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import numpy as np | |
from numba import jit | |
from numba import float64 | |
from numba import int64 | |
@jit((float64[:], int64), nopython=True, nogil=True) | |
def _ewma(arr_in, window): | |
r"""Exponentialy weighted moving average specified by a decay ``window`` | |
to provide better adjustments for small windows via: | |
y[t] = (x[t] + (1-a)*x[t-1] + (1-a)^2*x[t-2] + ... + (1-a)^n*x[t-n]) / | |
(1 + (1-a) + (1-a)^2 + ... + (1-a)^n). | |
Parameters | |
---------- | |
arr_in : np.ndarray, float64 | |
A single dimenisional numpy array | |
window : int64 | |
The decay window, or 'span' | |
Returns | |
------- | |
np.ndarray | |
The EWMA vector, same length / shape as ``arr_in`` | |
Examples | |
-------- | |
>>> import pandas as pd | |
>>> a = np.arange(5, dtype=float) | |
>>> exp = pd.DataFrame(a).ewm(span=10, adjust=True).mean() | |
>>> np.array_equal(_ewma_infinite_hist(a, 10), exp.values.ravel()) | |
True | |
""" | |
n = arr_in.shape[0] | |
ewma = np.empty(n, dtype=float64) | |
alpha = 2 / float(window + 1) | |
w = 1 | |
ewma_old = arr_in[0] | |
ewma[0] = ewma_old | |
for i in range(1, n): | |
w += (1-alpha)**i | |
ewma_old = ewma_old*(1-alpha) + arr_in[i] | |
ewma[i] = ewma_old / w | |
return ewma |
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