def break_test(endog, exog, nbreaks, trim=0.15, vcov=None):
"""
Test that `nbreaks` exists in the sample.
TODO again, better cache the SSRs
TODO add support for p-value calculation (Hansen 1997)
Parameters
----------
endog : array-like
The endogenous variable.
exog : array-like
The exogenous matrix.
nbreaks : integer
The number of breakpoints in the null hypothesis
trim : float or int, optional
If a float, the minimum percentage of observations in each regime,
if an integer, the minimum number of observations in each regime.
vcov : callback, optional
Optionally provide a callback to modify the variance / covariance
matrix used in calculating the test statistic.
Returns
-------
fstat : float
The test statistic.
crits : iterable
The critical values.
"""
nobs = len(endog)
if trim < 1:
trim = int(np.floor(trim * nobs))
exog = np.asarray(exog)
# TODO Is there a better way to test for and fix this? (the problem is
# that if the exog argument is a list, so that exog is 1dim,
# np.concatenate fails to create a matrix, instead just makes a
# long vector)
if exog.ndim == 1:
exog = exog[:, None]
breakpoints, ssr = find_breakpoints(endog, exog, nbreaks, trim)
built_exog, regime_indicators, nobs_regimes = build_exog(exog, breakpoints)
res = OLS(endog, built_exog).fit()
q = exog.shape[1] # number of parameters subject to break, hard-coded to entire exog for now
p = 0 # number of parameters not subject to break, hard-coded to zero for now
R = np.zeros((nbreaks, nbreaks+1))
R[np.diag_indices(nbreaks)] = [-1]*nbreaks
R[tuple(np.diag_indices(nbreaks) + np.array([[0]*nbreaks, [1]*nbreaks]))] = [1]*nbreaks
Rd = R.dot(res.params[:, None])
V = vcov(res) if vcov else res.cov_params()
const = (nobs - (nbreaks+1)*q - p) / (nobs*nbreaks*q)
fstat = const * Rd.T.dot(np.linalg.inv(R.dot(V).dot(R.T))).dot(Rd)
return fstat
def ocsb_test_value(diff_series, x_reg, period):
try:
fit = OLS(diff_series, x_reg).fit()
except ValueError:
# Regression Model cannot be fit
return -np.inf
t2 = np.sqrt(fit.cov_params()["x2"]["x2"])
return fit.params["x2"] / t2
def test_compatibility(self):
"""Hypothesis test for the compatibility of prior mean with data
"""
# TODO: should we store the OLS results ? not needed so far, but maybe cache
#params_ols = np.linalg.pinv(self.model.exog).dot(self.model.endog)
#res = self.wald_test(self.model.r_matrix, q_matrix=self.model.q_matrix, use_f=False)
#from scratch
res_ols = OLS(self.model.endog, self.model.exog).fit()
r_mat = self.model.r_matrix
r_diff = self.model.q_matrix - r_mat.dot(res_ols.params)[:,None]
ols_cov_r = res_ols.cov_params(r_matrix=r_mat)
statistic = r_diff.T.dot(np.linalg.solve(ols_cov_r + self.model.sigma_prior, r_diff))
from scipy import stats
df = np.linalg.matrix_rank(self.model.sigma_prior) # same as r_mat.shape[0]
pvalue = stats.chi2.sf(statistic, df)
# TODO: return results class
return statistic, pvalue, df
def test_compatibility(self):
"""Hypothesis test for the compatibility of prior mean with data
"""
# TODO: should we store the OLS results ? not needed so far, but maybe cache
#params_ols = np.linalg.pinv(self.model.exog).dot(self.model.endog)
#res = self.wald_test(self.model.r_matrix, q_matrix=self.model.q_matrix, use_f=False)
#from scratch
res_ols = OLS(self.model.endog, self.model.exog).fit()
r_mat = self.model.r_matrix
r_diff = self.model.q_matrix - r_mat.dot(res_ols.params)[:,None]
ols_cov_r = res_ols.cov_params(r_matrix=r_mat)
statistic = r_diff.T.dot(np.linalg.solve(ols_cov_r + self.model.sigma_prior, r_diff))
from scipy import stats
df = np.linalg.matrix_rank(self.model.sigma_prior) # same as r_mat.shape[0]
pvalue = stats.chi2.sf(statistic, df)
# TODO: return results class
return statistic, pvalue, df
def test_combine_subset_regression(self):
# split sample into two, use first sample as prior for second
endog = self.endog
exog = self.exog
nobs = len(endog)
n05 = nobs // 2
np.random.seed(987125)
# shuffle to get random subsamples
shuffle_idx = np.random.permutation(np.arange(nobs))
ys = endog[shuffle_idx]
xs = exog[shuffle_idx]
k = 10
res_ols0 = OLS(ys[:n05], xs[:n05, :k]).fit()
res_ols1 = OLS(ys[n05:], xs[n05:, :k]).fit()
w = res_ols1.scale / res_ols0.scale #1.01
mod_1 = TheilGLS(ys[n05:],
xs[n05:, :k],
r_matrix=np.eye(k),
q_matrix=res_ols0.params,
sigma_prior=w * res_ols0.cov_params())
res_1p = mod_1.fit(cov_type='data-prior')
res_1s = mod_1.fit(cov_type='sandwich')
res_olsf = OLS(ys, xs[:, :k]).fit()
assert_allclose(res_1p.params, res_olsf.params, rtol=1e-9)
corr_fact = np.sqrt(res_1p.scale / res_olsf.scale)
# corrct for differences in scale computation
assert_allclose(res_1p.bse, res_olsf.bse * corr_fact, rtol=1e-3)
# regression test, does not verify numbers
# especially why are these smaller than OLS on full sample
# in larger sample, nobs=600, those were close to full OLS
bse1 = np.array([
0.26589869, 0.15224812, 0.38407399, 0.75679949, 0.66084200,
0.54174080, 0.53697607, 0.66006377, 0.38228551, 0.53920485
])
assert_allclose(res_1s.bse, bse1, rtol=1e-7)
def test_combine_subset_regression(self):
# split sample into two, use first sample as prior for second
endog = self.endog
exog = self.exog
nobs = len(endog)
n05 = nobs // 2
np.random.seed(987125)
# shuffle to get random subsamples
shuffle_idx = np.random.permutation(np.arange(nobs))
ys = endog[shuffle_idx]
xs = exog[shuffle_idx]
k = 10
res_ols0 = OLS(ys[:n05], xs[:n05, :k]).fit()
res_ols1 = OLS(ys[n05:], xs[n05:, :k]).fit()
w = res_ols1.scale / res_ols0.scale #1.01
mod_1 = TheilGLS(ys[n05:],
xs[n05:, :k],
r_matrix=np.eye(k),
q_matrix=res_ols0.params,
sigma_prior=w * res_ols0.cov_params())
res_1p = mod_1.fit(cov_type='data-prior')
res_1s = mod_1.fit(cov_type='sandwich')
res_olsf = OLS(ys, xs[:, :k]).fit()
assert_allclose(res_1p.params, res_olsf.params, rtol=1e-9)
corr_fact = 0.96156318 # corrct for differences in scale computation
assert_allclose(res_1p.bse, res_olsf.bse * corr_fact, rtol=1e-3)
# regression test, does not verify numbers
# especially why are these smaller than OLS on full sample
# in larger sample, nobs=600, those were close to full OLS
bse1 = np.array([
0.27609914, 0.15808869, 0.39880789, 0.78583194, 0.68619331,
0.56252314, 0.55757562, 0.68538523, 0.39695081, 0.55988991
])
assert_allclose(res_1s.bse, bse1, rtol=1e-7)
def test_combine_subset_regression(self):
# split sample into two, use first sample as prior for second
endog = self.endog
exog = self.exog
nobs = len(endog)
n05 = nobs // 2
np.random.seed(987125)
# shuffle to get random subsamples
shuffle_idx = np.random.permutation(np.arange(nobs))
ys = endog[shuffle_idx]
xs = exog[shuffle_idx]
k = 10
res_ols0 = OLS(ys[:n05], xs[:n05, :k]).fit()
res_ols1 = OLS(ys[n05:], xs[n05:, :k]).fit()
w = res_ols1.scale / res_ols0.scale #1.01
mod_1 = TheilGLS(ys[n05:], xs[n05:, :k], r_matrix=np.eye(k),
q_matrix=res_ols0.params,
sigma_prior=w * res_ols0.cov_params())
res_1p = mod_1.fit(cov_type='data-prior')
res_1s = mod_1.fit(cov_type='sandwich')
res_olsf = OLS(ys, xs[:, :k]).fit()
assert_allclose(res_1p.params, res_olsf.params, rtol=1e-9)
corr_fact = np.sqrt(res_1p.scale / res_olsf.scale)
# corrct for differences in scale computation
assert_allclose(res_1p.bse, res_olsf.bse * corr_fact, rtol=1e-3)
# regression test, does not verify numbers
# especially why are these smaller than OLS on full sample
# in larger sample, nobs=600, those were close to full OLS
bse1 = np.array([
0.26589869, 0.15224812, 0.38407399, 0.75679949, 0.66084200,
0.54174080, 0.53697607, 0.66006377, 0.38228551, 0.53920485])
assert_allclose(res_1s.bse, bse1, rtol=1e-7)
def test_predict_se():
# this test doesn't use reference values
# checks conistency across options, and compares to direct calculation
# generate dataset
nsample = 50
x1 = np.linspace(0, 20, nsample)
x = np.c_[x1, (x1 - 5)**2, np.ones(nsample)]
np.random.seed(0) #9876789) #9876543)
beta = [0.5, -0.01, 5.]
y_true2 = np.dot(x, beta)
w = np.ones(nsample)
w[int(nsample * 6. / 10):] = 3
sig = 0.5
y2 = y_true2 + sig * w * np.random.normal(size=nsample)
x2 = x[:, [0, 2]]
# estimate OLS
res2 = OLS(y2, x2).fit()
#direct calculation
covb = res2.cov_params()
predvar = res2.mse_resid + (x2 * np.dot(covb, x2.T).T).sum(1)
predstd = np.sqrt(predvar)
prstd, iv_l, iv_u = wls_prediction_std(res2)
np.testing.assert_almost_equal(prstd, predstd, 15)
#stats.t.isf(0.05/2., 50 - 2)
q = 2.0106347546964458
ci_half = q * predstd
np.testing.assert_allclose(iv_u, res2.fittedvalues + ci_half, rtol=1e-12)
np.testing.assert_allclose(iv_l, res2.fittedvalues - ci_half, rtol=1e-12)
prstd, iv_l, iv_u = wls_prediction_std(res2, x2[:3, :])
np.testing.assert_equal(prstd, prstd[:3])
np.testing.assert_allclose(iv_u,
res2.fittedvalues[:3] + ci_half[:3],
rtol=1e-12)
np.testing.assert_allclose(iv_l,
res2.fittedvalues[:3] - ci_half[:3],
rtol=1e-12)
# check WLS
res3 = WLS(y2, x2, 1. / w).fit()
#direct calculation
covb = res3.cov_params()
predvar = res3.mse_resid * w + (x2 * np.dot(covb, x2.T).T).sum(1)
predstd = np.sqrt(predvar)
prstd, iv_l, iv_u = wls_prediction_std(res3)
np.testing.assert_almost_equal(prstd, predstd, 15)
#stats.t.isf(0.05/2., 50 - 2)
q = 2.0106347546964458
ci_half = q * predstd
np.testing.assert_allclose(iv_u, res3.fittedvalues + ci_half, rtol=1e-12)
np.testing.assert_allclose(iv_l, res3.fittedvalues - ci_half, rtol=1e-12)
# testing shapes of exog
prstd, iv_l, iv_u = wls_prediction_std(res3, x2[-1:, :], weights=3.)
np.testing.assert_equal(prstd, prstd[-1])
prstd, iv_l, iv_u = wls_prediction_std(res3, x2[-1, :], weights=3.)
np.testing.assert_equal(prstd, prstd[-1])
prstd, iv_l, iv_u = wls_prediction_std(res3, x2[-2:, :], weights=3.)
np.testing.assert_equal(prstd, prstd[-2:])
prstd, iv_l, iv_u = wls_prediction_std(res3, x2[-2:, :], weights=[3, 3])
np.testing.assert_equal(prstd, prstd[-2:])
prstd, iv_l, iv_u = wls_prediction_std(res3, x2[:3, :])
np.testing.assert_equal(prstd, prstd[:3])
np.testing.assert_allclose(iv_u,
res3.fittedvalues[:3] + ci_half[:3],
rtol=1e-12)
np.testing.assert_allclose(iv_l,
res3.fittedvalues[:3] - ci_half[:3],
rtol=1e-12)
#use wrong size for exog
#prstd, iv_l, iv_u = wls_prediction_std(res3, x2[-1,0], weights=3.)
np.testing.assert_raises(ValueError,
wls_prediction_std,
res3,
x2[-1, 0],
weights=3.)
# check some weight values
sew1 = wls_prediction_std(res3, x2[-3:, :])[0]**2
for wv in np.linspace(0.5, 3, 5):
sew = wls_prediction_std(res3, x2[-3:, :], weights=1. / wv)[0]**2
np.testing.assert_allclose(sew, sew1 + res3.scale * (wv - 1))
def test_predict_se():
# this test doesn't use reference values
# checks conistency across options, and compares to direct calculation
# generate dataset
nsample = 50
x1 = np.linspace(0, 20, nsample)
x = np.c_[x1, (x1 - 5)**2, np.ones(nsample)]
np.random.seed(0)#9876789) #9876543)
beta = [0.5, -0.01, 5.]
y_true2 = np.dot(x, beta)
w = np.ones(nsample)
w[int(nsample * 6. / 10):] = 3
sig = 0.5
y2 = y_true2 + sig * w * np.random.normal(size=nsample)
x2 = x[:,[0,2]]
# estimate OLS
res2 = OLS(y2, x2).fit()
#direct calculation
covb = res2.cov_params()
predvar = res2.mse_resid + (x2 * np.dot(covb, x2.T).T).sum(1)
predstd = np.sqrt(predvar)
prstd, iv_l, iv_u = wls_prediction_std(res2)
np.testing.assert_almost_equal(prstd, predstd, 15)
#stats.t.isf(0.05/2., 50 - 2)
q = 2.0106347546964458
ci_half = q * predstd
np.testing.assert_allclose(iv_u, res2.fittedvalues + ci_half, rtol=1e-12)
np.testing.assert_allclose(iv_l, res2.fittedvalues - ci_half, rtol=1e-12)
prstd, iv_l, iv_u = wls_prediction_std(res2, x2[:3,:])
np.testing.assert_equal(prstd, prstd[:3])
np.testing.assert_allclose(iv_u, res2.fittedvalues[:3] + ci_half[:3],
rtol=1e-12)
np.testing.assert_allclose(iv_l, res2.fittedvalues[:3] - ci_half[:3],
rtol=1e-12)
# check WLS
res3 = WLS(y2, x2, 1. / w).fit()
#direct calculation
covb = res3.cov_params()
predvar = res3.mse_resid * w + (x2 * np.dot(covb, x2.T).T).sum(1)
predstd = np.sqrt(predvar)
prstd, iv_l, iv_u = wls_prediction_std(res3)
np.testing.assert_almost_equal(prstd, predstd, 15)
#stats.t.isf(0.05/2., 50 - 2)
q = 2.0106347546964458
ci_half = q * predstd
np.testing.assert_allclose(iv_u, res3.fittedvalues + ci_half, rtol=1e-12)
np.testing.assert_allclose(iv_l, res3.fittedvalues - ci_half, rtol=1e-12)
# testing shapes of exog
prstd, iv_l, iv_u = wls_prediction_std(res3, x2[-1:,:], weights=3.)
np.testing.assert_equal(prstd, prstd[-1])
prstd, iv_l, iv_u = wls_prediction_std(res3, x2[-1,:], weights=3.)
np.testing.assert_equal(prstd, prstd[-1])
prstd, iv_l, iv_u = wls_prediction_std(res3, x2[-2:,:], weights=3.)
np.testing.assert_equal(prstd, prstd[-2:])
prstd, iv_l, iv_u = wls_prediction_std(res3, x2[-2:,:], weights=[3, 3])
np.testing.assert_equal(prstd, prstd[-2:])
prstd, iv_l, iv_u = wls_prediction_std(res3, x2[:3,:])
np.testing.assert_equal(prstd, prstd[:3])
np.testing.assert_allclose(iv_u, res3.fittedvalues[:3] + ci_half[:3],
rtol=1e-12)
np.testing.assert_allclose(iv_l, res3.fittedvalues[:3] - ci_half[:3],
rtol=1e-12)
#use wrong size for exog
#prstd, iv_l, iv_u = wls_prediction_std(res3, x2[-1,0], weights=3.)
np.testing.assert_raises(ValueError, wls_prediction_std, res3, x2[-1,0],
weights=3.)
# check some weight values
sew1 = wls_prediction_std(res3, x2[-3:,:])[0]**2
for wv in np.linspace(0.5, 3, 5):
sew = wls_prediction_std(res3, x2[-3:,:], weights=1. / wv)[0]**2
np.testing.assert_allclose(sew, sew1 + res3.scale * (wv - 1))
x = np.ones((nobs,2))
x[:,1] = np.arange(nobs)/20.
y = x.sum(1) + 1.01*(1+1.5*(x[:,1]>10))*np.random.rand(nobs)
print(het_goldfeldquandt(y,x, 1))
y = x.sum(1) + 1.01*(1+0.5*(x[:,1]>10))*np.random.rand(nobs)
print(het_goldfeldquandt(y,x, 1))
y = x.sum(1) + 1.01*(1-0.5*(x[:,1]>10))*np.random.rand(nobs)
print(het_goldfeldquandt(y,x, 1))
print(het_breuschpagan(y,x))
print(het_white(y,x))
f, fp, fo = het_goldfeldquandt(y,x, 1)
print(f, fp)
resgq = het_goldfeldquandt(y,x, 1, retres=True)
print(resgq)
#this is just a syntax check:
print(_neweywestcov(y, x))
resols1 = OLS(y, x).fit()
print(_neweywestcov(resols1.resid, x))
print(resols1.cov_params())
print(resols1.HC0_se)
print(resols1.cov_HC0)
y = x.sum(1) + 10.*(1-0.5*(x[:,1]>10))*np.random.rand(nobs)
print(HetGoldfeldQuandt().run(y,x, 1, alternative='dec'))
#transf = TransformRestriction(np.eye(exog.shape[1])[:2], res2.params[:2] / 2)
transf3 = TransformRestriction([[0, 0, 0, 1, 0],[0, 0, 0, 0, 1]], [0, 1])
exog3_st = transf3.reduce(exog)
res3 = OLS(endog, exog3_st).fit()
# need to correct for constant/offset in the optimization
res3 = OLS(endog - exog.dot(transf3.constant.squeeze()), exog3_st).fit()
params = transf3.expand(res3.params).squeeze()
assert_allclose(params[:-2], res3_ols.params, rtol=1e-13)
print(res3.params)
print(params)
print(res3_ols.params)
print(res3_ols.bse)
# the following raises `ValueError: cannot test a constant constraint`
#tt = res3.t_test(transf3.transf_mat, transf3.constant.squeeze())
#print tt.sd
cov_params3 = transf3.transf_mat.dot(res3.cov_params()).dot(transf3.transf_mat.T)
bse3 = np.sqrt(np.diag(cov_params3))
print(bse3)
tp = transform_params_constraint(res2.params, res2.normalized_cov_params,
transf3.R, transf3.q)
tp = transform_params_constraint(res2.params, res2.cov_params(), transf3.R, transf3.q)
import statsmodels.api as sm
rand_data = sm.datasets.randhie.load(as_pandas=False)
rand_exog = rand_data.exog.view(float).reshape(len(rand_data.exog), -1)
rand_exog = sm.add_constant(rand_exog, prepend=False)
# Fit Poisson model:
poisson_mod0 = sm.Poisson(rand_data.endog, rand_exog)
#transf = TransformRestriction(np.eye(exog.shape[1])[:2], res2.params[:2] / 2)
transf3 = TransformRestriction([[0, 0, 0, 1, 0],[0, 0, 0, 0, 1]], [0, 1])
exog3_st = transf3.reduce(exog)
res3 = OLS(endog, exog3_st).fit()
# need to correct for constant/offset in the optimization
res3 = OLS(endog - exog.dot(transf3.constant.squeeze()), exog3_st).fit()
params = transf3.expand(res3.params).squeeze()
assert_allclose(params[:-2], res3_ols.params, rtol=1e-13)
print(res3.params)
print(params)
print(res3_ols.params)
print(res3_ols.bse)
# the following raises `ValueError: can't test a constant constraint`
#tt = res3.t_test(transf3.transf_mat, transf3.constant.squeeze())
#print tt.sd
cov_params3 = transf3.transf_mat.dot(res3.cov_params()).dot(transf3.transf_mat.T)
bse3 = np.sqrt(np.diag(cov_params3))
print(bse3)
tp = transform_params_constraint(res2.params, res2.normalized_cov_params,
transf3.R, transf3.q)
tp = transform_params_constraint(res2.params, res2.cov_params(), transf3.R, transf3.q)
from statsmodels.discrete.discrete_model import Poisson
import statsmodels.api as sm
rand_data = sm.datasets.randhie.load(as_pandas=False)
rand_exog = rand_data.exog.view(float).reshape(len(rand_data.exog), -1)
rand_exog = sm.add_constant(rand_exog, prepend=False)
def test_combine_subset_regression(self):
# split sample into two, use first sample as prior for second
endog = self.endog
exog = self.exog
nobs = len(endog)
n05 = nobs // 2
np.random.seed(987125)
# shuffle to get random subsamples
shuffle_idx = np.random.permutation(np.arange(nobs))
ys = endog[shuffle_idx]
xs = exog[shuffle_idx]
k = 10
res_ols0 = OLS(ys[:n05], xs[:n05, :k]).fit()
res_ols1 = OLS(ys[n05:], xs[n05:, :k]).fit()
w = res_ols1.scale / res_ols0.scale #1.01
mod_1 = TheilGLS(ys[n05:], xs[n05:, :k], r_matrix=np.eye(k), q_matrix=res_ols0.params, sigma_prior=w * res_ols0.cov_params())
res_1p = mod_1.fit(cov_type='data-prior')
res_1s = mod_1.fit(cov_type='sandwich')
res_olsf = OLS(ys, xs[:, :k]).fit()
assert_allclose(res_1p.params, res_olsf.params, rtol=1e-9)
corr_fact = 0.96156318 # corrct for differences in scale computation
assert_allclose(res_1p.bse, res_olsf.bse * corr_fact, rtol=1e-3)
# regression test, does not verify numbers
# especially why are these smaller than OLS on full sample
# in larger sample, nobs=600, those were close to full OLS
bse1 = np.array([
0.27609914, 0.15808869, 0.39880789, 0.78583194, 0.68619331,
0.56252314, 0.55757562, 0.68538523, 0.39695081, 0.55988991])
assert_allclose(res_1s.bse, bse1, rtol=1e-7)
x = np.ones((nobs,2))
x[:,1] = np.arange(nobs)/20.
y = x.sum(1) + 1.01*(1+1.5*(x[:,1]>10))*np.random.rand(nobs)
print(het_goldfeldquandt(y,x, 1))
y = x.sum(1) + 1.01*(1+0.5*(x[:,1]>10))*np.random.rand(nobs)
print(het_goldfeldquandt(y,x, 1))
y = x.sum(1) + 1.01*(1-0.5*(x[:,1]>10))*np.random.rand(nobs)
print(het_goldfeldquandt(y,x, 1))
print(het_breuschpagan(y,x))
print(het_white(y,x))
f, fp, fo = het_goldfeldquandt(y,x, 1)
print(f, fp)
resgq = het_goldfeldquandt(y,x, 1, retres=True)
print(resgq)
#this is just a syntax check:
print(_neweywestcov(y, x))
resols1 = OLS(y, x).fit()
print(_neweywestcov(resols1.resid, x))
print(resols1.cov_params())
print(resols1.HC0_se)
print(resols1.cov_HC0)
y = x.sum(1) + 10.*(1-0.5*(x[:,1]>10))*np.random.rand(nobs)
print(HetGoldfeldQuandt().run(y,x, 1, alternative='dec'))
def test_ols_noncentrality(self):
k = self.k_groups
res_ols = OLS(self.y, self.ex).fit()
nobs_t = res_ols.model.nobs
# constraint
c_equal = -np.eye(k)[1:]
c_equal[:, 0] = 1
v = np.zeros(c_equal.shape[0])
# noncentrality at estimated parameters
wt = res_ols.wald_test(c_equal, scalar=True)
df_num, df_denom = wt.df_num, wt.df_denom
cov_p = res_ols.cov_params()
nc_wt = wald_test_noncent_generic(res_ols.params,
c_equal,
v,
cov_p,
diff=None,
joint=True)
assert_allclose(nc_wt, wt.statistic * wt.df_num, rtol=1e-13)
nc_wt2 = wald_test_noncent(res_ols.params,
c_equal,
v,
res_ols,
diff=None,
joint=True)
assert_allclose(nc_wt2, nc_wt, rtol=1e-13)
es_ols = nc_wt / nobs_t
es_oneway = smo.effectsize_oneway(res_ols.params,
res_ols.scale,
self.nobs,
use_var="equal")
assert_allclose(es_ols, es_oneway, rtol=1e-13)
alpha = 0.05
pow_ols = smpwr.ftest_power(np.sqrt(es_ols),
df_denom,
df_num,
alpha,
ncc=1)
pow_oneway = smpwr.ftest_anova_power(np.sqrt(es_oneway),
nobs_t,
alpha,
k_groups=k,
df=None)
assert_allclose(pow_ols, pow_oneway, rtol=1e-13)
# noncentrality at other params
params_alt = res_ols.params * 0.75
# compute constraint value so we can get noncentrality from wald_test
v_off = _offset_constraint(c_equal, res_ols.params, params_alt)
wt_off = res_ols.wald_test((c_equal, v + v_off), scalar=True)
nc_wt_off = wald_test_noncent_generic(params_alt,
c_equal,
v,
cov_p,
diff=None,
joint=True)
assert_allclose(nc_wt_off,
wt_off.statistic * wt_off.df_num,
rtol=1e-13)
# check vectorized version, joint=False
nc_wt_vec = wald_test_noncent_generic(params_alt,
c_equal,
v,
cov_p,
diff=None,
joint=False)
for i in range(c_equal.shape[0]):
nc_wt_i = wald_test_noncent_generic(
params_alt,
c_equal[i:i + 1], # noqa
v[i:i + 1],
cov_p,
diff=None, # noqa
joint=False)
assert_allclose(nc_wt_vec[i], nc_wt_i, rtol=1e-13)
def sequential_break_test(endog, exog, nbreaks_null=0, trim=0.15, vcov=None):
"""
Test that one more break exists in the sample, given that there are at
least `nbreaks_null` breaks.
TODO obviously in sequential estimation of breakpoints, this will right now
recalculate the SSRs for the segments of the model many times. Easy
optimization is possible
TODO add support for dates, and return breakdates as well
TODO add support for p-value calculation (Hansen 1997)
TODO add support for different trimming values when calculating the null
model and when estimating the additional break (see Footnote 4,
Bai and Perron 2003)
Parameters
----------
endog : array-like
The endogenous variable.
exog : array-like
The exogenous matrix.
nbreaks_null : integer
The number of breakpoints in the null hypothesis
trim : float or int, optional
If a float, the minimum percentage of observations in each regime,
if an integer, the minimum number of observations in each regime.
vcov : callback, optional
Optionally provide a callback to modify the variance / covariance
matrix used in calculating the test statistic.
Returns
-------
fstat : float
The test statistic.
crits : iterable
The critical values.
"""
nobs = len(endog)
if trim < 1:
trim = int(np.floor(trim * nobs))
exog = np.asarray(exog)
# TODO Is there a better way to test for and fix this? (the problem is
# that if the exog argument is a list, so that exog is 1dim,
# np.concatenate fails to create a matrix, instead just makes a
# long vector)
if exog.ndim == 1:
exog = exog[:, None]
# TODO add test to make sure trim is consistent with the number of breaks
# in both the null and alternative hypotheses
# Estimate the breakpoints under the null
breakpoints, ssr_null = find_breakpoints(endog, exog, nbreaks_null, trim)
# Get the indices for the start and end of each segment
segments = zip((0,) + breakpoints, breakpoints + (nobs,))
# For each segment (there are nbreaks_null+1), estimate an additional
# breakpoint
optimal_segment = None
new_breakpoints = None
min_ssr = np.Inf
for segment in range(nbreaks_null+1):
start, end = segments[segment]
# Add one to the end, since breakpoint is actually the last observation
# in the previous regime
end += 1
segment_endog = endog[start:end]
segment_exog = exog[start:end]
# TODO this involves re-calculating SSR for lots of segments. Should
# use a cache of the upper-triangular set of SSRs from the
# find_breakpoints estimation above
try:
breakpoint, ssr = find_breakpoints(segment_endog, segment_exog, 1,
trim)
if ssr < min_ssr:
min_ssr = ssr
optimal_segment = segment
new_breakpoints = breakpoint
except InvalidRegimeError:
pass
# Find the parameters
start, end = segments[optimal_segment]
end += 1
segment_exog, _, _ = build_exog(exog[start:end], new_breakpoints)
res = OLS(endog[start:end], segment_exog).fit()
# Calculate the test statistic
nbreaks = 1
q = exog.shape[1] # number of parameters subject to break, hard-coded to entire exog for now
p = 0 # number of parameters not subject to break, hard-coded to zero for now
R = np.zeros((nbreaks, nbreaks+1))
R[np.diag_indices(nbreaks)] = [-1]*nbreaks
R[tuple(np.diag_indices(nbreaks) + np.array([[0]*nbreaks, [1]*nbreaks]))] = [1]*nbreaks
Rd = R.dot(res.params[:, None])
V = vcov(res) if vcov else res.cov_params()
nobs_segment = end - start
const = (nobs_segment - (nbreaks+1)*q - p) / (nobs_segment*nbreaks*q)
fstat = const * Rd.T.dot(np.linalg.inv(R.dot(V).dot(R.T))).dot(Rd)
return fstat