Estimate Autocorrelation using Python

by

I don’t think there is a NumPy function for this particular calculation. Here is how I would write it:

def estimated_autocorrelation(x):
    """
    http://stackoverflow.com/q/14297012/190597
    http://en.wikipedia.org/wiki/Autocorrelation#Estimation
    """
    n = len(x)
    variance = x.var()
    x = x-x.mean()
    r = np.correlate(x, x, mode="full")[-n:]
    assert np.allclose(r, np.array([(x[:n-k]*x[-(n-k):]).sum() for k in range(n)]))
    result = r/(variance*(np.arange(n, 0, -1)))
    return result

The assert statement is there to both check the calculation and to document its intent.

When you are confident this function is behaving as expected, you can comment-out the assert statement, or run your script with python -O. (The -O flag tells Python to ignore assert statements.)

Leave a Comment