# Exercise 1 & 3
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):
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)
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