def test_x_reformat_1var(exog_format):
# (10,)
# (1,10)
# (n, 10)
# (1,1,10)
# (1,n,10)
# {"x1"} : (10,)
# {"x1"} : (1,10)
# {"x1"} : (n,10)
exog, ref = exog_format
if exog is None:
return
if isinstance(exog, dict):
nexog = len(exog)
else:
if np.ndim(exog) == 3:
nexog = exog.shape[0]
else:
nexog = 1
cols = [f"x{i}" for i in range(1, nexog + 1)]
rng = RandomState(12345)
x = pd.DataFrame(rng.standard_normal((SP500.shape[0], nexog)),
columns=cols,
index=SP500.index)
mod = ARX(SP500, lags=1, x=x)
res = mod.fit()
fcasts = res.forecast(horizon=10, x=exog, reindex=False)
ref = res.forecast(horizon=10, x=ref, reindex=False)
assert_allclose(fcasts.mean, ref.mean)
def run_garch_simple(y, mean_model, vol_model, split_date, x=None, verbose=False):
# specify mean model
if mean_model == "CONST":
ls = ConstantMean(y)
elif mean_model == 'LS':
ls = LS(y=y, x=x)
elif mean_model == 'ARX':
ls = ARX(y=y, lags=1)
else:
print("Misspecified mean model name. Please choose between CONST, LS, ARX.")
# specify volatility model
if vol_model == "GARCH":
ls.volatility = GARCH(p=1, q=1)
elif vol_model == "EGARCH":
ls.volatility = EGARCH(p=1, o=1, q=1)
elif vol_model == "EWMA":
ls.volatility = EWMAVariance(lam=None)
else:
print("Misspecified volatility process name. Please choose between GARCH, EGARCH, EWMA.")
res = ls.fit(disp='off', last_obs=split_date)
if verbose:
display(Markdown('#### <br> <br> GARCH model results'))
print(res.summary())
return res
def get_disaster_factors(innovation_method, agg_freq="mon", resample=True):
r'''
Function to get various disaster risk factors and their innovations.
Args:
innovation_method: String for how to compute innovations in disaster
risk factors.
'AR' uses an AR1 model
'fd' uses first-differences
agg_freq: can be either "mon" or "week"
Returns:
df: Dataframe where index is date and columns are various disaster
risk factors
df_innov: Dataframe containing innovations to disaster risk factors
'''
if agg_freq == "mon":
agg_freq = "date_mon"
elif agg_freq == "week":
agg_freq = "date_week"
else:
raise ValueError("agg_freq should be either 'mon' or 'week'")
# == Check inputs == #
if innovation_method not in ['AR', 'fd']:
raise ValueError("innovation_method must be either 'AR' or 'fd'")
# == Read in raw data == #
raw_f = pd.read_csv("estimated_data/disaster_risk_measures/" +\
"disaster_risk_measures.csv")
raw_f['date'] = pd.to_datetime(raw_f['date'])
raw_f = raw_f[raw_f.agg_freq == agg_freq]
# raw_f = raw_f[raw_f.variable.isin(["D_clamp", "rn_prob_5", "rn_prob_20", "rn_prob_80"]) &
# raw_f.maturity.isin(["level", "30", "180"])]
raw_f = raw_f[raw_f.variable.isin(["D_clamp"])
& raw_f.maturity.isin(["level"]) & (raw_f.level == "Ind")]
# == Create variable names == #
raw_f['name'] = raw_f['level'] + '_' + raw_f['variable'] +\
'_' + raw_f['maturity'].astype(str)
# == Create pivot table, then resample to end of month == #
pdf = raw_f.pivot_table(index='date', columns='name', values='value')
if resample:
pdf = pdf.resample('M').last()
# == Compute innovations in each factor == #
if innovation_method == 'fd':
df = pdf.diff()
elif innovation_method == 'AR':
df = pd.DataFrame(index=pdf.index, columns=pdf.columns)
for col in df.columns:
ar = ARX(pdf[col], lags=[1]).fit()
df.loc[ar.resid.index, col] = ar.resid.values
df = df.astype(float)
return pdf, df
def test_x_exceptions():
res = ARX(SP500, lags=1).fit(disp="off")
with pytest.raises(TypeError, match="x is not None but"):
res.forecast(reindex=False, x=SP500)
x = SP500.copy()
x[:] = np.random.standard_normal(SP500.shape)
x.name = "Exog"
res = ARX(SP500, lags=1, x=x).fit(disp="off")
with pytest.raises(TypeError, match="x is None but the model"):
res.forecast(reindex=False)
res = ARX(SP500, lags=1, x=x).fit(disp="off")
with pytest.raises(ValueError, match="x must have the same"):
res.forecast(reindex=False, x={})
with pytest.raises(ValueError, match="x must have the same"):
res.forecast(reindex=False, x={"x0": x, "x1": x})
with pytest.raises(KeyError, match="The keys of x must exactly"):
res.forecast(reindex=False, x={"z": x})
with pytest.raises(ValueError,
match="The arrays contained in the dictionary"):
_x = np.asarray(x).reshape((1, x.shape[0], 1))
res.forecast(reindex=False, x={"Exog": _x})
x2 = pd.concat([x, x], 1)
x2.columns = ["x0", "x1"]
x2.iloc[:, 1] = np.random.standard_normal(SP500.shape)
res = ARX(SP500, lags=1, x=x2).fit(disp="off")
with pytest.raises(ValueError, match="The shapes of the arrays contained"):
res.forecast(reindex=False,
x={
"x0": x2.iloc[:, 0],
"x1": x2.iloc[10:, 1:]
})
with pytest.raises(ValueError, match="1- and 2-dimensional x values"):
res.forecast(reindex=False, x=x2)
with pytest.raises(ValueError, match="The leading dimension of x"):
_x2 = np.asarray(x2)
_x2 = _x2.reshape((1, -1, 2))
res.forecast(reindex=False, x=_x2)
with pytest.raises(ValueError, match="The number of values passed"):
res.forecast(reindex=False, x=np.empty((2, SP500.shape[0], 3)))
with pytest.raises(ValueError,
match="The shape of x does not satisfy the"):
res.forecast(reindex=False, x=np.empty((2, SP500.shape[0] // 2, 1)))
def main(ticker1, ticker2):
df = pd.read_csv("./Data/close.csv", dtype={"date": str})
df2 = np.log(df.loc[:, [ticker1, ticker2]]).diff().dropna()
x = df2[ticker1].values
y = df2[ticker2].values
A = np.vstack((np.ones_like(x), x)).T
b = np.linalg.inv(A.T.dot(A)).dot(A.T).dot(y)
resid = y - A.dot(b)
resid_se = pd.Series(resid)
std2_se = resid_se.rolling(
window=100,
).apply(lambda x: sqrt(sum(np.diff(x)**2) / (len(x) - 1)))
mean_se = resid_se.rolling(
window=100,
).mean()
'''
s_score = (pd.Series(resid_se) - mean_se) / std2_se
'''
ar = ARX(resid_se, volatility=EGARCH(2, 0, 2))
ar.distribution = SkewStudent()
res = ar.fit()
s_score = pd.Series(resid)
arg_lst = [
(s_score, resid_se, i / 100.0, j / 100.0, k / 100.0, l / 100.0, m / 100.0, n / 100.0) for i in xrange(15, 35, 5) for j in xrange(i + 1, 49, 5) for k in xrange(j + 1, 50, 5) for l in xrange(85, 65, -5) for m in xrange(l - 1, 51, -5) for n in xrange(m - 1, 50, -5)
]
pool = mp.Pool(6)
result = pool.map(back_test_sharp, arg_lst)
pool.close()
pool.join()
with open("./pkl/EG_result_lst_{}_{}_sharp".format(ticker1, ticker2), "wb") as fp:
cp.dump(result, fp)
x_mean = x.mean()
y_mean = y.mean()
pearson = (x - x_mean).dot(y - y_mean) / sqrt(sum((x - x_mean)**2)) / sqrt(sum((y - y_mean)**2))
result.sort(key=lambda x: x[0], reverse=True)
best = result[0]
res = back_test((s_score, resid_se, best[1], best[2], best[3], best[4], best[5], best[6]))
fig = plt.figure(figsize=(20, 10))
plt.plot(res[0])
plt.savefig("./Pics/net_value/EG_{}_{}.png".format(ticker1, ticker2))
del fig
return pd.Series(res[0]).to_csv("./xlsx/EG_{}_{}_{}_{}_{}_{}_{}_{}_{}.csv".format(ticker1, ticker2, pearson, best[1], best[2], best[3], best[4], best[5], best[6]))
def estimate_qar(y, p=1, q=1, disp=1):
"""
Estimates a QAR(p, q) on data y.
disp
Returns statsmodels.fitted object.
"""
lags = p
qarpq = QAR(y, p=lags, q=1)
am = ARX(y, lags=lags, constant=True)
first_stage = am.fit()
params = np.r_[first_stage.params[:-1], 100 * np.zeros(lags),
100 * np.zeros(qarpq.q),
1 * np.sqrt(np.abs(first_stage.params[-1]))]
#]
results = qarpq.fit(maxiter=50000, start_params=params, disp=disp)
return results
HARX,
ConstantMean,
ConstantVariance,
EWMAVariance,
MIDASHyperbolic,
RiskMetrics2006,
ZeroMean,
arch_model,
)
from arch.univariate.mean import _ar_forecast, _ar_to_impulse
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(),
]
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
print(model.summary())
#5.
cny = web.DataReader('CNY=X', 'yahoo', dt.datetime(2015, 1, 1),
dt.datetime(2015, 12, 31))
ret = (cny.Close - cny.Close.shift(1)) / cny.Close.shift(1)
ret = ret.dropna()
cny.Close.plot()
ret.plot()
plot_acf(ret, lags=20)
plot_pacf(ret, lags=20)
LjungBox = stattools.q_stat(stattools.acf(ret)[1:13], len(ret))
LjungBox[1][-1]
(ret**2).plot()
plot_acf(ret**2, lags=20)
plot_pacf(ret**2, lags=20)
LjungBox = stattools.q_stat(stattools.acf(ret**2)[1:13], len(ret))
LjungBox[1][-1]
from arch.univariate import ARX, GARCH
model = ARX(ret, lags=1)
model.volatility = GARCH()
res = model.fit()
print(res.summary())
myfigpro = MyPackage.MyClass_PlotPro.MyClass_FigurePro() #Figure高级图系列 mynp = MyPackage.MyClass_Array.MyClass_NumPy() #多维数组类(整合Numpy) mypd = MyPackage.MyClass_Array.MyClass_Pandas() #矩阵数组类(整合Pandas) mypdpro = MyPackage.MyClass_ArrayPro.MyClass_PandasPro() #高级矩阵数组类 mytime = MyPackage.MyClass_Time.MyClass_Time() #时间类 myDA = MyPackage.MyClass_DataAnalysis.MyClass_DataAnalysis() #数据分析类 #MyPackage.MyClass_ToDefault.DefaultMatplotlibBackend() #恢复默认设置(仅main主界面) #------------------------------------------------------------ Path="C:\\Users\\i2011\\OneDrive\\Book_Code&Data\\量化投资以python为工具\\数据及源代码\\025" Path2="C:\\Users\\i2011\\OneDrive\\Book_Code&Data\\量化投资以python为工具\\习题解答" SHret=pd.read_table(Path+'\\TRD_IndexSum.txt',index_col='Trddt',sep='\t') SHret.index=pd.to_datetime(SHret.index) myDA.tsa_auto_ARCH(SHret) # 5. from arch.univariate import ARX, GARCH model = ARX(SHret, lags=1) model.volatility = GARCH() res = model.fit() print(res.summary())
def get_disaster_factors(innovation_method,
level_filter=None,
var_filter=None,
day_filter=None):
r'''
Function to get various disaster risk factors and their innovations.
Args:
innovation_method: String for how to compute innovations in disaster
risk factors.
'AR' uses an AR1 model
'fd' uses first-differences
level_filter: List of filters to apply to whether disaster risk comes
from sp_500 or individual firms (ind)
var_filter: List of filters to apply to the disaster risk measure
(D, rn_prob_2sigma, rn_prob_20, rn_prob_40, rb_prob_60)
day_filter: List of filters to apply to duration of options that
went into measure (30, 60, 120)
Returns:
df: Dataframe where index is date and columns are various disaster
risk factors
df_innov: Dataframe containing innovations to disaster risk factors
'''
# == Check inputs == #
if innovation_method not in ['AR', 'fd']:
raise ValueError("innovation_method must be either 'AR' or 'fd'")
# == Read in raw data == #
raw_f = pd.read_csv("estimated_data/disaster_risk_measures/" +\
"combined_disaster_df.csv")
raw_f['date_eom'] = pd.to_datetime(raw_f['date'])
raw_f.drop('date', axis=1, inplace=True)
# == Focus only on direct (for S&P 500) and filtered mean aggregation == #
raw_f = raw_f[raw_f.agg_type.isin(['direct', 'mean_filter'])]
# == Apply other filters == #
if level_filter is not None:
raw_f = raw_f[raw_f['level'].isin(level_filter)]
if var_filter is not None:
raw_f = raw_f[raw_f['var'].isin(var_filter)]
if day_filter is not None:
raw_f = raw_f[raw_f['days'].isin(day_filter)]
# == Create variable names == #
raw_f['name'] = raw_f['level'] + '_' + raw_f['var'] +\
'_' + raw_f['days'].astype(str)
# == Create pivot table, then resample to end of month == #
pdf = raw_f.pivot_table(index='date_eom', columns='name', values='value')
pdf = pdf.resample('M').last()
# == Compute innovations in each factor == #
if innovation_method == 'fd':
df = pdf.diff()
elif innovation_method == 'AR':
df = pd.DataFrame(index=pdf.index, columns=pdf.columns)
for col in df.columns:
ar = ARX(pdf[col], lags=[1]).fit()
df.loc[ar.resid.index, col] = ar.resid.values
df = df.astype(float)
return pdf, df
def main(fund_price_file=None, fund_region='EU', returns_type='pct', tag=''):
os.chdir(os.path.dirname(
__file__)) # switch to the folder where you script is stored
output_folder = '{}_{}_{}_return'.format(tag, fund_region, returns_type)
output_dir = os.path.join(os.path.dirname(__file__), output_folder)
##########################################################################
# read four factors of fama french data
##########################################################################
if fund_region == 'EU':
file_3_Factors = 'Europe_3_Factors_Daily.csv'
file_MOM_Factor = 'Europe_MOM_Factor_Daily.csv'
df_threefators = pd.read_csv(file_3_Factors,
parse_dates=[0],
index_col=0,
skiprows=6).drop('RF',
axis=1)['2013':'2018']
df_forthfactor = pd.read_csv(file_MOM_Factor,
parse_dates=[0],
index_col=0,
skiprows=6)['2013':'2018']
ff_rf = pd.read_csv(file_3_Factors,
parse_dates=[0],
index_col=0,
skiprows=6)['RF']['2013':'2018']
if fund_region == 'US':
file_3_Factors = 'F-F_Research_Data_Factors_daily.CSV'
file_MOM_Factor = 'F-F_Momentum_Factor_daily.csv'
df_threefators = pd.read_csv(file_3_Factors,
parse_dates=[0],
index_col=0,
skiprows=4).drop('RF',
axis=1)['2013':'2018']
df_forthfactor = pd.read_csv(file_MOM_Factor,
parse_dates=[0],
index_col=0,
skiprows=13)['2013':'2018']
ff_rf = pd.read_csv(file_3_Factors,
parse_dates=[0],
index_col=0,
skiprows=4)['RF']['2013':'2018']
if fund_region == 'Global':
file_3_Factors = 'Global_3_Factors_daily.CSV'
file_MOM_Factor = 'Global_MOM_Factor_daily.csv'
df_threefators = pd.read_csv(file_3_Factors,
parse_dates=[0],
index_col=0,
skiprows=6).drop('RF',
axis=1)['2013':'2018']
df_forthfactor = pd.read_csv(file_MOM_Factor,
parse_dates=[0],
index_col=0,
skiprows=6)['2013':'2018']
ff_rf = pd.read_csv(file_3_Factors,
parse_dates=[0],
index_col=0,
skiprows=6)['RF']['2013':'2018']
factors = pd.concat([df_threefators, df_forthfactor], axis=1)
factors.index = pd.to_datetime(factors.index)
factors = factors / 100
ff_rf = ff_rf / 100
print(factors.head())
print(factors.describe())
##########################################################################
# read green fund daily price
##########################################################################
file = fund_price_file
xl = pd.ExcelFile(file)
print(xl.sheet_names)
stats_list = []
ols_list = []
pvalues_list = []
garch_list = []
arx_list = []
if not os.path.exists(output_dir):
os.makedirs(output_dir)
os.chdir(output_dir)
for select_sheet in xl.sheet_names:
df = xl.parse(select_sheet,
parse_dates=[0],
index_col=0,
pase_dates=True,
skiprows=[0, 1, 2, 4],
header=0)
df.index = pd.to_datetime(df.index)
print('Import sheet: {}'.format(select_sheet))
# skip/filter Nan colomns
print('the following columns are not numeric ')
print(df.select_dtypes(exclude=['float64']))
df = df.select_dtypes(include=['float64'])
##########################################################################
# calculate daily average returns and describe stats ; https://stackoverflow.com/questions/35365545/calculating-cumulative-returns-with-pandas-dataframe
##########################################################################
if returns_type == 'pct': # simple return
returns = df.pct_change(limit=2).mean(axis=1)['2013':'2018']
if returns_type == 'cum': # cumulative_return
returns = df.pct_change(limit=2)['2013':'2018']
returns = ((1 + returns).cumprod() - 1).mean(axis=1)
if returns_type == 'log': # log return
returns = np.log(1 + df.pct_change(limit=2)).mean(
axis=1)['2013':'2018']
print(returns.describe())
# check data completeness
print('The following date have NaN return value')
print(returns[returns.isna().any()])
returns.fillna(method='bfill', inplace=True)
returns.plot()
plt.savefig('{}_daily_returns.png'.format(select_sheet))
plt.close()
stats_current = returns.describe()
stats_current.name = select_sheet
stats_list.append(stats_current)
##########################################################################
# linear regression of fama french factors
##########################################################################
slice_index_ols = returns.index.intersection(factors.index)
X = factors.loc[slice_index_ols]
y = returns.loc[slice_index_ols] - ff_rf[slice_index_ols]
X_with_constant = sm.add_constant(X)
model_static = sm.OLS(y, X_with_constant, missing='drop').fit()
print(model_static.params)
ols_current = model_static.params
ols_current.name = select_sheet
ols_list.append(ols_current)
pvalues_current = model_static.pvalues
pvalues_current.name = select_sheet
pvalues_list.append(pvalues_current)
with open('ols_summary_{}.csv'.format(select_sheet), 'w') as f:
f.write(model_static.summary().as_csv())
##########################################################################
# arch analysis of volatility
##########################################################################
am = arch_model(returns)
res = am.fit()
print(res.summary())
garch_current = res.params
garch_current.name = select_sheet
garch_list.append(garch_current)
with open('garch_summary_{}.csv'.format(select_sheet), 'w') as f:
f.write(res.summary().as_csv())
res.plot(annualize='D')
plt.savefig('garch_{}.png'.format(select_sheet))
plt.close()
##########################################################################
# arx analysis of volatility
##########################################################################
from arch.univariate import ARX
arx = ARX(returns, lags=[1])
res = arx.fit()
print(res.summary())
arx_current = res.params
arx_current.name = select_sheet
arx_list.append(arx_current)
with open('arx_summary_{}.csv'.format(select_sheet), 'w') as f:
f.write(res.summary().as_csv())
res.plot(annualize='D')
plt.savefig('arx_{}.png'.format(select_sheet))
plt.close()
##########################################################################
# write all results
##########################################################################
pd.concat(stats_list, axis=1).to_csv('greenfund_stats.csv')
pd.concat(ols_list, axis=1).to_csv('greenfund_ols.csv')
pd.concat(pvalues_list, axis=1).to_csv('greenfund_pvalues.csv')
pd.concat(garch_list, axis=1).to_csv('greenfund_garch.csv')
pd.concat(arx_list, axis=1).to_csv('greenfund_arx.csv')
sm.graphics.tsa.plot_acf(rates)
# ARCH effect
ar_res = ar_select_order(rates, 5).model.fit()
# Test of no serial correlation and homoskedasticity
print(ar_res.diagnostic_summary())
print(ar_res.summary())
plt.figure()
plt.plot(ar_res.resid)
# a = ar_res.resid
# a_res = ar_select_order(a, 5).model.fit()
# print(a_res.diagnostic_summary())
# Fit with GARCH(p, q)
ar = ARX(rates, lags=[1, 2]) # Mean model
ar.volatility = GARCH(p=1, q=1) # Volatility model
res = ar.fit()
res.plot()
print(res.summary())
# Forecast
drop = len(data) - len(rates)
start = 3254 - 2 - drop
end = 3262 - 2 - drop
var = res.forecast(start=start, horizon=5,
method='simulation').variance[start:1 + end]
var.plot()
entry = [
'2012:06:20',
from statsmodels.tsa.arima_model import ARMA
import pandas
import numpy
import statsmodels.api as sm
prices = pandas.read_csv("prices.csv", parse_dates=['Date'], index_col=0)
tickers = prices.columns[:-2]
prices = prices.resample('W').agg(lambda x: x[-1])
prices.dropna(axis=0, how='any', inplace=True)
rf = prices['^TNX'].values[:-1]
rf /= (52 * 100)
returns = prices.iloc[:, :-1].pct_change()[1:]
rm = returns['^GSPC'].values
ri = returns.iloc[:, :-1].values
Ri = ri - rf[:, numpy.newaxis]
Rm = rm - rf
model = sm.OLS(Ri, sm.add_constant(Rm))
results = model.fit()
alpha, beta = results.params
epsilon = numpy.sqrt(Ri.var(axis=0) - beta**2 * Rm.var(axis=0))
output = pandas.DataFrame(columns=['alpha', 'beta', 'epsilon'],
index=tickers,
data=numpy.array([alpha, beta, epsilon]).T)
output.to_csv("coefficients.csv")
from arch.univariate import ARX, GARCH
arx = ARX(rm, lags=1)
arx.volatility = GARCH()
res = arx.fit(disp='off')
pandas.DataFrame(res.params).to_csv("parameters.csv")
def test_arx_no_lags():
mod = ARX(SP500, volatility=GARCH())
res = mod.fit(disp="off")
assert res.params.shape[0] == 4
assert "lags" not in mod._model_description(include_lags=False)
eqCurves = pd.DataFrame(index=signal.index,
columns=['Buy and Hold', 'Strategy'])
eqCurves['Buy and Hold'] = returns['Buy and Hold'].cumsum() + 1
eqCurves['Strategy'] = returns['Strategy'].cumsum() + 1
eqCurves['Strategy'].plot(figsize=(10, 8))
eqCurves['Buy and Hold'].plot()
plt.legend()
plt.show()
# # From Arch website
# In[273]:
from arch.univariate import ARX
ar = ARX(Y, lags=30)
print(ar.fit().summary())
# In[270]:
from arch.univariate import ARCH, GARCH
ar.volatility = GARCH(p=3, o=0, q=3)
res = ar.fit(update_freq=0, disp='off')
p(res.summary())
# In[265]:
from arch.univariate import StudentsT
ar.distribution = StudentsT()
res = ar.fit(update_freq=0, disp='off')
p(res.summary())
print(res.summary()) res.plot(annualize='D') # In[56]: res.plot(annualize='D') # In[58]: # AR from arch.univariate import ARX ar = ARX(ts_data, lags = [1, 3, 12]) # print(ar.fit().summary()) # In[60]: # Volatility Processes from arch.univariate import ARCH, GARCH ar.volatility = ARCH(p=5) res = ar.fit(update_freq=0, disp='off') # print(res.summary()) fig = res.plot() # Distribution from arch.univariate import StudentsT