def test_johansen(self):
s1 = self.load_resource('s1.pickle')
s2 = self.load_resource('s2.pickle')
s3 = self.load_resource('s3.pickle')
a = 0.5
x_1t = numpy.cumsum(s1) + s2
x_2t = a * numpy.cumsum(s1) + s3
x_3t = s3
test_date = datetime(2015, 10, 1)
n = len(s1)
index = pandas.date_range(test_date - timedelta(10), periods=n, freq='D')
y = pandas.DataFrame(index=index, data={'col1': x_1t, 'col2': x_2t, 'col3': x_3t})
jres = cointeg.get_johansen(y, lag=1)
self.assertEquals(2, jres['count_cointegration_vectors'], 'number of cointegration vectors does not match')
v1 = jres['cointegration_vectors'][:, 0]
v2 = jres['cointegration_vectors'][:, 1]
v3 = jres['eigenvectors'][:, 2] # v3 is not a cointegration vector
expected_v1 = numpy.array([1.18712515, -2.37415904, 3.14587243])
numpy.testing.assert_almost_equal(v1, expected_v1)
expected_v2 = numpy.array([-0.76082907, 1.52149628, -0.32817785])
numpy.testing.assert_almost_equal(v2, expected_v2)
expected_v3 = numpy.array([0.00019993, 0.04721915, -0.04629564])
numpy.testing.assert_almost_equal(v3, expected_v3)
self.assertFalse(cointeg.is_not_stationary(numpy.dot(y.as_matrix(), v1), significance='10%'))
self.assertFalse(cointeg.is_not_stationary(numpy.dot(y.as_matrix(), v2), significance='10%'))
self.assertTrue(cointeg.is_not_stationary(numpy.dot(y.as_matrix(), v3), significance='5%'))
def __init__(self, prices, calibration_start, calibration_end, backtest_end):
calibration_period = (prices.index >= calibration_start) & (prices.index < calibration_end)
backtest_period = (prices.index >= calibration_end) & (prices.index < backtest_end)
calibration_set = prices[calibration_period].groupby([(pandas.TimeGrouper('D'))]).ffill().dropna(axis=0)
self._backtest_set = prices[backtest_period]
self._signal = None
self._calibration = None
self._half_life = None
self._vector = None
cointeg_vectors = cointeg.get_johansen(calibration_set, lag=1)
if len(cointeg_vectors) > 0:
self._vector = cointeg_vectors[0]
self._calibration = pandas.DataFrame(calibration_set.dot(self._vector))
self._calibration.columns = ['signal']
delta_calibration = self._calibration - self._calibration.shift(periods=1)
delta_calibration.columns = ['dy']
delta_calibration['y'] = self._calibration.shift(1)
regress = ols(data=delta_calibration, formula='dy ~ y').fit()
logging.info('regression results: %s', regress.summary())
self._half_life = -int(math.log(2) / regress.params.y)
def test_johansen(self):
s1 = self.load_resource('s1.pickle')
s2 = self.load_resource('s2.pickle')
s3 = self.load_resource('s3.pickle')
a = 0.5
x_1t = numpy.cumsum(s1) + s2
x_2t = a * numpy.cumsum(s1) + s3
x_3t = s3
test_date = datetime(2015, 10, 1)
n = len(s1)
index = pandas.date_range(test_date - timedelta(10), periods=n, freq='D')
y = pandas.DataFrame(index=index, data={'col1': x_1t, 'col2': x_2t, 'col3': x_3t})
vectors = cointeg.get_johansen(y, lag=1)
v1 = vectors[0]
v2 = vectors[1]
expected_v1 = numpy.array([1., -1.9999231, 2.6499922])
numpy.testing.assert_almost_equal(v1, expected_v1)
expected_v2 = numpy.array([-2.3183438, 4.6361944, -1.])
numpy.testing.assert_almost_equal(v2, expected_v2)
self.assertFalse(cointeg.is_not_stationary(numpy.dot(y.values, v1), significance='10%'))
self.assertFalse(cointeg.is_not_stationary(numpy.dot(y.values, v2), significance='10%'))
import os
import numpy
import pandas
from statsext import cointeg
from matplotlib import pyplot
from pandas.stats.api import ols
from mktdata import load_prices_quandl
__author__ = 'Christophe'
if __name__ == '__main__':
logging.basicConfig(format='%(asctime)-15s %(levelname)s %(name)s - %(message)s', level=logging.DEBUG)
codes = ['GOOG/NYSE_EWA', 'GOOG/NYSE_EWC']
quandl_data = load_prices_quandl(codes, start_date='2006-04-26', end_date='2012-04-09')
results = cointeg.get_johansen(quandl_data, lag=1, significance='90%')
print
print 'critical_values_trace', results['critical_values_trace']
print 'trace_statistic', results['trace_statistic']
print 'critical_values_max_eigenvalue', results['critical_values_max_eigenvalue']
print 'eigenvalue_statistics', results['eigenvalue_statistics']
cointeg_vector = results['cointegration_vectors']
print
print '------', results
print '------', cointeg_vector
signal = numpy.dot(quandl_data.as_matrix(), cointeg_vector)[:, 0]
signal_df = pandas.DataFrame({'signal': signal}, index=quandl_data.index)
signal_df.plot()
print '--- non-stationarity test', cointeg.is_not_stationary(signal, significance='1%')
quandl_data.plot(kind='scatter', x='GOOG.NYSE_EWA - Close', y='GOOG.NYSE_EWC - Close')
regression = ols(y=quandl_data['GOOG.NYSE_EWA - Close'], x=quandl_data[['GOOG.NYSE_EWC - Close']])
__author__ = 'Christophe'
if __name__ == '__main__':
mu, sigma = 0, 1 # mean and standard deviation
n = 10000
s1 = np.random.normal(mu, sigma, n)
s2 = np.random.normal(mu, sigma, n)
s3 = np.random.normal(mu, sigma, n)
a = 0.5
x_1t = np.cumsum(s1) + s2
x_2t = a * np.cumsum(s1) + s3
x_3t = s3
todays_date = datetime.datetime.now().date()
index = pd.date_range(todays_date - datetime.timedelta(10), periods=n, freq='D')
y = pd.DataFrame(index=index, data={'col1': x_1t, 'col2': x_2t, 'col3': x_3t})
print cointeg.is_not_stationary(x_1t)
print cointeg.is_not_stationary(np.diff(x_1t))
print cointeg.is_not_stationary(x_2t)
print cointeg.is_not_stationary(np.diff(x_2t))
print cointeg.is_not_stationary(x_3t)
jres = cointeg.get_johansen(y, lag=1)
print "There are ", jres['count_cointegration_vectors'], "cointegration vectors"
v1 = jres['cointegration_vectors'][:, 0]
v2 = jres['cointegration_vectors'][:, 1]
print v1
print v2
v3 = jres['eigenvectors'][:, 2] # v3 is not a cointegration vector
print v1 / -v1[1]
print v2 / -v2[1]
