diff --git a/README.md b/README.md
index e62903683a..03d4cc3168 100644
--- a/README.md
+++ b/README.md
@@ -203,13 +203,13 @@ cov_est.cov.long_run
 These requirements reflect the testing environment. It is possible
 that arch will work with older versions.
 
-- Python (3.6+)
-- NumPy (1.14+)
-- SciPy (1.0.1+)
+- Python (3.7+)
+- NumPy (1.16+)
+- SciPy (1.2+)
 - Pandas (0.23+)
-- statsmodels (0.9+)
-- matplotlib (2.0+), optional
-- property-cached (1.6.3+), optional
+- statsmodels (0.11+)
+- matplotlib (2.2+), optional
+- property-cached (1.6.4+), optional
 
 ### Optional Requirements
 
diff --git a/arch/univariate/recursions.pyx b/arch/univariate/recursions.pyx
index b57e4433d6..d959aee40f 100644
--- a/arch/univariate/recursions.pyx
+++ b/arch/univariate/recursions.pyx
@@ -4,20 +4,12 @@
 import numpy as np
 
 cimport numpy as np
-from libc.math cimport sqrt
+from libc.math cimport sqrt, log, exp, fabs
+from libc.float cimport DBL_MAX
 
 __all__ = ['harch_recursion', 'arch_recursion', 'garch_recursion', 'egarch_recursion',
            'midas_recursion', 'figarch_recursion', 'figarch_weights', 'aparch_recursion']
 
-cdef extern from 'math.h':
-    double log(double x)
-    double exp(double x)
-    double sqrt(double x)
-    double fabs(double x)
-
-cdef extern from 'float.h':
-    double DBL_MAX
-
 cdef double LNSIGMA_MAX = log(DBL_MAX)
 
 np.import_array()
diff --git a/pyproject.toml b/pyproject.toml
index bc6f394352..3f52ea258f 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -2,14 +2,14 @@
 requires = [
   "setuptools",
   "wheel",
-  "numpy==1.14.6; python_version=='3.6'",
-  "numpy==1.14.6; python_version=='3.7'",
+  "numpy==1.6.6; python_version<='3.7'",
   "numpy==1.17.5; python_version=='3.8'",
-  "numpy; python_version>='3.9'",
+  "numpy==1.19.5; python_version=='3.9'",
+  "numpy; python_version>='3.10'",
   "Cython>=0.29.14"]
 
 [tool.black]
-target-version = ['py36', 'py37', 'py38']
+target-version = ['py37', 'py38']
 exclude = '''
 (
     \.egg
diff --git a/requirements-dev.txt b/requirements-dev.txt
index ebb40c3203..fae8c79973 100644
--- a/requirements-dev.txt
+++ b/requirements-dev.txt
@@ -1,5 +1,5 @@
 # Performance
-cython>=0.29.14
+cython>=0.29.21
 numba>=0.49,!=0.50.*
 
 # Graphics
diff --git a/requirements.txt b/requirements.txt
index 6b0aad4008..04c38f1396 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -1,5 +1,5 @@
-numpy>=1.14
-scipy>=1.0.1
+numpy>=1.16
+scipy>=1.2.3
 pandas>=0.23
-statsmodels>=0.9
-property_cached>=1.6.3
+statsmodels>=0.11
+property_cached>=1.6.4
diff --git a/setup.py b/setup.py
index efda9ee81f..17f2e1e846 100644
--- a/setup.py
+++ b/setup.py
@@ -65,10 +65,10 @@ def build_extensions(self) -> None:
 INSTALL_REQUIREMENTS = SETUP_REQUIREMENTS.copy()
 INSTALL_REQUIREMENTS.update(
     {
-        "scipy": "1.0.1",
+        "scipy": "1.2.3",
         "pandas": "0.23",
-        "statsmodels": "0.9",
-        "property_cached": "1.6.3",
+        "statsmodels": "0.10",
+        "property_cached": "1.6.4",
     }
 )
 
@@ -177,9 +177,9 @@ def run_setup(binary: bool = True) -> None:
             "Development Status :: 5 - Production/Stable",
             "Intended Audience :: End Users/Desktop",
             "Intended Audience :: Financial and Insurance Industry",
-            "Programming Language :: Python :: 3.6",
             "Programming Language :: Python :: 3.7",
             "Programming Language :: Python :: 3.8",
+            "Programming Language :: Python :: 3.9",
             "License :: OSI Approved",
             "Operating System :: MacOS :: MacOS X",
             "Operating System :: Microsoft :: Windows",