TST: Add direct moment and jacobian test of GMM

Test GMM moment condtiions and jacobian

Author: bashtage

linearmodels/asset_pricing/model.py

@@ -752,6 +752,7 @@ def fit(self, center=True, use_cue=False, steps=2, disp=10, max_iter=1000,
                           df=self.factors.shape[1], **cov_config)
 
         full_vcv = cov_est.cov
+        self._testing = {'s': cov_est.s}
         sel = slice((n * k), (n * k + k + nrf))
         rp = params[sel]
         rp_cov = full_vcv[sel, sel]

linearmodels/tests/asset_pricing/test_linear_factor_gmm.py

@@ -0,0 +1,102 @@
+import numpy as np
+import pytest
+from numpy.testing import assert_allclose
+
+from linearmodels.asset_pricing.model import LinearFactorModelGMM
+from linearmodels.tests.asset_pricing._utility import generate_data, get_all
+
+
+@pytest.fixture(params=['numpy', 'pandas'])
+def data(request):
+    return generate_data(nportfolio=10, output=request.param)
+
+
+def test_linear_model_gmm_moments_jacobian(data):
+    mod = LinearFactorModelGMM(data.portfolios, data.factors)
+    res = mod.fit(cov_type='robust', disp=0, debiased=False)
+    params = np.r_[res.betas.values.ravel(),
+                   res.risk_premia.values.ravel(),
+                   mod.factors.ndarray.mean(0)]
+    mod_mom = mod._moments(params[:, None], True)
+
+    mom = []
+    p = mod.portfolios.ndarray
+    f = mod.factors.ndarray
+    n = f.shape[0]
+    fc = np.c_[np.ones((n, 1)), f]
+    mu = f.mean(0)[None, :]
+    lam = res.risk_premia.values[None, :]
+    x = f - mu + lam
+    b = res.betas.values
+    for i in range(p.shape[1]):
+        eps = p[:, i:(i + 1)] - x @ b[[i]].T
+        for j in range(fc.shape[1]):
+            mom.append(eps * fc[:, [j]])
+    mom.append(f - mu)
+    mom = np.hstack(tuple(mom))
+
+    mod_jac = mod._jacobian(params, True)
+    jac = np.zeros((mom.shape[1], params.shape[0]))
+    nport, nf = p.shape[1], f.shape[1]
+    # 1,1
+    jac[:(nport * (nf + 1)), :nport * nf] = np.kron(np.eye(nport), fc.T @ x / n)
+    # 1, 2
+    col = []
+    for i in range(nport):
+        col.append(fc.T @ np.ones((n, 1)) @ b[[i]] / n)
+    col = np.vstack(tuple(col))
+    jac[:(nport * (nf + 1)), nport * nf:nport * nf + nf] = col
+    # 1, 3
+    col = []
+    for i in range(nport):
+        col.append(-fc.T @ np.ones((n, 1)) @ b[[i]] / n)
+    col = np.vstack(tuple(col))
+    jac[:(nport * (nf + 1)), -nf:] = col
+    # 2,2
+    jac[-nf:, -nf:] = np.eye(nf)
+
+    assert_allclose(mom, mod_mom)
+    assert_allclose(jac, mod_jac)
+
+    me = mom - mom.mean(0)[None, :]
+    s = me.T @ me / n
+    s = (s + s.T) / 2
+    cov = np.linalg.inv(jac.T @ np.linalg.inv(s) @ jac) / n
+    cov = (cov + cov.T) / 2
+    assert_allclose(np.diag(cov), np.diag(res.cov), rtol=5e-3)
+    get_all(res)
+
+
+@pytest.mark.skip
+def test_linear_model_gmm_smoke_iterate(data):
+    mod = LinearFactorModelGMM(data.portfolios, data.factors)
+    res = mod.fit(cov_type='robust', disp=5, steps=20)
+    get_all(res)
+
+
+@pytest.mark.skip
+def test_linear_model_gmm_smoke_risk_free(data):
+    mod = LinearFactorModelGMM(data.portfolios, data.factors, risk_free=True)
+    res = mod.fit(cov_type='robust', disp=10)
+    get_all(res)
+
+
+@pytest.mark.skip
+def test_linear_model_gmm_kernel_smoke(data):
+    mod = LinearFactorModelGMM(data.portfolios, data.factors)
+    res = mod.fit(cov_type='kernel', disp=10)
+    get_all(res)
+
+
+@pytest.mark.skip
+def test_linear_model_gmm_kernel_bandwidth_smoke(data):
+    mod = LinearFactorModelGMM(data.portfolios, data.factors)
+    res = mod.fit(cov_type='kernel', bandwidth=10, disp=10)
+    get_all(res)
+
+
+@pytest.mark.skip
+def test_linear_model_gmm_cue_smoke(data):
+    mod = LinearFactorModelGMM(data.portfolios, data.factors, risk_free=True)
+    res = mod.fit(cov_type='robust', disp=10, use_cue=True)
+    get_all(res)