import matplotlib as mpl
import matplotlib.pyplot as plt
import numpy as np
from scipy import stats
import pandas as pd

indicator_url = "https://gist.githubusercontent.com/jtrive84/9955433e344ec773e5766657f961fde5/raw/b2e2c99db1e05aeb69186550b9c78cc9412df911/sample_returns.csv"

df = pd.read_csv(indicator_url)

df.head()

# Plot histogram for each indicator.
df = df.drop("date", axis=1)

indicators = df.columns

fig, ax = plt.subplots(nrows=1, ncols=3, figsize=(9, 3.5), tight_layout=True) 

for ii, ind_name in enumerate(indicators):
    
    ind_mean, ind_std = df[ind_name].mean(), df[ind_name].std()
    label0 = r"$\bar x = $" + f"{ind_mean:,.4f}"
    label1 = r"$s = $" + f"{ind_std:,.4f}"
    ax[ii].set_title(ind_name, color="#000000", loc="center", fontsize=9)
    ax[ii].hist(
        df[ind_name].values, 18, density=True, alpha=1, color="#ff7595", 
        edgecolor="#FFFFFF", linewidth=1.0
        )
    
    ax[ii].axvline(ind_mean, color="#000000", linewidth=1.25, linestyle="--", label=r"$\hat \mu$")
    ax[ii].set_yticklabels([])
    ax[ii].set_xlabel("")
    ax[ii].set_ylabel("")
    ax[ii].tick_params(axis="x", which="major", direction='in', labelsize=6)
    ax[ii].tick_params(axis="x", which="minor", direction='in', labelsize=6)
    ax[ii].tick_params(axis="y", which="major", direction='in', labelsize=6)
    ax[ii].tick_params(axis="y", which="minor", direction='in', labelsize=6)
    ax[ii].xaxis.set_ticks_position("none")
    ax[ii].yaxis.set_ticks_position("none")
    ax[ii].grid(True)   
    ax[ii].set_axisbelow(True) 
    
    ax[ii].annotate(
        label0, xy=(.05, .90), xycoords="axes fraction", ha="left", va="bottom", 
        fontsize=9, rotation=0, weight="normal", color="#000000"
        ) 
    ax[ii].annotate(
        label1, xy=(.05, .85), xycoords="axes fraction", ha="left", va="bottom", 
        fontsize=9, rotation=0, weight="normal", color="#000000"
        ) 
    ax[ii].legend(loc="upper right", fancybox=True, framealpha=1, fontsize="x-small")
    
plt.show();

from scipy.stats import norm

# Get normal parameter estimates (mean & standard deviation) via maximum likelihood.
mu0, std0 = norm.fit(df["us_credit"], method="MLE")
mu1, std1 = norm.fit(df["us_market"], method="MLE")
mu2, std2 = norm.fit(df["global_market"], method="MLE")

dparams = {
    "us_credit": {"mean": mu0, "std": std0},
    "us_market": {"mean": mu1, "std": std1},
    "global_market": {"mean": mu2, "std": std2},
    }

print(f"\n- us_credit    : mean={mu0:,.5f} std=={std0:,.5f}")
print(f"- us_market    : mean={mu1:,.5f} std=={std1:,.5f}")
print(f"- global_market: mean={mu2:,.5f} std=={std2:,.5f}\n")

- us_credit    : mean=0.00015 std==0.02138
- us_market    : mean=0.00595 std==0.04442
- global_market: mean=0.00517 std==0.04605

# Plot histogram for each indicator along with parameterized normal distribution.
hist_color = "#ff7595"
dist_color = "#0000FF"

fig, ax = plt.subplots(nrows=1, ncols=3, figsize=(9.5, 3.5), tight_layout=True) 

for ii, ind_name in enumerate(indicators):

    vals = df[ind_name]
    mle_mean, mle_std = dparams[ind_name]["mean"], dparams[ind_name]["std"]

    # Get PDF values associated with distribution.
    ndist = norm(mle_mean, mle_std)
    xvals = np.linspace(vals.min() * .90, vals.max() * 1.10, 1000)
    yvals = ndist.pdf(xvals)

    label0 = r"$\hat \mu = $" + f"{mle_mean:,.4f}"
    label1 = r"$\hat \sigma = $" + f"{mle_std:,.4f}"
    
    ax[ii].set_title(ind_name, color="#000000", loc="center", fontsize=9)
    ax[ii].hist(
        df[ind_name].values, 18, density=True, alpha=1, color=hist_color, 
        edgecolor="#FFFFFF", linewidth=1.0
        )

    # Plot normal distribution.
    ax[ii].plot(xvals, yvals, linewidth=1.5, color=dist_color, linestyle="--")
    ax[ii].set_yticklabels([])
    ax[ii].set_xlabel("")
    ax[ii].set_ylabel("")
    ax[ii].tick_params(axis="x", which="major", direction='in', labelsize=6)
    ax[ii].tick_params(axis="x", which="minor", direction='in', labelsize=6)
    ax[ii].tick_params(axis="y", which="major", direction='in', labelsize=6)
    ax[ii].tick_params(axis="y", which="minor", direction='in', labelsize=6)
    ax[ii].xaxis.set_ticks_position("none")
    ax[ii].yaxis.set_ticks_position("none")
    ax[ii].grid(True)   
    ax[ii].set_axisbelow(True) 
    
    ax[ii].annotate(
        label0, xy=(.05, .90), xycoords="axes fraction", ha="left", va="bottom", 
        fontsize=9, rotation=0, weight="normal", color="#000000"
        ) 
    ax[ii].annotate(
        label1, xy=(.05, .85), xycoords="axes fraction", ha="left", va="bottom", 
        fontsize=9, rotation=0, weight="normal", color="#000000"
        ) 
    #ax[ii].legend(loc="upper right", fancybox=True, framealpha=1, fontsize="x-small")
plt.suptitle("Indicator histograms w/ parametric overlay", fontsize=10)
plt.show();

# Specify number of samples to generate.
nbr_sims = 500

# Copying dparams from previous cell.
dparams = {
    "us_credit": {"mean": mu0, "std": std0},
    "us_market": {"mean": mu1, "std": std1},
    "global_market": {"mean": mu2, "std": std2},
    }

# us_credit.
mean0, std0 = dparams["us_credit"]["mean"], dparams["us_credit"]["std"]
rv0 = norm(mean0, std0)

# us_market.
mean1, std1 = dparams["us_market"]["mean"], dparams["us_market"]["std"]
rv1 = norm(mean1, std1)

# global_market.
mean2, std2 = dparams["global_market"]["mean"], dparams["global_market"]["std"]
rv2 = norm(mean2, std2)

# Create DataFrame to hold simulated indicators. 
dfsims1 = pd.DataFrame(
    np.vstack([rv0.rvs(nbr_sims), rv1.rvs(nbr_sims), rv2.rvs(nbr_sims)]).T,
    columns=indicators
    )

dfsims1.describe()

df.corr()

dfsims1.corr()

# Generate correlated random samples.
# Specify number of simulations to generate.
nbr_sims = 500

# Create vector of means.
means = [mean0, mean1, mean2]

# Bind reference to covariance matrix.
V = df.cov().values

dfsims2 = pd.DataFrame(
    np.random.multivariate_normal(means, V, nbr_sims),
    columns=indicators
    )

dfsims2.describe()

dfsims2.corr()

# Generate pair-wise scatter plots for each indicator for independent and dependent draws. 

dindices = {
    (0, 0): {"data": "independent", "x": "us_credit", "y": "us_market"},
    (0, 1): {"data": "independent", "x": "global_market", "y": "us_credit"},
    (0, 2): {"data": "independent", "x": "us_market", "y": "global_market"},
    (1, 0): {"data": "dependent", "x": "us_credit", "y": "us_market"},
    (1, 1): {"data": "dependent", "x": "global_market", "y": "us_credit"},
    (1, 2): {"data": "dependent", "x": "us_market", "y": "global_market"},
    }


fig, ax = plt.subplots(nrows=2, ncols=3, figsize=(10, 6.5), tight_layout=True) 

for kk, vv in dindices.items():
    
    ii, jj = kk
    data_desc, x_desc, y_desc = vv["data"], vv["x"], vv["y"]

    if data_desc == "independent":
        xx = dfsims1[x_desc].values
        yy = dfsims1[y_desc].values
    else:
        xx = dfsims2[x_desc].values
        yy = dfsims2[y_desc].values
        
    titlestr = f"{data_desc}: {x_desc} vs. {y_desc}"
    ax[ii, jj].set_title(titlestr, color="#000000", loc="center", weight="bold", fontsize=7)
    ax[ii, jj].scatter(
        xx, yy, s=30, c="#FFFFFF", alpha=.85, edgecolor="#000000", linewidth=.75)

    # ax[ii].set_yticklabels([])
    ax[ii, jj].set_xlabel(x_desc, fontsize=7)
    ax[ii, jj].set_ylabel(y_desc, fontsize=7)
    ax[ii, jj].tick_params(axis="x", which="major", direction='in', labelsize=6)
    ax[ii, jj].tick_params(axis="x", which="minor", direction='in', labelsize=6)
    ax[ii, jj].tick_params(axis="y", which="major", direction='in', labelsize=6)
    ax[ii, jj].tick_params(axis="y", which="minor", direction='in', labelsize=6)
    ax[ii, jj].xaxis.set_ticks_position("none")
    ax[ii, jj].yaxis.set_ticks_position("none")
    ax[ii, jj].grid(True)   
    ax[ii, jj].set_axisbelow(True) 

plt.show();