def test_conditional_value_at_risk_mc(self):
for mu, sigma, alpha in [(1, 1, 0.05), (0.4, 0.1, 0.02),
(0.1, 2, 0.01)]:
# prepare estimator dummy
mu1 = np.array([mu])
sigma1 = np.identity(n=1) * sigma
est = GaussianDummy(mean=mu1,
cov=sigma1**2,
ndim_x=1,
ndim_y=1,
has_pdf=True)
est.fit(None, None)
CVaR_true = mu - sigma / alpha * norm.pdf(norm.ppf(alpha))
CVaR_est = est.conditional_value_at_risk(x_cond=np.array([[0],
[1]]),
alpha=alpha)
print("CVaR True (%.2f, %.2f):" % (mu, sigma), CVaR_true)
print("CVaR_est (%.2f, %.2f):" % (mu, sigma), CVaR_est)
print("VaR (%.2f, %.2f):" % (mu, sigma),
est.value_at_risk(x_cond=np.array([[0], [1]]), alpha=alpha))
self.assertAlmostEqual(CVaR_est[0], CVaR_true, places=2)
self.assertAlmostEqual(CVaR_est[1], CVaR_true, places=2)
def test_covariance1(self):
# prepare estimator dummy
mu = np.array([-1])
sigma = np.array([[0.1]])
est = GaussianDummy(mean=mu, cov=sigma, ndim_x=2, ndim_y=1)
est.fit(None, None)
cov_est = est.covariance(x_cond=np.array([[0.5, 2]]))
self.assertAlmostEqual(cov_est[0][0][0], sigma[0][0], places=2)
def test_covariance2(self):
# prepare estimator dummy
mu = np.array([0, 1])
sigma = np.array([[1, -0.2], [-0.2, 2]])
est = GaussianDummy(mean=mu,
cov=sigma,
ndim_x=2,
ndim_y=2,
can_sample=False)
est.fit(None, None)
cov_est = est.covariance(x_cond=np.array([[0, 1]]))
self.assertAlmostEqual(cov_est[0][0][0], sigma[0][0], places=2)
self.assertAlmostEqual(cov_est[0][1][0], sigma[1][0], places=2)
def test_std2(self):
# prepare estimator dummy
mu = np.array([14])
sigma = np.array([[0.1]])
est = GaussianDummy(mean=mu,
cov=sigma,
ndim_x=1,
ndim_y=1,
can_sample=False)
est.fit(None, None)
std_est = est.std_(x_cond=np.array([[0.0], [1.0]]))
self.assertAlmostEqual(std_est[0][0]**2, sigma[0][0], places=2)
self.assertAlmostEqual(std_est[1][0]**2, sigma[0][0], places=2)
def test_std1(self):
# prepare estimator dummy
mu = np.array([0, 1])
sigma = np.array([[1, -0.2], [-0.2, 2]])
est = GaussianDummy(mean=mu,
cov=sigma,
ndim_x=2,
ndim_y=2,
can_sample=False)
est.fit(None, None)
std = est.std_(x_cond=np.array([[0, 1]]))
self.assertAlmostEqual(std[0][0], np.sqrt(sigma[0][0]), places=2)
self.assertAlmostEqual(std[0][1], np.sqrt(sigma[1][1]), places=2)
def test_mean_pdf(self):
# prepare estimator dummy
mu = np.array([0, 1])
sigma = np.identity(n=2) * 1
est = GaussianDummy(mean=mu,
cov=sigma,
ndim_x=2,
ndim_y=2,
can_sample=False)
est.fit(None, None)
mean_est = est.mean_(x_cond=np.array([[0, 1]]))
self.assertAlmostEqual(mean_est[0][0], mu[0], places=2)
self.assertAlmostEqual(mean_est[0][1], mu[1], places=2)
def test_mean_std(self):
mu = np.array([0, 1])
sigma = np.array([[1, -0.2], [-0.2, 2]])
est = GaussianDummy(mean=mu,
cov=sigma,
ndim_x=2,
ndim_y=2,
can_sample=False)
est.fit(None, None)
mean_est, std_est = est.mean_std(x_cond=np.array([[0, 1]]))
self.assertAlmostEqual(mean_est[0][0], mu[0], places=2)
self.assertAlmostEqual(mean_est[0][1], mu[1], places=2)
self.assertAlmostEqual(std_est[0][0]**2, sigma[0][0], places=2)
self.assertAlmostEqual(std_est[0][1]**2, sigma[1][1], places=2)
def test_kurtosis1(self):
mu = np.array([-0.001])
sigma = np.array([[0.02]])
est = GaussianDummy(mean=mu,
cov=sigma,
ndim_x=2,
ndim_y=1,
can_sample=False)
est.fit(None, None)
kurt = est._kurtosis_mc(x_cond=np.array([[0, 1]]), n_samples=10**6)
print("Kurtosis sample estimate:", kurt)
self.assertAlmostEqual(kurt[0], 0, places=1)
kurt = est._kurtosis_pdf(x_cond=np.array([[0, 1]]), n_samples=10**6)
print("Kurtosis pdf estimate:", kurt)
self.assertAlmostEqual(kurt[0], 0, places=1)
def test_skewness1(self):
mu = np.array([-0.001])
sigma = np.array([[0.02]])
est = GaussianDummy(mean=mu,
cov=sigma,
ndim_x=2,
ndim_y=1,
can_sample=False)
est.fit(None, None)
skew = est._skewness_mc(x_cond=np.array([[0, 1]]))
print("Skewness sample estimate:", skew)
self.assertAlmostEqual(skew[0], 0, places=1)
skew = est._skewness_pdf(x_cond=np.array([[0, 1]]))
print("Skewness pdf estimate:", skew)
self.assertAlmostEqual(skew[0], 0, places=1)
def test_value_at_risk_cdf(self):
for mu, sigma in [(-2, 0.5), (0.4, 0.01), (22, 3)]:
# prepare estimator dummy
mu1 = np.array([mu])
sigma1 = np.identity(n=1) * sigma
est = GaussianDummy(mean=mu1,
cov=sigma1**2,
ndim_x=1,
ndim_y=1,
has_cdf=True)
est.fit(None, None)
alpha = 0.05
VaR_est = est.value_at_risk(x_cond=np.array([[0], [1]]),
alpha=alpha)
VaR_true = norm.ppf(alpha, loc=mu, scale=sigma)
self.assertAlmostEqual(VaR_est[0], VaR_true, places=2)
self.assertAlmostEqual(VaR_est[1], VaR_true, places=2)
def test_conditional_value_at_risk_sample(self):
# prepare estimator dummy
for mu, sigma in [(-6, 0.25), (0.4, 0.1), (22, 3)]:
mu1 = np.array([mu])
sigma1 = np.identity(n=1) * sigma
est = GaussianDummy(mean=mu1,
cov=sigma1**2,
ndim_x=1,
ndim_y=1,
has_pdf=False)
est.fit(None, None)
alpha = 0.02
CVaR_true = mu - sigma / alpha * norm.pdf(norm.ppf(alpha))
CVaR_est = est.conditional_value_at_risk(x_cond=np.array([[0],
[1]]),
alpha=alpha,
n_samples=2 * 10**6)
self.assertAlmostEqual(CVaR_est[0], CVaR_true, places=2)
self.assertAlmostEqual(CVaR_est[1], CVaR_true, places=2)