using kalman filter for rolling window instead of average for faster convergence esp 2 sigma

two_sigma_kalman_rolling.py

# https://scipy-cookbook.readthedocs.io/items/KalmanFiltering.html
# https://github.com/pykalman/pykalman

import pandas as pd
from pykalman import KalmanFilter
import numpy as np

def rolling_window(a, step):
    shape   = a.shape[:-1] + (a.shape[-1] - step + 1, step)
    strides = a.strides + (a.strides[-1],)
    return np.lib.stride_tricks.as_strided(a, shape=shape, strides=strides)

def get_kf_value(y_values):
    kf = KalmanFilter()
    Kc, Ke = kf.em(y_values, n_iter=1).smooth(0)
    return Kc

n = 2000
index = pd.date_range(start='2000-01-01', periods=n)
data = np.random.randn(n, 4)
df = pd.DataFrame(data, columns=list('ABCD'), index=index)

wsize = 3
arr = rolling_window(df.D.values, wsize)
zero_padding = np.zeros(shape=(wsize-1,wsize))
arrst = np.concatenate((zero_padding, arr))
arrkalman = np.zeros(shape=(len(arrst),1))

for i in range(len(arrst)):
    arrkalman[i] = get_kf_value(arrst[i])

kalmandf = pd.DataFrame(arrkalman, columns=['D_kalman'], index=index)
df = pd.concat([df,kalmandf], axis=1)