numpy and statsmodels give different values when calculating correlations, How to interpret this?

cross-correlation, numpy, python, statsmodels

Solution

`statsmodels.tsa.stattools.ccf` is based on `np.correlate` but does some additional things to give the correlation in the statistical sense instead of the signal processing sense, see cross-correlation on Wikipedia. What happens exactly you can see in the source code, it's very simple.

For easier reference I copied the relevant lines below:

def ccovf(x, y, unbiased=True, demean=True):
    n = len(x)
    if demean:
        xo = x - x.mean()
        yo = y - y.mean()
    else:
        xo = x
        yo = y
    if unbiased:
        xi = np.ones(n)
        d = np.correlate(xi, xi, 'full')
    else:
        d = n
    return (np.correlate(xo, yo, 'full') / d)[n - 1:]

def ccf(x, y, unbiased=True):
    cvf = ccovf(x, y, unbiased=unbiased, demean=True)
    return cvf / (np.std(x) * np.std(y))

Problem

I can't find a reason why calculating the correlation between two series A and B using `numpy.correlate` gives me different results than the ones I obtain using `statsmodels.tsa.stattools.ccf` Here's an example of this difference I mention: ``` import numpy as np from matplotlib import pyplot as plt from statsmodels.tsa.stattools import ccf #Calculate correlation using numpy.correlate def corr(x,y): result = numpy.correlate(x, y, mode='full') return result[result.size/2:] #This are the data series I want to analyze A = np.array([np.absolute(x) for x in np.arange(-1,1.1,0.1)]) B = np.array([x for x in np.arange(-1,1.1,0.1)]) #Using numpy i get this plt.plot(corr(B,A)) ``` ``` #Using statsmodels i get this plt.plot(ccf(B,A,unbiased=False)) ``` The results seem qualitatively different, where does this difference come from?

Original source