Hurst Exponent

hurst.py

def hurst(ts):
    """
    Returns the Hurst Exponent of the time series vector ts
    """
    # make sure we are working with an array, convert if necessary
    ts = np.asarray(ts)

    # Helper variables used during calculations
    lagvec = []
    tau = []
    # Create the range of lag values
    lags = range(2, 100)

    #  Step through the different lags
    for lag in lags:
        #  produce value difference with lag
        pdiff = np.subtract(ts[lag:],ts[:-lag])
        #  Write the different lags into a vector
        lagvec.append(lag)
        #  Calculate the variance of the difference vector
        tau.append(np.sqrt(np.std(pdiff)))

    #  linear fit to double-log graph
    m = np.polyfit(np.log10(np.asarray(lagvec)),
                   np.log10(np.asarray(tau).clip(min=0.0000000001)),
                   1)
    # return the calculated hurst exponent
    return m[0]*2.0