def get_HARCH(process, iters, params):
# HARCH
if params == None:
params = {'LAGS': [1, 5, 17], 'INIT': [1], 'PARAMS': [0.2, 0.05, 0.01]}
metadata = {"NAME": process, "number_of_iterations": iters}
metadata.update(params)
model = HARCH(lags=params['LAGS'])
param_vect = params['INIT'] + params['PARAMS']
y = model.simulate(nobs=iters,
burn=1000,
parameters=param_vect,
rng=np.random.standard_normal)
true_var = y[1] * sps.norm.ppf(0.01)
y = y[0]
data = pd.DataFrame(data={'Returns': y, 'True_VAR_0.01': true_var})
return metadata, data
SP500 = 100 * sp500.load()["Adj Close"].pct_change().dropna()
MEAN_MODELS = [
HARX(SP500, lags=[1, 5]),
ARX(SP500, lags=2),
ConstantMean(SP500),
ZeroMean(SP500),
]
VOLATILITIES = [
ConstantVariance(),
GARCH(),
FIGARCH(),
EWMAVariance(lam=0.94),
MIDASHyperbolic(),
HARCH(lags=[1, 5, 22]),
RiskMetrics2006(),
APARCH(),
EGARCH(),
]
MODEL_SPECS = list(product(MEAN_MODELS, VOLATILITIES))
IDS = [
f"{str(mean).split('(')[0]}-{str(vol).split('(')[0]}"
for mean, vol in MODEL_SPECS
]
@pytest.fixture(params=MODEL_SPECS, ids=IDS)
def model_spec(request):
mean, vol = request.param
def return_sampler_garch(
N_train: int,
mean_process: str = "Constant",
lags_mean_process: int = None,
vol_process: str = "GARCH",
distr_noise: str = "normal",
seed: int = None,
seed_param: int = None,
p_arg: list = None,
) -> Tuple[np.ndarray, pd.Series]:
# https://stats.stackexchange.com/questions/61824/how-to-interpret-garch-parameters
# https://arch.readthedocs.io/en/latest/univariate/introduction.html
# https://arch.readthedocs.io/en/latest/univariate/volatility.html
# https://github.com/bashtage/arch/blob/master/arch/univariate/volatility.py
"""
Generates financial returns driven by mean-reverting factors.
Parameters
----------
N_train: int
Length of the experiment
mean_process: str
Mean process for the returns. It can be 'Constant' or 'AR'
lags_mean_process: int
Order of autoregressive lag if mean_process is AR
vol_process: str
Volatility process for the returns. It can be 'GARCH', 'EGARCH', 'TGARCH',
'ARCH', 'HARCH', 'FIGARCH' or 'Constant'. Note that different volatility
processes requires different parameter, which are hard coded. If you want to
pass them explicitly, use p_arg.
distr_noise: str
Distribution for the unpredictable component of the returns. It can be
'normal', 'studt', 'skewstud' or 'ged'. Note that different distributions
requires different parameter, which are hard coded. If you want to
pass them explicitly, use p_arg.
seed: int
Seed for experiment reproducibility
seed_param: int
Seed for drawing randomly the parameters needed for the simulation. The
ranges provided are obtained as average lower and upper bounds of several
GARCH-type model fitting on real financial time-series.
p_arg: pd.Series
Pandas series of parameters that you want to pass explicitly.
They need to be passed in the right order. Check documentation of the
arch python package (https://arch.readthedocs.io/en/latest/index.html) for more details.
Returns
-------
simulations['data'].values: np.ndarray
Simulated series of returns
p: pd.Series
Series of parameters used for simulation
"""
names = []
vals = []
if seed_param is None:
seed_param = seed
rng = np.random.RandomState(seed_param)
# choose mean process
if mean_process == "Constant":
model = ConstantMean(None)
names.append("const")
if seed_param:
vals.append(rng.uniform(0.01, 0.09))
else:
vals.append(0.0)
elif mean_process == "AR":
model = ARX(None, lags=lags_mean_process)
names.append("const")
vals.append(0.0)
if seed_param:
for i in range(lags_mean_process):
names.append("lag{}".format(i))
vals.append(rng.uniform(-0.09, 0.09))
else:
for i in range(lags_mean_process):
names.append("lag{}".format(i))
vals.append(0.9)
else:
return print("This mean process doesn't exist or it's not available.")
sys.exit()
# choose volatility process
if vol_process == "GARCH":
model.volatility = GARCH(p=1, q=1)
names.extend(["omega", "alpha", "beta"])
if seed_param:
om = rng.uniform(0.03, 0.1)
alph = rng.uniform(0.05, 0.1)
b = rng.uniform(0.86, 0.92)
garch_p = np.array([om, alph, b]) / (np.array([om, alph, b]).sum())
else:
om = 0.01
alph = 0.05
b = 0.94
garch_p = np.array([om, alph, b])
vals.extend(list(garch_p))
elif vol_process == "ARCH":
model.volatility = GARCH(p=1, q=0)
names.extend(["omega", "alpha"])
if seed_param:
om = rng.uniform(1.4, 4.0)
alph = rng.uniform(0.1, 0.6)
else:
om = 0.01
alph = 0.4
garch_p = np.array([om, alph])
vals.extend(list(garch_p))
elif vol_process == "HARCH":
model.volatility = HARCH(lags=[1, 5, 22])
names.extend(["omega", "alpha[1]", "alpha[5]", "alpha[22]"])
if seed_param:
om = rng.uniform(1.2, 0.5)
alph1 = rng.uniform(0.01, 0.1)
alph5 = rng.uniform(0.05, 0.3)
alph22 = rng.uniform(0.4, 0.7)
else:
om = 0.01
alph1 = 0.05
alph5 = 0.15
alph22 = 0.5
garch_p = np.array([om, alph1, alph5, alph22])
vals.extend(list(garch_p))
elif vol_process == "FIGARCH":
model.volatility = FIGARCH(p=1, q=1)
names.extend(["omega", "phi", "d", "beta"])
if seed_param:
om = rng.uniform(0.05, 0.03)
phi = rng.uniform(0.1, 0.35)
d = rng.uniform(0.3, 0.5)
beta = rng.uniform(0.4, 0.7)
else:
om = 0.01
phi = 0.2
d = 0.2
beta = 0.55
garch_p = np.array([om, phi, d, beta])
vals.extend(list(garch_p))
elif vol_process == "TGARCH":
model.volatility = GARCH(p=1, o=1, q=1)
names.extend(["omega", "alpha", "gamma", "beta"])
if seed_param:
om = rng.uniform(0.02, 0.15)
alph = rng.uniform(0.01, 0.07)
gamma = rng.uniform(0.03, 0.1)
b = rng.uniform(0.88, 0.94)
else:
om = 0.01
alph = 0.05
gamma = 0.04
b = 0.90
garch_p = np.array([om, alph, gamma, b])
vals.extend(list(garch_p))
elif vol_process == "EGARCH":
model.volatility = EGARCH(p=1, o=1, q=1)
names.extend(["omega", "alpha", "gamma", "beta"])
if seed_param:
om = rng.uniform(0.01, 0.03)
alph = rng.uniform(0.06, 0.17)
gamma = rng.uniform(-0.05, -0.02)
b = rng.uniform(0.97, 0.99)
garch_p = np.array([om, alph, gamma, b]) / (np.array(
[om, alph, gamma, b]).sum())
else:
om = 0.01
alph = 0.05
gamma = -0.02
b = 0.94
garch_p = np.array([om, alph, gamma, b])
vals.extend(list(garch_p))
elif vol_process == "Constant":
model.volatility = ConstantVariance()
names.append("sigma_const")
vals.append(rng.uniform(0.02, 0.05))
else:
print("This volatility process doesn't exist or it's not available.")
sys.exit()
if distr_noise == "normal":
model.distribution = Normal(np.random.RandomState(seed))
elif distr_noise == "studt":
model.distribution = StudentsT(np.random.RandomState(seed))
names.append("nu")
if seed_param:
vals.append(rng.randint(6.0, 10.0))
else:
vals.append(8.0)
elif distr_noise == "skewstud":
model.distribution = SkewStudent(np.random.RandomState(seed))
names.extend(["nu", "lambda"])
if seed_param:
vals.extend([rng.uniform(6.0, 10.0), rng.uniform(-0.1, 0.1)])
else:
vals.extend([8.0, 0.05])
elif distr_noise == "ged":
model.distribution = GeneralizedError(np.random.RandomState(seed))
names.append("nu")
if seed_param:
vals.append(rng.uniform(1.05, 3.0))
else:
vals.append(2.0)
else:
print("This noise distribution doesn't exist or it's not available.")
sys.exit()
p = pd.Series(data=vals, index=names)
if p_arg:
p = p_arg
simulations = model.simulate(p, N_train) / 100
return simulations["data"].values, p
def model(self):
self.__model.volatility = HARCH(lags=self.__lags)
return self.__model
def __bic_with(self, lag_list):
self.__model.volatility = HARCH(lags=lag_list)
result = self.__model.fit(update_freq=0, disp='off')
return round(result.bic, 4)