Half-Life of Mean Reversion

half_life.py

import numpy as np

def half_life(ts):  
    """ 
    Calculates the half life of a mean reversion
    """
    # make sure we are working with an array, convert if necessary
    ts = np.asarray(ts)
    
    # delta = p(t) - p(t-1)
    delta_ts = np.diff(ts)
    
    # calculate the vector of lagged values. lag = 1
    lag_ts = np.vstack([ts[1:], np.ones(len(ts[1:]))]).T
   
    # calculate the slope of the deltas vs the lagged values 
    beta = np.linalg.lstsq(lag_ts, delta_ts)
    
    # compute and return half life
    return (np.log(2) / beta[0])[0]

Hi, I think we should do regression y_t-1 - y_t on y_t-1

    # calculate the vector of lagged values. lag = 1
    lag_ts = np.vstack([ts[1:], np.ones(len(ts[1:]))]).T
... ...
    # compute and return half life
    return (np.log(2) / beta[0])[0]

should be

    # calculate the vector of lagged values. lag = 1
    lag_ts = np.vstack([ts[:-1], np.ones(len(ts[:-1]))]).T
... ...
    # compute and return half life
    return -(np.log(2) / beta[0])[0]

Let me know if my understanding is not correct. Cheers!