OU_halflife.py

import yfinance
import numpy as np
import statsmodels.api as sm
import matplotlib.pyplot as mplt

# Download dos dados
data = yfinance.download(
    tickers = 'PSSA3.SA ITUB4.SA',
    start="2020-05-01",
    end="2020-08-05",
    interval = '1d',
    treads = False
)

series_x = data['Close']['PSSA3.SA']
series_y = data['Close']['ITUB4.SA']

# Regressão e Resíduo
X = sm.add_constant(series_x.values)
mod = sm.OLS(series_y, X) 
results = mod.fit()

def half_life(ts):
    lagged = ts.shift(1).fillna(method="bfill")
    delta = ts-lagged
    X = sm.add_constant(lagged.values)
    ar_res = sm.OLS(delta, X).fit()
    half_life = -1*np.log(2)/ar_res.params['x1']
    return half_life, ar_res 

half_life, _ = half_life(results.resid)
print('halflife: ', half_life)