cor_num = stats.pearsonr(cut['sp'], cut['tn'])
cor0.loc[p, 'cor'] = cor_num[0]
else:
cut = returns.loc[(returns['sp'] > score_sp) &
(returns['tn'] > score_tn), ]
cor_num = stats.pearsonr(cut['sp'], cut['tn'])
cor0.loc[p, 'cor'] = cor_num[0]
cor0.plot()
tsm_sp = ZeroMean(returns['sp'])
garch = GARCH()
tsm_sp.volatility = garch
tsm_sp.distribution = StudentsT()
rst_sp = tsm_sp.fit()
filtered_sp = rst_sp.std_resid
tsm_tn = ZeroMean(returns['tn'])
garch = GARCH()
tsm_tn.volatility = garch
tsm_tn.distribution = StudentsT()
rst_tn = tsm_tn.fit()
filtered_tn = rst_tn.std_resid
filtered_returns = pd.DataFrame(dict(sp=filtered_sp, tn=filtered_tn),
index=returns.index)
data = pd.read_csv('data/Chapter8_Data.csv',
parse_dates=True,
index_col='date')
returns = data.apply(np.log) - data.apply(np.log).shift()
returns.dropna(inplace=True)
returns *= scale
returns.plot()
# FHS
fhs = ZeroMean(returns['Close'])
garch = GARCH(p=1, q=1)
fhs.distribution = StudentsT()
fhs.volatility = garch
rst = fhs.fit()
print(rst)
rst.plot(annualize='D')
sns.distplot(rst.std_resid, fit=stats.t)
forecast_variance_1day = rst.forecast(horizon=1).variance.iloc[-1, 0]
rs = np.random.RandomState(1234)
def Bootstrap(samples, random_state: np.random.RandomState, size: int):
max_idx = len(samples)
def simulate_2(PARS, sample_size):
zm = ZeroMean()
zm.volatility = GARCH(p=1, q=1)
sim_data = zm.simulate(PARS, sample_size)
return sim_data['data']
VaRsp = -stats.norm.ppf(0.01, 0, scale=std_sp)
VaRtn = -stats.norm.ppf(q=0.01, scale=std_tn)
VaRp = -stats.norm.ppf(q=0.01, scale=std_p)
print(VaRp < (VaRsp + VaRtn) / 2)
# Exercise 4
omega = 1.5E-6 * scale**2
alpha = 0.05
beta = 0.8
theta = 1.25
tsm = ZeroMean(returns['sp500'])
ngarch = NGARCH11(np.array([omega, alpha, beta, theta]))
tsm.volatility = ngarch
tsm.distribution = StudentsT()
sp500_rst = tsm.fit()
print(sp500_rst)
sp500_rst.plot(annualize='D')
sns.distplot(sp500_rst.std_resid, fit=stats.t)
print(
ngarch.is_valid(sp500_rst.params['alpha'], sp500_rst.params['beta'],
sp500_rst.params['theta']))
sm.graphics.qqplot(sp500_rst.std_resid, line='45')
returns['std_sp500'] = sp500_rst.std_resid
def two_pass_est( self, print_results = True, plot_results = False ):
#
# See Chapter 8.4.1 of the lecture notes
#
# TODO: First, specify 'mean equation' and estimate it via OLS
#
# Choosing the 'right' (best) model
# -> Use information criteria, e.g. AIC/ BIC
#
# We use a parsimonious model here
# -> AR(1)
#
n = len(self.returns)
Y = list(self.returns[1:n])
X = self.returns[0:n-1]
X = sm.add_constant(X) # Add constant
model_mean = sm.OLS(Y, X)
results_mean = model_mean.fit() # Fit the model
if print_results == True:
print( results_mean.summary() )
# TODO: Second, take residuals eps_t and square them (eps^2_t)
#
resid = results_mean.resid
resid_squ = resid**2
if plot_results == True:
plt.plot( resid_squ )
#
# Test for ARCH effects (not implemented here)
# TODO: Third, run MLE optimization with eps^2_t as observed time series to estimate ARCH model
#
# ARCH(1) model:
# sigma^2_t-1 := alpha_0 + alpha_1 * eps^2_t-1,
# with alpha_0 > 0 and alpha_1 >= 0
#
# Note, 'arch' package requires 'not squared' residuals as input
# #
model_vol = ZeroMean(resid) # Instantiate object (mean equation) (mean is included in resid)
model_vol.volatility = ARCH(p=1)
results_vol = model_vol.fit() # Fit the model
volatility = results_vol.conditional_volatility # Extract the volatility
if print_results == True:
print( results_vol.summary() )
if plot_results == True:
results_vol.plot()
return volatility, results_vol, resid_squ