del out
# annual credit transition matrix
out = pd.DataFrame({'p_credit': pd.Series(p_credit.reshape(-1))})
out.to_csv(path + 'db_invariants_p_credit.csv', index=None)
del out
# -
# ## [Step 7](https://www.arpm.co/lab/redirect.php?permalink=s_checklist_scenariobased_step02-implementation-step07): Perform invariance tests
# +
plt.style.use('arpm')
invar = db_invariants[i_plot - 1][~np.isnan(db_invariants[i_plot - 1])]
_ = invariance_test_ellipsoid(invar, lag_)
fig_ellipsoid = plt.gcf()
fig_ellipsoid.set_dpi(72.0)
fig_ellipsoid.set_size_inches(1280.0 / 72.0, 720.0 / 72.0)
add_logo(fig_ellipsoid, set_fig_size=False)
plt.show()
invariance_test_ks(invar)
fig_ks = plt.gcf()
fig_ks.set_dpi(72.0)
fig_ks.set_size_inches(1280.0 / 72.0, 720.0 / 72.0)
add_logo(fig_ks, set_fig_size=False)
plt.tight_layout()
_ = invariance_test_copula(invar, lag_)
fig_cop = plt.gcf()
nok_stock_long = df_nokia_stock[(df_nokia_stock.date_tmstmp >= t_first) &
(df_nokia_stock.date_tmstmp < t_last)]
nok_dividends = df_nok_dividends[(df_nok_dividends.date_tmstmp >= t_first) &
(df_nok_dividends.date_tmstmp < t_last)]
# extract values
dates = nok_stock_long.date_tmstmp.values
r = nok_dividends.date_tmstmp.values
cf_r = nok_dividends.dividends.values
v_stock = nok_stock_long.close.values
# -
# ## [Step 1](https://www.arpm.co/lab/redirect.php?permalink=s_elltest_compret-implementation-step01): Dividend-adjusted values and invariant series
v_adj = adjusted_value(v_stock, dates, cf_r, r, fwd)
epsi = np.diff(np.log(v_adj))
# ## [Step 2](https://www.arpm.co/lab/redirect.php?permalink=s_elltest_compret-implementation-step02): Ellipsoid test
# +
plt.style.use('arpm')
# perform and show ellipsoid test for invariance
rho, conf_int = \
invariance_test_ellipsoid(epsi, l_,
conf_lev=conf_lev, fit=0, r=2,
title='Invariance test on daily yield changes')
fig = plt.gcf()
add_logo(fig, set_fig_size=False, size_frac_x=1/8)
log_underlying = np.log(np.array(db_stocks.loc[dates, 'GE']))
# compounded return and its absolute value
comp_return = np.diff(log_underlying)
abs_comp_return = np.abs(comp_return)
# -
# ## Plots
# +
plt.style.use('arpm')
fig = plt.figure(figsize=(15.5, 9))
plt.plot(dates[1:], comp_return.flatten(), '*', markersize=3)
plt.title('Compounded return')
add_logo(fig, set_fig_size=False)
plt.figure()
acf_x, conf_int_x = \
invariance_test_ellipsoid(comp_return, l_, conf_lev=conf_lev,
title='Compounded return', plot_test=True)
fig = plt.gcf()
add_logo(fig, set_fig_size=False, size_frac_x=1/8)
plt.figure()
acf_delta_x, conf_int_detal_x = \
invariance_test_ellipsoid(abs_comp_return, l_, conf_lev=conf_lev, bl=-0.025,
title='Absolute compounded return', plot_test=True)
fig = plt.gcf()
add_logo(fig, set_fig_size=False, size_frac_x=1/8)
# -
# ## [Step 1](https://www.arpm.co/lab/redirect.php?permalink=s_elltest_ytm_ns-implementation-step01): Compute increments NS aprameters
# +
delta_theta = np.diff(theta, axis=0)
# -
# ## [Step 2](https://www.arpm.co/lab/redirect.php?permalink=s_elltest_ytm_ns-implementation-step02): Ellipsoid tests
# +
plt.style.use('arpm')
# names of figures
name = {}
name[0] = r'Invariance test(increments of level parameter $\theta_1$)'
name[1] = r'Invariance test(increments of slope parameter $\theta_2$)'
name[2] = r'Invariance test(increments of curvature parameter $\theta_3$)'
name[3] = r'Invariance test(increments of decay parameter $\theta_4^2$)'
acf = np.zeros((4, l_))
conf_int_x = np.zeros((4, 2))
# perform and show ellipsoid test for invariance on NS parameters
for k in range(4):
acf[k, :], conf_int_x[k, :] = invariance_test_ellipsoid(delta_theta[:, k],
l_,
conf_lev=conf_lev,
title=name[k])
fig = plt.gcf()
add_logo(fig, set_fig_size=False, size_frac_x=1 / 8)
db_stocks.index = pd.to_datetime(db_stocks.index)
dates = pd.to_datetime(db_stocks.index)
# ## [Step 1](https://www.arpm.co/lab/redirect.php?permalink=s_elltest_garchres_stock-implementation-step01): Compute risk drivers for GE and compounded return
# +
# risk drivers
log_underlying = np.log(np.array(db_stocks.loc[dates, 'GE']))
# compounded return
comp_return = np.diff(log_underlying)
# -
# ## [Step 2](https://www.arpm.co/lab/redirect.php?permalink=s_elltest_garchres_stock-implementation-step02): Fit GARCH(1,1), compute residuals and their absolute values
# +
_, _, epsi = fit_garch_fp(comp_return)
abs_epsi = np.abs(epsi)
# -
# ## Plots
fig = plt.figure()
acf_x, conf_int_x = \
invariance_test_ellipsoid(abs_epsi, l_, conf_lev=conf_lev, bl=-0.75,
title='Absolute residuals of a GARCH(1, 1) model fitted on stock compounded return',
plot_test=True)
fig = plt.gcf()
add_logo(fig, set_fig_size=False, size_frac_x=1/8)
p = np.ones(x.shape) / x.shape
b_hat, _, _ = fit_var1(x)
# realized invariant
epsi = x[1:] - x[:-1] * b_hat
# -
# ## [Step 2](https://www.arpm.co/lab/redirect.php?permalink=s_elltest_ytm_monthly-implementation-step02): ellipsoid tests
# +
plt.style.use('arpm')
# perform and show ellipsoid test for invariance on monthly yield
name1 = 'Invariance test on monthly yield'
acf_x, conf_int_x = \
invariance_test_ellipsoid(x, l_, conf_lev=conf_lev, fit=0, r=2,
title=name1)
fig = plt.gcf()
add_logo(fig, set_fig_size=False, size_frac_x=1/8)
plt.style.use('arpm')
# perform and show ellipsoid test for invariance on AR(1) residuals
name2 = 'Invariance test on AR(1) residuals'
acf_epsi, conf_int_epsi = \
invariance_test_ellipsoid(epsi, l_, conf_lev=conf_lev, fit=0,
r=2, title=name2)
fig = plt.gcf()
add_logo(fig, set_fig_size=False, size_frac_x=1/8)
plt.style.use('arpm')
# -
epsi_abs = abs(epsi)
# ## [Step 2](https://www.arpm.co/lab/redirect.php?permalink=s_elltest_normal-implementation-step02): Compute normalized absolute values
# grades of absolute values
epsi_abs_grade, *_ = cop_marg_sep(epsi_abs)
# normalized absolute values
epsiabs_tilde = st.norm.ppf(epsi_abs_grade).squeeze()
# ## [Step 3](https://www.arpm.co/lab/redirect.php?permalink=s_elltest_normal-implementation-step03): Ellipsoid test on normal simulations
plt.style.use('arpm')
name1 = 'Invariance test on normal simulations'
acf_epsi, conf_int = \
invariance_test_ellipsoid(epsi, l_, conf_lev=conf_lev,
fit=0, r=1.8,
title=name1)
fig = plt.gcf()
add_logo(fig, set_fig_size=False, size_frac_x=1 / 8)
# ## [Step 4](https://www.arpm.co/lab/redirect.php?permalink=s_elltest_normal-implementation-step04): Ellipsoid test on absolute value of normal simulations
plt.style.use('arpm')
name2 = 'Invariance test on absolute values of normal simulations'
acf_abs, conf_int = \
invariance_test_ellipsoid(epsi_abs, l_, conf_lev=conf_lev,
fit=0, r=1.8,
title=name2,
bl=[-0.1], bu=[0.7])
fig = plt.gcf()
add_logo(fig, set_fig_size=False, size_frac_x=1 / 8)