def test_corr_dist(self):
"""
Test the calculation of the correlation matrix distance
"""
tic = TIC()
# Taking the original correlation matrix and the TIC matrix
etf_prices = self.returns_data.iloc[:, :5]
etf_corr = etf_prices.corr()
tic_corr = pd.DataFrame(
[[1, 0.72177129, -0.30629381, 0.7144813, 0.72177129],
[0.72177129, 1, -0.30729469, 0.716816, 0.72412981],
[-0.30629381, -0.30729469, 1, -0.30419096, -0.30729469],
[0.7144813, 0.716816, -0.30419096, 1, 0.716816],
[0.72177129, 0.72412981, -0.30729469, 0.716816, 1]],
index=etf_corr.index,
columns=etf_corr.index)
# Expected distance between the matrices
dist_ecpected = 0.0130404424083
# Calculating the distance between the correlation matrices
distance = tic.corr_dist(etf_corr, tic_corr)
# Testing that the calculated distance is right
np.testing.assert_almost_equal(distance, dist_ecpected, decimal=2)
def test_link2corr(self):
"""
Test the process of deriving a correlation matrix from the linkage object
"""
tic = TIC()
# Creating a sample input
etf_prices = self.returns_data.iloc[:, :5]
etf_corr = etf_prices.corr()
lnk = np.array([(1, 4, 0.10526126, 2), (5, 3, 0.23105119, 3),
(0, 6, 0.40104189, 4), (7, 2, 0.59567056, 5)],
dtype=[('i0', int), ('i1', int), ('dist', float),
('num', int)])
lbls = etf_corr.index
# Expected correlation matrix
corr_expected = pd.DataFrame(
[[1, 0.678331, 0.290353, 0.678331, 0.678331],
[0.678331, 1, 0.290353, 0.893231, 0.977840],
[0.290353, 0.290353, 1, 0.290353, 0.290353],
[0.678331, 0.893231, 0.290353, 1, 0.893231],
[0.678331, 0.977840, 0.290353, 0.893231, 1]],
index=lbls,
columns=lbls)
# Getting the correlation matrix
corr = tic._link2corr(lnk, lbls)
# Testing that the correlation matrix is right
np.testing.assert_almost_equal(np.array(corr),
np.array(corr_expected),
decimal=2)
def test_update_dist():
"""
Testing the update of the general distance matrix to take the new clusters into account
"""
tic = TIC()
# Creating a sample input
dist0 = pd.DataFrame([[0.0, 0.595671], [0.595671, 0.0]],
columns=[20, 10],
index=[20, 10])
lnk0 = np.array([[1, 4, 0.10526126, 2], [5, 3, 0.23105119, 3],
[0, 6, 0.40104189, 4], [7, 2, 0.59567056, 5]])
lnk_ = np.array([[7, 2, 0.59567056, 5]])
items0 = [1010, 1020, 20, 1040, 1030, 5, 6, 10, 8]
# Alternative criterion - simple average
alt_criterion = pd.DataFrame.mean
# Expected distance matrix
dist_expected = pd.DataFrame([0], columns=[8], index=[8])
# Calculating distance matrix
dist_new = tic._update_dist(dist0, lnk0, lnk_, items0, criterion=None)
# Calculating the distance matrix with an alternative criterion
dist_new_alt = tic._update_dist(dist0,
lnk0,
lnk_,
items0,
criterion=alt_criterion)
# Testing that the obtained distance matrix is right
np.testing.assert_almost_equal(np.array(dist_new),
np.array(dist_expected),
decimal=2)
# Testing that the obtained distance matrix is right
np.testing.assert_almost_equal(np.array(dist_new_alt),
np.array(dist_expected),
decimal=2)
def test_get_linkage_corr(self):
"""
Testing the creation of a linkage object from empirical correlation matrix and tree graph
"""
tic = TIC()
# Taking the first 5 ETFs for test purposes
etf_prices = self.returns_data.iloc[:, :5]
etf_classification_tree = self.classification_tree.iloc[:5]
# Expected dendrogram
dend_expected = np.array([(1, 4, 0.16853455, 2), (5, 0, 0.22227236, 3),
(3, 6, 0.26530006, 4),
(7, 2, 0.76268129, 5)])
# Calculating simple correlation matrix for the TIC algorithm input
etf_corr = etf_prices.corr()
# Also testing on the tree that has a single element on the top level
etf_classification_tree_alt = etf_classification_tree.copy()
etf_classification_tree_alt['All'] = 0
# Using the function
dendrogram = tic._get_linkage_corr(etf_classification_tree, etf_corr)
# Using the function on a tree with an extra level
dendrogram_alt = tic._get_linkage_corr(etf_classification_tree_alt,
etf_corr)
# Testing that the obtained dendrogram is right
# Transforming to DataFrames to get the same types
np.testing.assert_almost_equal(np.array(pd.DataFrame(dendrogram)),
np.array(pd.DataFrame(dend_expected)),
decimal=2)
# Checking that the tree with an extra level returned the same result
np.testing.assert_almost_equal(np.array(pd.DataFrame(dendrogram)),
np.array(pd.DataFrame(dendrogram_alt)),
decimal=2)
def test_get_atoms():
"""
Testing the obtaining of the atoms included in an element from a linkage object
"""
tic = TIC()
# Creating a sample input
lnk = np.array([(1, 4, 0.10526126, 2), (5, 3, 0.23105119, 3),
(0, 6, 0.40104189, 4), (7, 2, 0.59567056, 5)],
dtype=[('i0', int), ('i1', int), ('dist', float),
('num', int)])
item = 5
# Expected list of atoms
atoms_expected = [1, 4]
# Getting the atoms list
atoms = tic._get_atoms(lnk, item)
# Testing that the obtained atoms are right
np.testing.assert_almost_equal(atoms, atoms_expected, decimal=2)
def test_link_clusters():
"""
Testing the transformation of linkage object from local linkage to global linkage
"""
tic = TIC()
# Creating a sample input
lnk0 = np.array([])
lnk1 = np.array([[1, 3, 0.10526126, 2], [4, 2, 0.23105119, 3],
[0, 5, 0.40104189, 4]])
items0 = [1010, 1020, 2030, 1040, 1030]
items1 = [1010, 1020, 1040, 1030]
# Expected link array
link_expected = np.array([[1, 4, 0.10526126, 2], [5, 3, 0.23105119, 3],
[0, 6, 0.40104189, 4]])
# Calculating new link array
link_new = tic._link_clusters(lnk0, lnk1, items0, items1)
# Testing that the obtained new link is right
np.testing.assert_almost_equal(link_new, link_expected, decimal=2)
def test_tic_correlation(self):
"""
Test the calculation the Theory-Implies Correlation (TIC) matrix.
"""
tic = TIC()
# Taking the first 5 ETFs for test purposes
etf_prices = self.returns_data.iloc[:, :5]
etf_classification_tree = self.classification_tree.iloc[:5]
# Calculating simple correlation matrix for the TIC algorithm input
etf_corr = etf_prices.corr()
# Calculating the relation of the number of observations to the number of elements
tn_relation = etf_prices.shape[0] / etf_prices.shape[1]
# Expected correlation matrix
corr_expected = pd.DataFrame(
[[1, 0.72177129, -0.30629381, 0.7144813, 0.72177129],
[0.72177129, 1, -0.30729469, 0.716816, 0.72412981],
[-0.30629381, -0.30729469, 1, -0.30419096, -0.30729469],
[0.7144813, 0.716816, -0.30419096, 1, 0.716816],
[0.72177129, 0.72412981, -0.30729469, 0.716816, 1]],
index=etf_corr.index,
columns=etf_corr.index)
# Getting the correlation matrix
corr = tic.tic_correlation(etf_classification_tree,
etf_corr,
tn_relation=tn_relation,
kde_bwidth=0.25)
# Testing that the correlation matrix is right
np.testing.assert_almost_equal(np.array(corr),
np.array(corr_expected),
decimal=2)