Hurst指數python實現

def Hurst(data):
    n = 6
    data = pd.Series(data).pct_change()[1:]
    ARS = list()
    lag = list()
    for i in range(n):
        m = 2 ** i
        size = np.size(data) // m
        lag.append(size)
        panel = {}
        for j in range(m):
            panel[str(j)] = data[j*size:(j+1)*size].values
            
        panel = pd.DataFrame(panel)
        mean = panel.mean()
        Deviation = (panel - mean).cumsum()
        maxi = Deviation.max()
        mini = Deviation.min()
        sigma = panel.std()
        RS = maxi - mini
        RS = RS / sigma
        ARS.append(RS.mean())
        
    lag = np.log10(lag)
    ARS = np.log10(ARS)
    hurst_exponent = np.polyfit(lag, ARS, 1)
    hurst = hurst_exponent[0]
    
    return hurst 

 注意：Hurst指數描述的記憶性僅對線性過程有效；對於復雜非線性過程，其記憶性需要除Hurst指數之外的其他參數來描述（Kamenshchikov 2014）。而投資品價格和收益率變化是非線性過程。