def distributions_plot(N: float, K: float, L: float, l: float) -> None:
"""Plots the distributions in linear and logarithmic scale.
:return: None -- The function saves the plot in a file and does not return
a value.
"""
x_vals_lin: np.ndarray = np.arange(-10, 10, 0.2)
x_vals_log: np.ndarray = np.arange(-10, 10, 0.5)
gg_distribution_lin: np.ndarray = exact_distributions_tools.pdf_gaussian_gaussian(
x_vals_lin, N, 1
)
ga_distribution_lin: np.ndarray = exact_distributions_tools.pdf_gaussian_algebraic(
x_vals_lin, K, L, N, 1
)
ag_distribution_lin: np.ndarray = exact_distributions_tools.pdf_algebraic_gaussian(
x_vals_lin, K, l, N, 1
)
aa_distribution_lin: np.ndarray = exact_distributions_tools.pdf_algebraic_algebraic(
x_vals_lin, K, L, l, N, 1
)
gg_distribution_log: np.ndarray = exact_distributions_tools.pdf_gaussian_gaussian(
x_vals_log, N, 1
)
ga_distribution_log: np.ndarray = exact_distributions_tools.pdf_gaussian_algebraic(
x_vals_log, K, L, N, 1
)
ag_distribution_log: np.ndarray = exact_distributions_tools.pdf_algebraic_gaussian(
x_vals_log, K, l, N, 1
)
aa_distribution_log: np.ndarray = exact_distributions_tools.pdf_algebraic_algebraic(
x_vals_log, K, L, l, N, 1
)
markers: List[str] = ["-o", "-^", "-s", "-P"]
figure, (ax1, ax2) = plt.subplots(1, 2, figsize=(16, 9))
# Linear plot
ax1.plot(x_vals_lin, gg_distribution_lin, markers[0], ms=10, label=f"GG")
ax1.plot(x_vals_lin, ga_distribution_lin, markers[1], ms=10, label=f"GA")
ax1.plot(x_vals_lin, ag_distribution_lin, markers[2], ms=10, label=f"AG")
ax1.plot(x_vals_lin, aa_distribution_lin, markers[3], ms=10, label=f"AA")
ax1.set_xlabel(r"$\tilde{r}$", fontsize=20)
ax1.set_ylabel(r"PDF", fontsize=20)
ax1.tick_params(axis="x", labelsize=15)
ax1.tick_params(axis="y", labelsize=15)
ax1.set_xlim(-2, 2)
ax1.set_ylim(0, 0.65)
ax1.grid(True)
# Logarithmic plot
ax2.semilogy(x_vals_log, gg_distribution_log, markers[0], ms=10, label=f"GG")
ax2.semilogy(x_vals_log, ga_distribution_log, markers[1], ms=10, label=f"GA")
ax2.semilogy(x_vals_log, ag_distribution_log, markers[2], ms=10, label=f"AG")
ax2.semilogy(x_vals_log, aa_distribution_log, markers[3], ms=10, label=f"AA")
ax2.legend(loc="upper center", bbox_to_anchor=(1.13, 0.6), ncol=1, fontsize=20)
ax2.set_xlabel(r"$\tilde{r}$", fontsize=20)
ax2.set_ylabel(r"PDF", fontsize=20)
ax2.tick_params(axis="both", which="both", labelsize=15)
ax2.set_xlim(-6, 6)
ax2.set_ylim(10 ** -4, 1)
ax2.grid(True)
plt.tight_layout()
# Save Plot
figure.savefig(f"../plot/07_distributions_comparison.png")
def pdf_ag_distributions_plot(
dates: List[str],
time_step: str,
N_values: List[int],
K_value: int,
l_values: List[int],
) -> None:
"""Plots all the distributions and compares with agg. returns of a market.
:param dates: List of the interval of dates to be analyzed
(i.e. ['1980-01', '2020-12']).
:param time_step: time step of the data (i.e. '1m', '2m', '5m', ...).
:param N_values: fit parameter (i.e. [3, 4, 5, 6]).
:param K_value: number of companies.
:param l_values: shape parameter (i.e. [3, 4, 5, 6]).
:return: None -- The function saves the plot in a file and does not return
a value.
"""
figure, (ax1, ax2) = plt.subplots(1, 2, figsize=(16, 9))
markers: List[str] = ["o", "^", "s", "P"]
try:
# Load data
agg_returns_data: pd.Series = pickle.load(
open(
"../../project/data/exact_distributions_covariance/aggregated_dist"
+ f"_returns_market_data_{dates[0]}_{dates[1]}_step_{time_step}"
+ f".pickle",
"rb",
)
)
agg_returns_data = agg_returns_data.rename(r"$\tilde{r}$")
except FileNotFoundError as error:
print("No data")
print(error)
print()
# Log plot
plot_1 = agg_returns_data.plot(
kind="density", style=markers[0], logy=True, ax=ax1, legend=False, ms=7
)
plot_2 = agg_returns_data.plot(
kind="density", style=markers[0], loglog=True, ax=ax2, legend=False, ms=7
)
x_val_log: np.ndarray = np.arange(-10, 10, 0.05)
for N_value in N_values:
for l_value in l_values:
ag_distribution_log: np.ndarray = (
exact_distributions_tools.pdf_algebraic_gaussian(
x_val_log, K_value, l_value, N_value, 1
)
)
ax1.semilogy(
x_val_log,
ag_distribution_log,
"-",
lw=5,
label=f"N = {N_value} - l = {l_value}",
)
ax2.loglog(
x_val_log,
ag_distribution_log,
"-",
lw=5,
label=f"N = {N_value} - l = {l_value}",
)
ax1.set_xlabel(r"$\tilde{r}$", fontsize=25)
ax1.set_ylabel("PDF", fontsize=25)
ax1.tick_params(axis="both", which="both", labelsize=15)
ax1.set_xlim(-6, 6)
ax1.set_ylim(10 ** -4, 1)
ax1.grid(True)
ax2.legend(loc="upper right", fontsize=20)
ax2.set_xlabel(r"$\tilde{r}$", fontsize=20)
ax2.set_ylabel("PDF", fontsize=20)
ax2.tick_params(axis="both", which="both", labelsize=15)
ax2.set_xlim(3, 5)
ax2.set_ylim(0.5 * 10 ** -3, 10 ** -2)
ax2.grid(True)
plt.tight_layout()
# Save plot
figure.savefig(f"../plot/08_ag.png")
plt.close()
del agg_returns_data
del figure
del plot_1
del plot_2
def pdf_log_all_distributions_plot(dates: List[str], time_step: str) -> None:
"""Plots all the distributions and compares with agg. returns of a market.
:param dates: List of the interval of dates to be analyzed
(i.e. ['1980-01', '2020-12']).
:param time_step: time step of the data (i.e. '1m', '2m', '5m', ...).
:return: None -- The function saves the plot in a file and does not return
a value.
"""
function_name: str = pdf_log_all_distributions_plot.__name__
exact_distributions_covariance_tools.function_header_print_plot(
function_name, dates, time_step)
try:
# Load data
agg_returns_data: pd.Series = pickle.load(
open(
"../data/exact_distributions_covariance/aggregated_dist_returns"
+
f"_market_data_{dates[0]}_{dates[1]}_step_{time_step}.pickle",
"rb",
))
agg_returns_data = agg_returns_data.rename("Agg. returns")
x_val: np.ndarray = np.arange(-10, 10, 0.1)
# Log plot
plot_log = agg_returns_data.plot(kind="density",
style="-",
logy=True,
figsize=(16, 9),
legend=True,
lw=3)
if dates[0] == "1972-01":
N = 5.5
N_aa = 6
K = 23
L = 55
l = 55
gg_distribution: np.ndarray = (
exact_distributions_covariance_tools.pdf_gaussian_gaussian(
x_val, N, 1))
plt.semilogy(x_val,
gg_distribution,
"o",
lw=3,
label=f"GG - N = {N}")
ga_distribution: np.ndarray = (
exact_distributions_covariance_tools.pdf_gaussian_algebraic(
x_val, K, L, N, 1))
plt.semilogy(
x_val,
ga_distribution,
"o",
lw=3,
label=f"GA - N = {N} - K = {K} - L = {L}",
)
ag_distribution: np.ndarray = (
exact_distributions_covariance_tools.pdf_algebraic_gaussian(
x_val, K, l, N, 1))
plt.semilogy(
x_val,
ag_distribution,
"o",
lw=3,
label=f"AG - N = {N} - K = {K} - l = {l}",
)
aa_distribution: np.ndarray = (
exact_distributions_covariance_tools.pdf_algebraic_algebraic(
x_val, K, L, l, N_aa, 1))
plt.semilogy(
x_val,
aa_distribution,
"o",
lw=3,
label=f"AA - N = {N_aa} - K = {K} - L = {L}" + f" - l = {l}",
)
elif dates[0] == "1992-01":
N = 5
N_gg = 4
N_aa = 6
K = 277
L = 150
l = 150
gg_distribution: np.ndarray = (
exact_distributions_covariance_tools.pdf_gaussian_gaussian(
x_val, N_gg, 1))
plt.semilogy(x_val,
gg_distribution,
"o",
lw=3,
label=f"GG - N = {N_gg}")
ga_distribution: np.ndarray = (
exact_distributions_covariance_tools.pdf_gaussian_algebraic(
x_val, K, L, N, 1))
plt.semilogy(
x_val,
ga_distribution,
"o",
lw=3,
label=f"GA - N = {N} - K = {K} - L = {L}",
)
ag_distribution: np.ndarray = (
exact_distributions_covariance_tools.pdf_algebraic_gaussian(
x_val, K, l, N, 1))
plt.semilogy(
x_val,
ag_distribution,
"o",
lw=3,
label=f"AG - N = {N} - K = {K} - l = {l}",
)
aa_distribution: np.ndarray = (
exact_distributions_covariance_tools.pdf_algebraic_algebraic(
x_val, K, L, l, N_aa, 1))
plt.semilogy(
x_val,
aa_distribution,
"o",
lw=3,
label=f"AA - N = {N_aa} - K = {K} - L = {L}" + f" - l = {l}",
)
else:
N = 7
N_gg = 6
K = 461
L = 280
l = 280
gg_distribution: np.ndarray = (
exact_distributions_covariance_tools.pdf_gaussian_gaussian(
x_val, N_gg, 1))
plt.semilogy(x_val,
gg_distribution,
"o",
lw=3,
label=f"GG - N = {N_gg}")
ga_distribution: np.ndarray = (
exact_distributions_covariance_tools.pdf_gaussian_algebraic(
x_val, K, L, N, 1))
plt.semilogy(
x_val,
ga_distribution,
"o",
lw=3,
label=f"GA - N = {N} - K = {K} - L = {L}",
)
ag_distribution: np.ndarray = (
exact_distributions_covariance_tools.pdf_algebraic_gaussian(
x_val, K, l, N, 1))
plt.semilogy(
x_val,
ag_distribution,
"o",
lw=3,
label=f"AG - N = {N} - K = {K} - l = {l}",
)
aa_distribution: np.ndarray = (
exact_distributions_covariance_tools.pdf_algebraic_algebraic(
x_val, K, L, l, N, 1))
plt.semilogy(
x_val,
aa_distribution,
"o",
lw=3,
label=f"AA - N = {N} - K = {K} - L = {L} - l = {l}",
)
plt.legend(fontsize=20)
plt.title(
f"Aggregated distribution returns from {dates[0]} to" +
f" {dates[1]} - {time_step}",
fontsize=30,
)
plt.xlabel("Aggregated returns", fontsize=25)
plt.ylabel("PDF", fontsize=25)
plt.xticks(fontsize=15)
plt.yticks(fontsize=15)
plt.xlim(-10, 10)
plt.ylim(10**-9, 1)
plt.grid(True)
plt.tight_layout()
figure_log: plt.Figure = plot_log.get_figure()
# Plotting
exact_distributions_covariance_tools.save_plot(figure_log,
function_name, dates,
time_step)
plt.close()
del agg_returns_data
del figure_log
del plot_log
gc.collect()
except FileNotFoundError as error:
print("No data")
print(error)
print()