def test_cov_with_confidence(self):
for noise in [0.01, 0.1, 0.2, 0.5, 1, 2, 5, 10]:
x = np.random.normal(0, 1, 1000)
y = 3 * x + np.random.normal(0, noise, x.shape)
cov, pv, lb, ub = stats.cov_with_confidence(x, y, confidence=0.95)
self.assertGreater(cov, 1)
self.assertGreater(cov, lb)
self.assertLess(cov, ub)
x = np.random.uniform(0, 10, 1000)
y = 3 * x + np.random.normal(0, 0.01, x.shape)
cov, pv, lb, ub = stats.cov_with_confidence(x, y, confidence=0.95)
self.assertGreater(cov, 1)
def test_cov_with_confidence(self):
for noise in [0.01, 0.1, 0.2, 0.5, 1, 2, 5, 10]:
x = np.random.normal(0, 1, 1000)
y = 3 * x + np.random.normal(0, noise, x.shape)
cov, pv, lb, ub = stats.cov_with_confidence(x, y, confidence=0.95)
self.assertGreater(cov, 1)
self.assertGreater(cov, lb)
self.assertLess(cov, ub)
x = np.random.uniform(0, 10, 1000)
y = 3 * x + np.random.normal(0, 0.01, x.shape)
cov, pv, lb, ub = stats.cov_with_confidence(x, y, confidence=0.95)
self.assertGreater(cov, 1)
def xcov_multi_with_confidence(xs, ys, lag_backward, lag_forward, confidence=0.95, normed=False):
"""
Calculate cross-covariance between x and y when multiple time-series are available.
This function is to be used when it is believed that y is created by filtering x
with a causal linear filter. If that is the case, then as the number of samples
increases, the result will approach the shape of the original filter.
:param xs: list of input time-series
:param ys: list of output time-series
:param lag_forward: number of lags to look forward (causal (x yields y))
:param lag_backward: number of lags to look back (acausal (y yields x))
:param confidence: confidence of confidence interval desired
:param normed: if True, results will be normalized by geometric mean of x's & y's variances
:return: cross-covariance, p-value, lower bound, upper bound
"""
if not np.all([len(x) == len(y) for x, y in zip(xs, ys)]):
raise ValueError('Arrays within xs and ys must all be of the same size!')
covs = []
p_values = []
lbs = []
ubs = []
for lag in range(-lag_backward, lag_forward):
if lag == 0:
x_rel = xs
y_rel = ys
elif lag < 0:
x_rel = [x[-lag:] for x in xs if len(x) > -lag]
y_rel = [y[:lag] for y in ys if len(y) > -lag]
else:
# calculate the cross covariance between x and y with a specific lag
# first get the relevant xs and ys from each time-series
x_rel = [x[:-lag] for x in xs if len(x) > lag]
y_rel = [y[lag:] for y in ys if len(y) > lag]
all_xs = np.concatenate(x_rel)
all_ys = np.concatenate(y_rel)
cov, p_value, lb, ub = stats.cov_with_confidence(all_xs, all_ys, confidence)
covs.append(cov)
p_values.append(p_value)
lbs.append(lb)
ubs.append(ub)
covs = np.array(covs)
p_values = np.array(p_values)
lbs = np.array(lbs)
ubs = np.array(ubs)
if normed:
# normalize by average variance of signals
var_x = np.cov(np.concatenate(xs), np.concatenate(xs))[0, 0]
var_y = np.cov(np.concatenate(ys), np.concatenate(ys))[0, 0]
norm_factor = np.sqrt(var_x * var_y)
covs /= norm_factor
lbs /= norm_factor
ubs /= norm_factor
return covs, p_values, lbs, ubs
def xcov_multi_with_confidence(xs, ys, lag_backward, lag_forward, confidence=0.95, normed=False):
"""
Calculate cross-covariance between x and y when multiple time-series are available.
This function is to be used when it is believed that y is created by filtering x
with a causal linear filter. If that is the case, then as the number of samples
increases, the result will approach the shape of the original filter.
:param xs: list of input time-series
:param ys: list of output time-series
:param lag_forward: number of lags to look forward (causal (x yields y))
:param lag_backward: number of lags to look back (acausal (y yields x))
:param confidence: confidence of confidence interval desired
:param normed: if True, results will be normalized by geometric mean of x's & y's variances
:return: cross-covariance, p-value, lower bound, upper bound
"""
if not np.all([len(x) == len(y) for x, y in zip(xs, ys)]):
raise ValueError('Arrays within xs and ys must all be of the same size!')
covs = []
p_values = []
lbs = []
ubs = []
for lag in range(-lag_backward, lag_forward):
if lag == 0:
x_rel = xs
y_rel = ys
elif lag < 0:
x_rel = [x[-lag:] for x in xs if len(x) > -lag]
y_rel = [y[:lag] for y in ys if len(y) > -lag]
else:
# calculate the cross covariance between x and y with a specific lag
# first get the relevant xs and ys from each time-series
x_rel = [x[:-lag] for x in xs if len(x) > lag]
y_rel = [y[lag:] for y in ys if len(y) > lag]
all_xs = np.concatenate(x_rel)
all_ys = np.concatenate(y_rel)
cov, p_value, lb, ub = stats.cov_with_confidence(all_xs, all_ys, confidence)
covs.append(cov)
p_values.append(p_value)
lbs.append(lb)
ubs.append(ub)
covs = np.array(covs)
p_values = np.array(p_values)
lbs = np.array(lbs)
ubs = np.array(ubs)
if normed:
# normalize by average variance of signals
var_x = np.cov(np.concatenate(xs), np.concatenate(xs))[0, 0]
var_y = np.cov(np.concatenate(ys), np.concatenate(ys))[0, 0]
norm_factor = np.sqrt(var_x * var_y)
covs /= norm_factor
lbs /= norm_factor
ubs /= norm_factor
return covs, p_values, lbs, ubs
