def small_data():
rs = np.random.RandomState([2389280, 238901, 382908031])
mod = ZeroMean(None,
volatility=GARCH(),
distribution=Normal(random_state=rs))
sim = mod.simulate([1e-4, 0.05, 0.90], nobs=1000)
return sim.data
def getvolatility(self):
df = volatility.getyieldrate(self)
vol = 0.0
for i in range(1, len(df)):
vol = vol + df[i] * df[i] / 10000.0
am = ConstantMean(df)
am.volatility = GARCH(1, 0, 1)
am.distribution = Normal()
res = am.fit()
print('vol =' + str(vol))
print(res.summary)
return 0
def test_simulate():
normal = Normal(random_state=np.random.RandomState(0))
gim = ARCHInMean(SP500, volatility=GARCH(), distribution=normal)
res = gim.fit(disp="off")
sim = gim.simulate(res.params, 1000)
assert sim.shape == (1000, 3)
assert "data" in sim
assert "volatility" in sim
assert "errors" in sim
mean = sim.data - sim.errors
vol = mean - res.params.iloc[0]
kappa = res.params.iloc[1]
rescaled_vol = vol / kappa
np.testing.assert_allclose(rescaled_vol, sim.volatility)
with pytest.raises(ValueError, match="initial_value has the wrong shape"):
gim.simulate(res.params, 1000, initial_value=np.array([0.0, 0.0]))
def test_simulate_arx(form):
normal = Normal(random_state=np.random.RandomState(0))
gim = ARCHInMean(
SP500,
constant=False,
lags=2,
volatility=GARCH(),
distribution=normal,
x=X,
form=form,
)
res = gim.fit(disp="off")
sim = gim.simulate(res.params, 1000, x=X.iloc[:1500], initial_value=0.0)
assert sim.shape == (1000, 3)
assert "data" in sim
assert "volatility" in sim
assert "errors" in sim
gim.simulate(res.params, 1000, x=X.iloc[:1500], initial_value=np.zeros(2))
def _get_ARCH_model(self, returns: LogReturnsSeries, vol_process: VolatilityProcess):
am = ConstantMean(returns)
am.volatility = vol_process
am.distribution = Normal()
return am
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
import datetime as dt
import pandas_datareader.data as web
from arch import arch_model
from arch.univariate import ConstantMean, GARCH, Normal
#from arch.univariate import ZeroMean, GARCH, Normal
start = dt.datetime(2000, 1, 1)
end = dt.datetime(2014, 1, 1)
sp500 = web.DataReader('^GSPC', 'yahoo', start=start, end=end)
returns = 100 * sp500['Adj Close'].pct_change().dropna()
am = ConstantMean(returns)
am.volatility = GARCH(1, 0, 1)
am.distribution = Normal()
res = am.fit()
res.summary()
# %%
# import the packages
import numpy as np
from scipy.optimize import minimize
import scipy.stats as stats
import time
# Set up your x values
x = np.linspace(0, 100, num=100)
def bruteforce_ts_model(returns, start_p, start_q, max_p, max_q):
""" This methods bruteforce each possible combination of the ARCH family models. (e.g. ARCH(3), GARCH(3,4), EGARCH(1,3))
Records its score and save it.
Args:
returns (pandas.Series) : Contains the list of all the returns.
start_p (int) : Integer who gives the starting point of the range of p parameter
start_q (int) : Integer who gives the starting point of the range of q parameter
max_p (int) : Integer who gives the ending point of the range of p parameter
max_q (int) : Integer who gives the ending point of the range of q parameter
Output:
df (pandas.DataFrame) : Dataframe containing all the models and Information criteria
"""
# We define our list of models to test
model_types = ['ARCH', 'GARCH', 'EGARCH']
# We define our list of distribution to test
dist_types = ['normal', 'studentst', 'skewstudent']
# We define our list
AIC_score = []
BIC_score = []
LL_score = []
model_list = []
mean_model_list = []
dist_list = []
q_list = []
p_list = []
# We compute the total number of models
max_iter = max_p * max_q * len(model_types) * len(dist_types)
current_iter = 0
# For each model we have
for model in model_types:
# For each parameter p
for each_p in range(start_p, max_p):
# For each parameter q
for each_q in range(start_q, max_q):
# For each distribution type
for dist in dist_types:
# We define our mean model
am = ConstantMean(returns)
# We define our constant mean
mean_model_list.append('ConstantMean')
# Our distribution
if dist is 'normal':
am.distribution = Normal()
elif dist is 'studentst':
am.distribution = StudentsT()
elif dist is 'skewstudent':
am.distribution = SkewStudent()
# Our volatility process
if model is "ARCH":
am.volatility = ARCH(p=each_p)
elif model is "GARCH":
am.volatility = GARCH(p=each_p, q=each_q)
elif model is "EGARCH":
am.volatility = EGARCH(p=each_p, q=each_q)
# We fit our model
res = am.fit(update_freq=5, disp='off')
# We record our model and distribution
model_list.append(model)
dist_list.append(dist)
# We record the scores
AIC_score.append(res.aic)
BIC_score.append(res.bic)
LL_score.append(res.loglikelihood)
# We record the parameters
q_list.append(each_q)
p_list.append(each_p)
# We log the information about each computed model
print(
f"it: {current_iter}/{max_iter}\tmodel:{model}\tdist:{dist[:6]}\tp:{each_p}\tq:{each_q}\tAIC_score:{round(res.aic,2)}\tBIC_score:{round(res.bic,2)}\tLog Likelihood:{round(res.loglikelihood,2)}"
)
# If a model has been added then we add one to the iterator
current_iter += 1
# For each computed model
print("=" * 20, f"{model} finished", "=" * 20)
# We combine everything to a dataframe
df = pd.DataFrame({
'volatility_model': model_list,
'mean_model': mean_model_list,
'dist': dist_list,
'p': p_list,
'q': q_list,
'AIC_score': AIC_score,
'BIC_score': BIC_score,
'LL_score': LL_score
})
return df
forecast variance(10 days): 3.6425481901571626
forecast VaR: 4.439942146600405
forecast ES: 5.086684187983292
'''
# NGARCH(1,1)
omega = 1.5E-6 * scale**2
alpha = 0.05
beta = 0.8
theta = 1.25
ngarch = ZeroMean(returns['Close'])
ngarch11 = NGARCH11(np.array([omega, alpha, beta, theta]))
ngarch.volatility = ngarch11
ngarch.distribution = Normal()
rst = ngarch.fit()
print(rst)
rst.plot(annualize='D')
print(
ngarch11.is_valid(rst.params['alpha'], rst.params['beta'],
rst.params['theta']))
rs = np.random.RandomState(1234)
forecast_variance_10days = rst.forecast(horizon=10,
method='simulation',
rng=lambda x: rs.normal(size=x),
simulations=1000).variance.iloc[-1, :]