def test_cov_nw_axis(self):
y = np.random.randn(100, 2)
e = y - y.mean(0)
gamma_0 = e.T.dot(e)
gamma_1 = e[1:].T.dot(e[:-1])
gamma_2 = e[2:].T.dot(e[:-2])
w1, w2 = 1.0 - (1.0 / 3.0), 1.0 - (2.0 / 3.0)
expected = (gamma_0 + w1 * (gamma_1 + gamma_1.T) +
w2 * (gamma_2 + gamma_2.T)) / 100.0
assert_almost_equal(cov_nw(y.T, lags=2, axis=1), expected)
def test_cov_nw_axis(self):
y = self.rng.randn(100, 2)
e = y - y.mean(0)
gamma_0 = e.T.dot(e)
gamma_1 = e[1:].T.dot(e[:-1])
gamma_2 = e[2:].T.dot(e[:-2])
w1, w2 = 1.0 - (1.0 / 3.0), 1.0 - (2.0 / 3.0)
expected = (gamma_0 + w1 * (gamma_1 + gamma_1.T) + w2 *
(gamma_2 + gamma_2.T)) / 100.0
assert_almost_equal(cov_nw(y.T, lags=2, axis=1), expected)
def _compute_statistic(self):
"""Core routine to estimate PP test statistics"""
# 1. Estimate Regression
y, trend = self._y, self._trend
nobs = y.shape[0]
if self._lags is None:
self._lags = int(ceil(12. * power(nobs / 100., 1 / 4.)))
lags = self._lags
rhs = y[:-1, None]
rhs = _add_column_names(rhs, 0)
lhs = y[1:, None]
if trend != 'nc':
rhs = add_trend(rhs, trend)
resols = OLS(lhs, rhs).fit()
k = rhs.shape[1]
n, u = resols.nobs, resols.resid
lam2 = cov_nw(u, lags, demean=False)
lam = sqrt(lam2)
# 2. Compute components
s2 = u.dot(u) / (n - k)
s = sqrt(s2)
gamma0 = s2 * (n - k) / n
sigma = resols.bse[0]
sigma2 = sigma**2.0
rho = resols.params[0]
# 3. Compute statistics
self._stat_tau = sqrt(gamma0 / lam2) * ((rho - 1) / sigma) \
- 0.5 * ((lam2 - gamma0) / lam) * (n * sigma / s)
self._stat_rho = n * (rho - 1) \
- 0.5 * (n ** 2.0 * sigma2 / s2) * (lam2 - gamma0)
self._nobs = int(resols.nobs)
if self._test_type == 'rho':
self._stat = self._stat_rho
dist_type = 'ADF-z'
else:
self._stat = self._stat_tau
dist_type = 'ADF-t'
self._pvalue = mackinnonp(self._stat,
regression=trend,
dist_type=dist_type)
critical_values = mackinnoncrit(regression=trend,
nobs=n,
dist_type=dist_type)
self._critical_values = {
"1%": critical_values[0],
"5%": critical_values[1],
"10%": critical_values[2]
}
self._title = self._test_name + ' (Z-' + self._test_type + ')'
def _compute_statistic(self):
"""Core routine to estimate PP test statistics"""
# 1. Estimate Regression
y, trend = self._y, self._trend
nobs = y.shape[0]
if self._lags is None:
self._lags = int(ceil(12. * power(nobs / 100., 1 / 4.)))
lags = self._lags
rhs = y[:-1, None]
lhs = y[1:, None]
if trend != 'nc':
rhs = add_trend(rhs, trend)
resols = OLS(lhs, rhs).fit()
k = rhs.shape[1]
n, u = resols.nobs, resols.resid
lam2 = cov_nw(u, lags, demean=False)
lam = sqrt(lam2)
# 2. Compute components
s2 = u.dot(u) / (n - k)
s = sqrt(s2)
gamma0 = s2 * (n - k) / n
sigma = resols.bse[0]
sigma2 = sigma ** 2.0
rho = resols.params[0]
# 3. Compute statistics
self._stat_tau = sqrt(gamma0 / lam2) * ((rho - 1) / sigma) \
- 0.5 * ((lam2 - gamma0) / lam) * (n * sigma / s)
self._stat_rho = n * (rho - 1) \
- 0.5 * (n ** 2.0 * sigma2 / s2) * (lam2 - gamma0)
self._nobs = int(resols.nobs)
if self._test_type == 'rho':
self._stat = self._stat_rho
dist_type = 'ADF-z'
else:
self._stat = self._stat_tau
dist_type = 'ADF-t'
self._pvalue = mackinnonp(self._stat,
regression=trend,
dist_type=dist_type)
critical_values = mackinnoncrit(regression=trend,
nobs=n,
dist_type=dist_type)
self._critical_values = {"1%": critical_values[0],
"5%": critical_values[1],
"10%": critical_values[2]}
self._title = self._test_name + ' (Z-' + self._test_type + ')'
def test_errors(self):
y = self.rng.randn(100, 2)
with pytest.raises(ValueError):
cov_nw(y, 200)
with pytest.raises(ValueError):
cov_nw(y, axis=3)
with pytest.raises(ValueError):
cov_nw(y, ddof=200)
def test_errors(self):
y = np.random.randn(100, 2)
with pytest.raises(ValueError):
cov_nw(y, 200)
with pytest.raises(ValueError):
cov_nw(y, axis=3)
with pytest.raises(ValueError):
cov_nw(y, ddof=200)
def _compute_statistic(self):
# 1. Estimate model with trend
nobs, y, trend = self._nobs, self._y, self._trend
z = add_trend(nobs=nobs, trend=trend)
res = OLS(y, z).fit()
# 2. Compute KPSS test
u = res.resid
if self._lags is None:
self._lags = int(ceil(12. * power(nobs / 100., 1 / 4.)))
lam = cov_nw(u, self._lags, demean=False)
s = cumsum(u)
self._stat = 1 / (nobs ** 2.0) * sum(s ** 2.0) / lam
self._nobs = u.shape[0]
self._pvalue, critical_values = kpss_crit(self._stat, trend)
self._critical_values = {"1%": critical_values[0],
"5%": critical_values[1],
"10%": critical_values[2]}
def test_cov_nw_2d(self):
y = self.rng.randn(100, 2)
simple_cov = cov_nw(y, lags=0)
e = y - y.mean(0)
assert_almost_equal(e.T.dot(e) / e.shape[0], simple_cov)
def test_cov_nw_no_demean(self):
y = self.inflation
simple_cov = cov_nw(y, lags=0, demean=False)
assert_almost_equal(y.dot(y) / y.shape[0], simple_cov)
def test_cov_nw_ddof(self):
y = self.inflation
simple_cov = cov_nw(y, lags=0, ddof=1)
e = y - y.mean()
n = e.shape[0]
assert_almost_equal(e.dot(e) / (n - 1), simple_cov)
def test_cov_nw(self):
y = self.inflation
simple_cov = cov_nw(y, lags=0)
e = y - y.mean()
assert_almost_equal(e.dot(e) / e.shape[0], simple_cov)
def test_cov_nw_2d(self):
y = np.random.randn(100, 2)
simple_cov = cov_nw(y, lags=0)
e = y - y.mean(0)
assert_almost_equal(e.T.dot(e) / e.shape[0], simple_cov)
def test_cov_nw_no_demean(self):
y = self.inflation
simple_cov = cov_nw(y, lags=0, demean=False)
assert_almost_equal(y.dot(y) / y.shape[0], simple_cov)
def test_cov_nw_ddof(self):
y = self.inflation
simple_cov = cov_nw(y, lags=0, ddof=1)
e = y - y.mean()
n = e.shape[0]
assert_almost_equal(e.dot(e) / (n - 1), simple_cov)
def test_cov_nw(self):
y = self.inflation
simple_cov = cov_nw(y, lags=0)
e = y - y.mean()
assert_almost_equal(e.dot(e) / e.shape[0], simple_cov)
