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DCCEGARCH.py
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from __future__ import annotations
import numpy as np
import CARCHINMean
from scipy.stats import norm
from scipy.stats import multivariate_normal
from arch.univariate import EGARCH
def vecl(matrix):
lower_matrix = np.tril(matrix, k=-1)
array_with_zero = np.matrix(lower_matrix).A1
array_without_zero = array_with_zero[array_with_zero != 0]
return array_without_zero
def garch_to_u(res):
cv = res.conditional_volatility
std_res = res.std_resid
resid = res.resid
udata = norm.cdf(std_res)
return udata, cv, resid.values
def loglike_norm_dcc_copula(theta, udata, Dt_mat, resid_list):
N, T = np.shape(udata)
llf = np.zeros((T, 1))
llf = llf
trdata = np.array(norm.ppf(udata).T, ndmin=2)
Rt, veclRt, Qt, Qbar = dcceq(theta, trdata, Dt_mat, resid_list)
for i in range(0, T):
llf[i] = -0.5 * np.log(np.linalg.det(Rt[:, :, i]))
llf[i] = llf[i] - 0.5 * np.matmul(np.matmul(trdata[i, :], (np.linalg.inv(Rt[:, :, i]) - np.eye(N))),
trdata[i, :].T)
llf = np.sum(llf)
return -llf
def dcceq(theta, trdata, Dt_mat, resid_list):
T, N = np.shape(trdata)
a, b = theta
if min(a, b) < 0 or max(a, b) > 1 or a + b > .999999:
a = .9999 - b
eps = np.zeros((N, T))
for i in range(T):
eps[:, i] = np.matmul(np.diag(1 / np.diag(Dt_mat[:, :, i])), resid_list[:, i])
Qbar = np.cov(eps)
Qt = np.zeros((N, N, T))
Qt[:, :, 0] = Qbar
Rt = np.zeros((N, N, T))
veclRt = np.zeros((T, int(N * (N - 1) / 2)))
Qstar_inv = np.diag(1.0 / np.sqrt(np.diag(Qt[:, :, 0])))
Rt[:, :, 0] = Qstar_inv @ Qt[:, :, 0] @ Qstar_inv
for j in range(1, T):
Qt[:, :, j] = Qbar * (1 - a - b)
Qt[:, :, j] = Qt[:, :, j] + a * np.outer(eps[:, j - 1], eps[:, j - 1])
Qt[:, :, j] = Qt[:, :, j] + b * Qt[:, :, j - 1]
Qstar_inv = np.diag(1.0 / np.sqrt(np.diag(Qt[:, :, j])))
Rt[:, :, j] = Qstar_inv @ Qt[:, :, j] @ Qstar_inv
for j in range(0, T):
veclRt[j, :] = vecl(Rt[:, :, j].T)
return Rt, veclRt, Qt, Qbar
def run_garch_on_return(rets, udata_list, model_parameters, Dt_mat, resid_list, arch_mean_type,
model="EGARCH_with_vol_in_mean"):
i = 0
short_name = None
for x in rets:
tmp = rets[x].dropna()
if model == "EGARCH_with_vol_in_mean":
egim = CARCHINMean.CustomARCHInMean(tmp, form='var', volatility=EGARCH(p=1, o=1, q=1))
result = egim.fit(arch_mean_type=arch_mean_type, update_freq=4, disp='off')
short_name = '_'.join(x.split())
model_parameters[short_name] = result
udata, Dt, resid = garch_to_u(model_parameters[short_name])
udata_list.append(udata)
Dt_mat[i, i, :] = Dt
resid_list[i, :] = resid
i += 1
return udata_list, Dt_mat, model_parameters
# DCC_EGARCH class
class DCC_EGARCH:
def __init__(self, trdata, dccparams, a, b, sims, nburn=2000):
self.params = dccparams
self.a = a
self.b = b
self.burn = nburn
self.sims = nburn + sims
self.N = dccparams.shape[0]
self.trdata = trdata
self.volatility = None
self.unierrors = None
# Simulate univariate EGARCH(1,1) processes
def simulate_egarch(self):
variance_uni = np.empty([self.sims, self.N])
uniret = np.empty([self.sims, self.N])
unierrors = np.empty([self.sims, self.N])
variance_uni[0, :] = np.exp(self.params[:, 2] / (1 - self.params[:, 5]))
zt = multivariate_normal.rvs(mean=np.zeros(self.N), cov=np.eye(self.N), size=self.sims)
unierrors[0, :] = np.sqrt(variance_uni[0, :]) * zt[0, :]
uniret[0, :] = self.params[:, 0] + self.params[:, 1] * variance_uni[0, :]
for t in range(1, self.sims):
variance_uni[t, :] = np.exp(
self.params[:, 2] + self.params[:, 3] * (np.abs(zt[t - 1, :]) - np.sqrt(2 / np.pi))
+ self.params[:, 4] * zt[t - 1, :] + self.params[:, 5] * np.log(variance_uni[t - 1, :]))
unierrors[t, :] = np.sqrt(variance_uni[t, :]) * zt[t, :]
uniret[t, :] = self.params[:, 0] + self.params[:, 1] * variance_uni[t, :] + unierrors[t, :]
self.volatility = np.sqrt(variance_uni)
self.unierrors = unierrors
def simulate_dcc2(self):
std_err = np.empty([self.sims, self.N]) # matrix storing standard errors
voltry = np.empty([self.sims, self.N])
R = np.zeros((self.N, self.N, self.sims))
aQ = np.zeros((self.N, self.N, self.sims))
DCC_COVAR = np.zeros((self.N, self.N, self.sims))
DCC_returns = np.zeros((self.sims, self.N))
self.simulate_egarch()
variance = self.volatility ** 2
mQ = np.cov(self.trdata.T)
aQ[:, :, 0] = mQ
Qstar_inv = np.diag(1.0 / np.sqrt(np.diag(aQ[:, :, 0])))
R[:, :, 0] = Qstar_inv @ aQ[:, :, 0] @ Qstar_inv
D = np.diag(np.sqrt(variance[0, :]))
H = D @ R[:, :, 0] @ D
DCC_COVAR[:, :, 0] = H
at_lag = multivariate_normal.rvs(mean=np.zeros(self.N), cov=DCC_COVAR[:, :, 0])
DCC_returns[0, :] = self.params[:, 0] + self.params[:, 1] * np.diag(H) + at_lag
# Boucle principale pour la mise à jour de Q
for t in range(1, self.sims):
std_err[t - 1, :] = np.diag(1.0 / np.diag(D)) @ at_lag
aQ[:, :, t] = mQ * (1 - self.a - self.b) + self.a * np.outer(std_err[t - 1, :],
std_err[t - 1, :]) + self.b * aQ[:, :, t - 1]
Qstar_inv = np.diag(1.0 / np.sqrt(np.diag(aQ[:, :, t])))
R[:, :, t] = Qstar_inv @ aQ[:, :, t] @ Qstar_inv
D = np.diag(np.sqrt(variance[t, :]))
H = D @ R[:, :, t] @ D
DCC_COVAR[:, :, t] = H
at_lag = multivariate_normal.rvs(mean=np.zeros(self.N), cov=DCC_COVAR[:, :, t])
DCC_returns[t, :] = self.params[:, 0] + self.params[:, 1] * np.diag(H) + at_lag
out = {
"Rt": R[:, :, self.burn:], # Corrélations dynamiques
"volatility": np.sqrt(variance[self.burn:, :]), # Volatilités univariées
"voltry": voltry[self.burn:, :], # Volatilités univariées
"Ht": DCC_COVAR[:, :, self.burn:], # Matrices de covariance
"DCC_returns": DCC_returns[self.burn:, :], # Rendements simulés
"mQ": mQ,
"aQ": aQ[:, :, self.burn:]
}
return out