Python Implementation of the Jump Detection Algorithm as described in the Paper "Jumps in Equilibrium Prices and Market Microstructure Noise" by Suzanne S. Lee and Per A. Mykland

lee_mykland_jumps.py

from math import ceil, sqrt
import numpy as np
import pandas as pd

def movmean(v, kb, kf):
    """
    Computes the mean with a window of length kb+kf+1 that includes the element 
    in the current position, kb elements backward, and kf elements forward.
    Nonexisting elements at the edges get substituted with NaN.

    Args:
        v (list(float)): List of values.
        kb (int): Number of elements to include before current position
        kf (int): Number of elements to include after current position

    Returns:
        list(float): List of the same size as v containing the mean values
    """
    m = len(v) * [np.nan]
    for i in range(kb, len(v)-kf):
        m[i] = np.mean(v[i-kb:i+kf+1])
    return m


def LeeMykland(S, sampling, significance_level=0.01):
    """
    "Jumps in Equilibrium Prices and Market Microstructure Noise"
    - by Suzanne S. Lee and Per A. Mykland
    
    "https://galton.uchicago.edu/~mykland/paperlinks/LeeMykland-2535.pdf"
    
    Args:
        S (list(float)): An array containing prices, where each entry 
                         corresponds to the price sampled every 'sampling' minutes.
        sampling (int): Minutes between entries in S
        significance_level (float): Defaults to 1% (0.001)
        
    Returns:
        A pandas dataframe containing a row covering the interval 
        [t_i, t_i+sampling] containing the following values:
        J:   Binary value is jump with direction (sign)
        L:   L statistics
        T:   Test statistics
        sig: Volatility estimate
    """
    tm = 252*24*60 # Trading minutes
    k   = ceil(sqrt(tm/sampling))
    r = np.append(np.nan, np.diff(np.log(S)))
    bpv = np.multiply(np.absolute(r[:]), np.absolute(np.append(np.nan, r[:-1])))
    bpv = np.append(np.nan, bpv[0:-1]).reshape(-1,1) # Realized bipower variation
    sig = np.sqrt(movmean(bpv, k-3, 0)) # Volatility estimate
    L   = r/sig
    n   = np.size(S) # Length of S
    c   = (2/np.pi)**0.5
    Sn  = c*(2*np.log(n))**0.5
    Cn  = (2*np.log(n))**0.5/c - np.log(np.pi*np.log(n))/(2*c*(2*np.log(n))**0.5)
    beta_star   = -np.log(-np.log(1-significance_level)) # Jump threshold
    T   = (abs(L)-Cn)*Sn
    J   = (T > beta_star).astype(float)
    J   = J*np.sign(r) # Add direction
    # First k rows are NaN involved in bipower variation estimation are set to NaN.
    J[0:k] = np.nan
    # Build and retunr result dataframe
    return pd.DataFrame({'L': L,'sig': sig, 'T': T,'J':J})

Hi, very nice coding, but you may made a mistake.
This method is not from Jumps in Equilibrium Prices and Market Microstructure Noise, but from Jumps in Financial Markets: A New Nonparametric Test and Jump Dynamics.
I am working on the new method, but stucked by some questions. If possible, can we talk about the new method?

Hi @zzyxlab, thanks for the hint! Sure, just drop me an email at [email protected]! Looking forward to hearing from you

Hey very nice have you managed to finish the new method. I'm looking for the BNS jump test. Do you happen to have an implementation of that.
Thx a lot!

Hi @Fux002, you might find this helpful for the BNS jump test: https://github.com/jeromeku/Python-Financial-Tools/blob/master/jumps.py

@devanshu125 Thanks for sharing!