAC long-run covariance estimation

arch/conftest.py

@@ -2,6 +2,7 @@
 
 pytest_plugins = [
     "arch.tests.unitroot.cointegration_data",
+    "arch.tests.covariance.covariance_data",
 ]
 
 

arch/covariance/__init__.py

@@ -0,0 +1,12 @@
+from typing import Dict, Type
+
+from . import kernel
+
+KERNEL_ESTIMATORS: Dict[str, Type[kernel.CovarianceEstimator]] = {
+    est_name.lower(): getattr(kernel, est_name) for est_name in kernel.KERNELS
+}
+KERNEL_ESTIMATORS.update(
+    {est_name: getattr(kernel, est_name) for est_name in kernel.KERNELS}
+)
+KNOWN_KERNELS = "\n".join(sorted([k for k in KERNEL_ESTIMATORS]))
+KERNEL_ERR = f"kernel is not a known estimator. Must be one of:\n {KNOWN_KERNELS}"

arch/covariance/kernel.py

@@ -24,6 +24,8 @@
     "Andrews",
     "Gallant",
     "NeweyWest",
+    "normalize_kernel_name",
+    "ZeroLag",
 ]
 
 KERNELS = [
@@ -39,9 +41,26 @@
     "Andrews",
     "Gallant",
     "NeweyWest",
+    "ZeroLag",
 ]
 
 
+def normalize_kernel_name(name: str) -> str:
+    """
+    Normalize a Kernel name using standard replacements
+
+    Removes - and _ and converts to lower case.
+
+    Returns
+    -------
+    str
+        The normalized kernel name.
+    """
+    name = name.replace("-", "").replace("_", "")
+    name = name.lower()
+    return name
+
+
 class CovarianceEstimate(object):
     r"""
     Covariance estimate using a long-run covariance estimator
@@ -172,6 +191,7 @@ class CovarianceEstimator(ABC):
     def __init__(
         self,
         x: ArrayLike,
+        *,
         bandwidth: Optional[float] = None,
         df_adjust: int = 0,
         center: bool = True,
@@ -699,3 +719,29 @@ class NeweyWest(Bartlett):
     --------
     Bartlett
     """
+
+
+zero_lag_name = "Zero-lag (No autocorrelation)"
+zero_lag_formula = """\
+w= 1 & z=0\\\\ \
+\\ 0 & z>0 \
+\\end{cases} \
+"""
+
+
+@Substitution(kernel_name=zero_lag_name, formula=zero_lag_formula)
+class ZeroLag(CovarianceEstimator, metaclass=AbstractDocStringInheritor):
+    @property
+    def kernel_const(self) -> float:
+        return 1.0
+
+    @property
+    def bandwidth_scale(self) -> float:
+        return 0.0
+
+    @property
+    def rate(self) -> float:
+        return 0.0
+
+    def _weights(self) -> NDArray:
+        return np.ones(1)