Estimate Autocorrelation using Python

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.)

I took a part of code from pandas autocorrelation_plot() function. I checked the answers with R and the values are matching exactly.

import numpydef acf(series):    n = len(series)    data = numpy.asarray(series)    mean = numpy.mean(data)    c0 = numpy.sum((data - mean) ** 2) / float(n)    def r(h):        acf_lag = ((data[:n - h] - mean) * (data[h:] - mean)).sum() / float(n) / c0        return round(acf_lag, 3)    x = numpy.arange(n) # Avoiding lag 0 calculation    acf_coeffs = map(r, x)    return acf_coeffs

The statsmodels package adds a autocorrelation function that internally uses np.correlate (according to the statsmodels documentation).

See:http://statsmodels.sourceforge.net/stable/generated/statsmodels.tsa.stattools.acf.html#statsmodels.tsa.stattools.acf