The normality of log-returns in stocks

# computing/log_returns_normality.py

import numpy as np
import pandas as pd

from pathlib import Path
from scipy.stats import kstest


# path containing the individual stocks OHLCOV data in .csv format
dataset_dir = Path.cwd() / "datasets" / "US_equities_OHLCOV"


def normality_test(time_series, var_name):
    """
    Perform Normality test based Kolmogorov-Smirnoff (KS) approach.
    The KS test works well with large data sets.

    :param time_series: the input time series -> list-like or pandas-like obj
    :param var_name: name of variable -> str
    :return: p-value of the normality test --> float
    """
    if time_series.empty:
        return None
    return kstest(time_series, "norm")


significance_level = 0.01
obs = 0
normal= 0
non_normal = 0
# dict below will have shape d = {"AAPL": No|Yes}, where No indicates non-normal log-returns
d = {}
for file_path in dataset_dir.iterdir():
    stock_ticker = file_path.stem
    stock_OHLCOV = pd.read_csv(dataset_dir / f"{stock_ticker}.csv")
    # log return = ln(P_t / (P_t-1) )
    stock_log_return = np.log(stock_OHLCOV["Close"] / stock_OHLCOV["Close"].shift(1))[1:]  # [1:] to ignore 1st Nan val.
    test_results = normality_test(stock_log_return, stock_ticker)
    if test_results is not None:
        obs += 1
        if test_results.pvalue < significance_level:  # reject null hypothesis of normality
            non_normal += 1
            d[stock_ticker] = "No"
        else:
            normal += 1
            d[stock_ticker] = "Yes"

# Summary statistics
print("Total observations: ", obs)
print("Normal log-returns: ", normal)
print("Non-normal log-returns: ", non_normal)
normal_over_total = round((normal / obs) * 100, 2)
print("Normal/Total: ", normal_over_total, "%")
# Convert dictionary d to pandas Dataframe
df = pd.DataFrame(d.items(), columns=["Symbol", "Normal log-returns"])