I wrote a function for Hurst exponent’s calculation. I decided to test my function with “random walk” series.

difs = np.random.normal(0, 1, 100000)
series = np.cumsum(difs)

According to several sources Hurst exponent for random walk series should be approximately equal to 0.5. However all that I got there is H = 1. Is there something wrong with my function or I just misunderstood something? Would appreciate any explanations.

Function for Hurst exponent calculation:

def rs(series: np.ndarray):
    n, m = 0, 0
    shape = series.shape
    if len(shape) == 1:
        m = 1
        n = shape[0]
        series = series.reshape(-1, 1)
    else:
        n, m = shape
    result = []
    Hs = []
    for col in range(m):
        scales = utils.get_scales(n)
        rs_values = []
        for scale in scales:
            current_rs_values = []
            for i in range(n//scale):
                segment = series[i*scale:(i + 1)*scale, col]
                mean = segment.mean()
                corr_segment = segment - mean
                cum_dev = np.cumsum(corr_segment)
                R = np.max(cum_dev) - np.min(cum_dev)
                S = np.std(corr_segment)
                current_rs_values.append(R/S)
            rs = np.mean(current_rs_values)
            rs_values.append((log(scale), log(rs)))
        result.append(np.array(rs_values))
        H, _ = np.polyfit(result[-1][:,0], result[-1][:,1], 1)
        Hs.append(H)
    return Hs, np.array(result)

There I use get_scales that I wrote:

def get_scales(n: int):
    scales = np.logspace(np.log10(4), np.log10(n//2), 30, dtype='int')
    scales = np.unique(scales)
    return scales