def testFrankFrozen(self):
# Load matlab data set
stocks = np.loadtxt(dataDir + 'stocks.csv', delimiter=',')
x = stocks[:, 0]
y = stocks[:, 1]
stockModel = PairCopula(x, y, family={
'frank': 0,
})
# Try to fit all copula
stockModel.copulaTournament(verbosity=0)
# Eval the frozen model
frzU, frzV = stockModel.copulaModel.sample(40000)
# Eval a model with specified params
setU, setV = stockModel.copulaModel.sample(40000,
*stockModel.copulaParams[1])
# Ensure both frozen model and specified param model produce same result
frzModel = PairCopula(frzU, frzV)
setModel = PairCopula(setU, setV)
frzKtau, fp = frzModel.empKTau()
setKtau, sp = setModel.empKTau()
self.assertAlmostEqual(frzKtau, setKtau, places=2)
self.assertAlmostEqual(fp, sp, places=2)
def testKtauFitGauss(self):
# Load matlab data set
stocks = np.loadtxt(dataDir + 'stocks.csv', delimiter=',')
x = stocks[:, 0]
y = stocks[:, 1]
stockModel = PairCopula(x, y)
# Try to fit all copula
stockModel.copulaTournament()
# Check gaussian copula parameters for correctness
self.assertAlmostEqual(stockModel.copulaParams[1], 0.73874003, 4)
# Obtain Ktau
kTauFitted = stockModel.copulaModel.kTau()
# Use fitted kTau to specify a new copula
stockModelRefit = Copula("gauss")
# Fit gauss copula param given kTau
fittedParam = stockModelRefit.fitKtau(kTauFitted)[0]
print("Fitted Ktau = %f" % kTauFitted)
print("Expected Theta = %f" % 0.738740)
print("Computed Theta = %f" % fittedParam)
# check result
self.assertAlmostEqual(0.73874003, fittedParam, delta=0.01)
def testBivariateBase(self):
print(
"--------------------- MULTI COPULA FIT TEST --------------------------"
)
# Load matlab data set
stocks = np.loadtxt(dataDir + 'stocks.csv', delimiter=',')
x = stocks[:, 0]
y = stocks[:, 1]
stockModel = PairCopula(x, y)
empTau = stockModel.empKTau() # kendall's tau corr coeff
empSRho = stockModel.empSRho() # spearmans corr coeff
empPRho = stockModel.empPRho() # pearson's corr coeff
print("Emprical kTau, spearmanr, pearsonr: " + str(empTau[0]) + ", " +
str(empSRho[0]) + ", " + str(empPRho[0]))
# Try to fit all copula
stockModel.copulaTournament()
# Ensure that the gaussian copula was chosen as the best fit
self.assertTrue(stockModel.copulaModel.name == "gauss")
self.assertTrue(stockModel.copulaParams[0] == "gauss")
# Check gaussian copula parameters for correctness
self.assertAlmostEqual(stockModel.copulaParams[1], 0.73874003, 4)
def testClaytonRotate(self):
expectedKtaus = {
0: 0.7777777,
1: -0.7777777,
2: 0.7777777,
3: -0.7777777
}
shapeParam = 7.0
for rotation, expectedKtau in iteritems(expectedKtaus):
clayton = Copula("clayton", rotation)
u, v = clayton.sample(10000, *(shapeParam, ))
g = sns.jointplot(u, v, stat_func=kendalltau)
g.savefig("clayton_sample_pdf_" + str(rotation) + ".png")
clayton.fittedParams = (shapeParam, )
c_kTau = clayton.kTau()
# check kTau
self.assertAlmostEqual(c_kTau, expectedKtau, delta=0.001)
# compute rank corr coeff from resampled data
clayton_model = PairCopula(u, v)
clayton_model.copulaTournament()
print(clayton_model.copulaParams)
self.assertTrue("clayton" in clayton_model.copulaModel.name)
# Ensure fitted shape parameter is same as original
self.assertAlmostEqual(shapeParam,
clayton_model.copulaParams[1][0],
delta=0.2)
self.assertEqual(rotation, clayton_model.copulaParams[3])
# Ensure kTau is nearly the same from resampled data
self.assertAlmostEqual(c_kTau,
clayton_model.copulaModel.kTau(),
delta=0.02)
# fit to resampled data
u_model, v_model = clayton_model.copulaModel.sample(10000)
clayton_refit = PairCopula(u_model, v_model)
clayton_refit.copulaTournament()
u_resample, v_resample = clayton_refit.copulaModel.sample(1000)
self.assertAlmostEqual(c_kTau,
clayton_refit.copulaModel.kTau(),
delta=0.05)
# plot resampled data
g_resample = sns.jointplot(u_resample,
v_resample,
stat_func=kendalltau)
g_resample.savefig("clayton_resample_pdf_" + str(rotation) +
".png")
def testFrankRotate(self):
expectedKtaus = {
0: 0.602619667,
1: -0.602619667,
2: 0.602619667,
3: -0.602619667
}
shapeParam = 8.0
for rotation, expectedKtau in iteritems(expectedKtaus):
frank = Copula("frank", rotation)
u, v = frank.sample(10000, *(shapeParam, ))
g = sns.jointplot(u, v, stat_func=kendalltau)
g.savefig("frank_sample_pdf_" + str(rotation) + ".png")
frank.fittedParams = (shapeParam, )
c_kTau = frank.kTau()
# check kTau
self.assertAlmostEqual(c_kTau, expectedKtau, delta=0.001)
# compute rank corr coeff from resampled data
frank_model = PairCopula(u, v)
frank_model.copulaTournament()
print(frank_model.copulaParams)
self.assertTrue("frank" in frank_model.copulaModel.name)
# Ensure refitted shape parameter is same as original
self.assertAlmostEqual(shapeParam,
frank_model.copulaParams[1][0],
delta=0.2)
# Ensure kTau is nearly the same from resampled data
self.assertAlmostEqual(c_kTau,
frank_model.copulaModel.kTau(),
delta=0.02)
# fit to resampled data
u_model, v_model = frank_model.copulaModel.sample(10000)
frank_refit = PairCopula(u_model, v_model)
frank_refit.copulaTournament()
u_resample, v_resample = frank_refit.copulaModel.sample(1000)
self.assertAlmostEqual(c_kTau,
frank_refit.copulaModel.kTau(),
delta=0.05)
# plot resampled data
g_resample = sns.jointplot(u_resample,
v_resample,
stat_func=kendalltau)
g_resample.savefig("frank_resample_pdf_" + str(rotation) + ".png")
def testClaytonSample(self):
# 0 deg
clayton00 = Copula("clayton", 0)
u00, v00 = clayton00.sample(10000, *(0.5, ))
clayton00.fittedParams = (0.5, )
c00_kTau = clayton00.kTau()
# check kTau
self.assertAlmostEqual(c00_kTau, 0.2)
# compute rank corr coeff from resampled data
clayton00_model = PairCopula(u00, v00)
clayton00_model.copulaTournament()
# check that clayton copula won since
# we seeded with samples from a clayton df
self.assertTrue("clayton" in clayton00_model.copulaModel.name)
# Ensure kTau is nearly the same from resampled data
kTauDelta = c00_kTau - clayton00_model.copulaModel.kTau()
self.assertTrue(abs(kTauDelta) < 0.01)
# 90 deg
clayton90 = Copula("clayton", 1)
u90, v90 = clayton90.sample(10000, *(0.5, ))
clayton90.fittedParams = (0.5, )
c90_kTau = clayton90.kTau()
self.assertAlmostEqual(c90_kTau, -0.2)
# compute rank corr coeff from resampled data
clayton90_model = PairCopula(u90, v90, family={"clayton": 1})
clayton90_model.copulaTournament()
# check that clayton copula won since
# we seeded with samples from a clayton df
self.assertTrue("clayton" in clayton90_model.copulaModel.name)
self.assertTrue(1 == clayton90_model.copulaModel.rotation)
# Ensure kTau is nearly the same from resampled data
kTauDelta = c90_kTau - clayton90_model.copulaModel.kTau()
self.assertTrue(abs(kTauDelta) < 0.01)
# 180 deg
clayton180 = Copula("clayton", 2)
u180, v180 = clayton180.sample(1000, *(0.5, ))
# 270 deg
clayton270 = Copula("clayton", 3)
u270, v270 = clayton270.sample(1000, *(0.5, ))
def testGumbelRotate(self):
expectedKtaus = {0: 0.87499, 1: -0.87499, 2: 0.87499, 3: -0.87499}
shapeParam = 8.0
for rotation, expectedKtau in iteritems(expectedKtaus):
gumbel = Copula("gumbel", rotation)
u, v = gumbel.sample(10000, *(shapeParam, ))
g = sns.jointplot(u, v, stat_func=kendalltau)
g.savefig("gumbel_sample_pdf_" + str(rotation) + ".png")
gumbel.fittedParams = (shapeParam, )
c_kTau = gumbel.kTau()
# check kTau
self.assertAlmostEqual(c_kTau, expectedKtau, delta=0.001)
# compute rank corr coeff from resampled data
gumbel_model = PairCopula(u, v)
gumbel_model.copulaTournament()
print(gumbel_model.copulaParams)
self.assertTrue("gumbel" in gumbel_model.copulaModel.name)
# Ensure fitted shape parameter is same as original
self.assertAlmostEqual(shapeParam,
gumbel_model.copulaParams[1][0],
delta=0.2)
self.assertEqual(rotation, gumbel_model.copulaParams[3])
# Ensure kTau is nearly the same from resampled data
self.assertAlmostEqual(c_kTau,
gumbel_model.copulaModel.kTau(),
delta=0.02)
# fit to resampled data
u_model, v_model = gumbel_model.copulaModel.sample(10000)
gumbel_refit = PairCopula(u_model, v_model)
gumbel_refit.copulaTournament()
u_resample, v_resample = gumbel_refit.copulaModel.sample(1000)
self.assertAlmostEqual(c_kTau,
gumbel_refit.copulaModel.kTau(),
delta=0.05)
# plot resampled data
g_resample = sns.jointplot(u_resample,
v_resample,
stat_func=kendalltau)
g_resample.savefig("gumbel_resample_pdf_" + str(rotation) + ".png")
def testGaussRotate(self):
shapes = {0: 0.7777777, 1: -0.7777777, 2: 0.7777777, 3: -0.7777777}
for rotation, shapeParam in iteritems(shapes):
gauss = Copula("gauss", 0)
u, v = gauss.sample(10000, *(shapeParam, ))
g = sns.jointplot(u, v, stat_func=kendalltau)
g.savefig("gauss_sample_pdf_" + str(rotation) + ".png")
gauss.fittedParams = (shapeParam, )
c_kTau = gauss.kTau()
# compute rank corr coeff from resampled data
gauss_model = PairCopula(u, v)
gauss_model.copulaTournament()
print(gauss_model.copulaParams)
self.assertTrue("gauss" in gauss_model.copulaModel.name)
# Ensure fitted shape parameter is same as original
self.assertAlmostEqual(shapeParam,
gauss_model.copulaParams[1][0],
delta=0.2)
# Ensure kTau is nearly the same from resampled data
self.assertAlmostEqual(c_kTau,
gauss_model.copulaModel.kTau(),
delta=0.02)
# fit to resampled data
u_model, v_model = gauss_model.copulaModel.sample(10000)
gauss_refit = PairCopula(u_model, v_model)
gauss_refit.copulaTournament()
u_resample, v_resample = gauss_refit.copulaModel.sample(1000)
self.assertAlmostEqual(c_kTau,
gauss_refit.copulaModel.kTau(),
delta=0.05)
self.assertAlmostEqual(shapeParam,
gauss_refit.copulaParams[1][0],
delta=0.2)
# plot resampled data
g_resample = sns.jointplot(u_resample,
v_resample,
stat_func=kendalltau)
g_resample.savefig("gauss_resample_pdf_" + str(rotation) + ".png")
def testFrankSample(self):
# 0 deg
frank00 = Copula("frank", 0)
u00, v00 = frank00.sample(30000, *(8.0, ))
frank00.fittedParams = (8.0, )
c00_kTau = frank00.kTau()
# check kTau
print(c00_kTau)
self.assertAlmostEqual(c00_kTau, 0.602619667, 6)
# compute rank corr coeff from resampled data
frank00_model = PairCopula(u00, v00, family={"frank": 0})
frank00_model.copulaTournament()
print(frank00_model.copulaParams)
# check that frank copula won since
# we seeded with samples from a frank df
self.assertTrue("frank" in frank00_model.copulaModel.name)
# Ensure kTau is nearly the same from resampled data
kTauDelta = c00_kTau - frank00_model.copulaModel.kTau()
self.assertTrue(abs(kTauDelta) < 0.01)
self.assertAlmostEqual(c00_kTau, frank00_model.copulaModel.kTau(), 2)
# 90 deg
frank90 = Copula("frank", 1)
u90, v90 = frank90.sample(30000, *(8.0, ))
frank90.fittedParams = (8.0, )
c90_kTau = frank90.kTau()
self.assertAlmostEqual(c90_kTau, -0.602619667, 6)
# compute rank corr coeff from resampled data
frank90_model = PairCopula(u90, v90, family={"frank": 1})
frank90_model.copulaTournament()
print(frank90_model.copulaParams)
# check that frank copula won since
# we seeded with samples from a frank df
self.assertTrue("frank" in frank90_model.copulaModel.name)
# Ensure kTau is nearly the same from resampled data
kTauDelta = c90_kTau - frank90_model.copulaModel.kTau()
self.assertTrue(abs(kTauDelta) < 0.01)
self.assertAlmostEqual(c90_kTau, frank90_model.copulaModel.kTau(), 2)
def testGumbelSample(self):
# TODO: TEST FAILS FOR SMALL GUMBEL PARAMETER VALUES
# 0 deg
gumbel00 = Copula("gumbel", 0)
u00, v00 = gumbel00.sample(10000, *(8.0, ))
gumbel00.fittedParams = (8.0, )
c00_kTau = gumbel00.kTau()
# check kTau
self.assertAlmostEqual(c00_kTau, 0.8749999999999, 6)
# compute rank corr coeff from resampled data
gumbel00_model = PairCopula(u00, v00, family={"gumbel": 0})
gumbel00_model.copulaTournament()
print(gumbel00_model.copulaParams)
# check that gumbel copula won since
# we seeded with samples from a gumbel df
self.assertTrue("gumbel" in gumbel00_model.copulaModel.name)
# Ensure kTau is nearly the same from resampled data
kTauDelta = c00_kTau - gumbel00_model.copulaModel.kTau()
self.assertTrue(abs(kTauDelta) < 0.01)
self.assertAlmostEqual(c00_kTau, gumbel00_model.copulaModel.kTau(), 2)
# 90 deg
gumbel90 = Copula("gumbel", 1)
u90, v90 = gumbel90.sample(10000, *(8.0, ))
gumbel90.fittedParams = (8.0, )
c90_kTau = gumbel90.kTau()
self.assertAlmostEqual(c90_kTau, -0.87499999999, 6)
# compute rank corr coeff from resampled data
gumbel90_model = PairCopula(u90, v90, family={"gumbel": 1})
gumbel90_model.copulaTournament()
print(gumbel90_model.copulaParams)
# check that gumbel copula won since
# we seeded with samples from a gumbel df
self.assertTrue("gumbel" in gumbel90_model.copulaModel.name)
# Ensure kTau is nearly the same from resampled data
kTauDelta = c90_kTau - gumbel90_model.copulaModel.kTau()
self.assertTrue(abs(kTauDelta) < 0.04)
def testGaussFrozen(self):
# Load matlab data set
stocks = np.loadtxt(dataDir + 'stocks.csv', delimiter=',')
x = stocks[:, 0]
y = stocks[:, 1]
stockModel = PairCopula(x, y)
# Try to fit all copula
stockModel.copulaTournament(verbosity=0)
# Ensure that the gaussian copula was chosen as the best fit
self.assertTrue(stockModel.copulaModel.name == "gauss")
self.assertTrue(stockModel.copulaParams[0] == "gauss")
# Check gaussian copula parameters for correctness
self.assertAlmostEqual(stockModel.copulaParams[1], 0.73874003, 4)
# Eval the frozen model
frzU, frzV = stockModel.copulaModel.sample(30000)
# Eval a model with specified params
setU, setV = stockModel.copulaModel.sample(30000, (0.73874003, ))
# Ensure both frozen model and specified param model produce same result
frzModel = PairCopula(frzU, frzV)
setModel = PairCopula(setU, setV)
frzKtau, fp = frzModel.empKTau()
setKtau, sp = setModel.empKTau()
self.assertAlmostEqual(frzKtau, setKtau, places=2)
self.assertAlmostEqual(fp, sp, places=2)
# Eval a model with different specified params
setU2, setV2 = stockModel.copulaModel.sample(10000, (0.3, ))
setModel2 = PairCopula(setU2, setV2)
setKtau2, sp2 = setModel2.empKTau()
self.assertTrue(setKtau2 != setKtau)
self.assertTrue(abs(setKtau2 - setKtau) > 0.2)