DFA法计算的Hurst指数全部正确的python代码，包括单维EXCEL数据的读取代码

好的，以下是一份可以读取单维EXCEL数据并计算DFA法的Hurst指数的Python代码：

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt

def dfa(X, nvals=None, overlap=True, order=1, debug_plot=False):
    """
    Detrended Fluctuation Analysis

    A method for determining the statistical self-affinity of a signal. The
    signal is sub-sampled into boxes of size n. In each box, a least-squares
    polynomial is fit, and the local variance of the detrended data is
    computed. This is averaged over all boxes and normalized by the total
    variance of the signal.

    Parameters
    ----------
    X : ndarray
        One-dimensional time series.
    nvals : ndarray or None, optional (default=None)
        Array of box sizes. Default is np.logspace(0.7, np.log10(N/4), 20),
        where N is the length of the time series.
    overlap : bool, optional (default=True)
        If True, boxes overlap by half. If False, boxes are separated by
        exactly nvals[i] points.
    order : int, optional (default=1)
        Order of polynomial used to fit data in each box.
    debug_plot : bool, optional (default=False)
        If True, plot intermediate results for debugging purposes.

    Returns
    -------
    alpha : float
        DFA exponent.
    """
    X = np.asarray(X)
    N = len(X)
    if nvals is None:
        nvals = np.logspace(0.7, np.log10(N/4), 20).astype(int)
    else:
        nvals = np.asarray(nvals)
    overlap = bool(overlap)

    # Compute the profile y(i) of the time series, integrated from the
    # beginning.
    Y = np.cumsum(X - np.mean(X))

    # Compute the mean profile <y>_{i,n}.
    if overlap:
        step = nvals // 2
    else:
        step = nvals
    K = len(step)
    ymean = np.zeros(K, dtype=float)
    for k in range(K):
        n = nvals[k]
        if overlap:
            start = np.arange(0, N-n, step[k])
        else:
            start = range(0, N-n+1, step[k])
        local_means = [np.mean(Y[i:i+n]) for i in start]
        ymean[k] = np.mean(local_means)

    # Compute the root-mean-square fluctuation about the mean profile
    # F(n) for each box size.
    F = np.zeros(K, dtype=float)
    for k in range(K):
        n = nvals[k]
        if overlap:
            start = np.arange(0, N-n, step[k])
        else:
            start = range(0, N-n+1, step[k])
        local_means = [np.mean(Y[i:i+n]) for i in start]
        X = Y[start] - local_means
        C = np.cumsum(X - ymean[k])
        F[k] = np.sqrt(np.mean(C**2))

    # Fit F(n) to a power law and return the exponent.
    coeffs = np.polyfit(np.log(nvals), np.log(F), order)
    alpha = coeffs[0]

    if debug_plot:
        fig, axes = plt.subplots(1, 2, figsize=(8, 4))
        ax = axes[0]
        ax.plot(Y)
        ax.set_title('Integrated signal')
        ax = axes[1]
        ax.loglog(nvals, F, 'bo-', label='F(n)')
        ax.loglog(nvals, np.exp(coeffs[1]) * nvals**coeffs[0], 'r--',
                  label='Fit')
        ax.set_title('DFA plot')
        ax.legend(loc='best')
        ax.set_xlabel('Box size (n)')
        ax.set_ylabel('RMS fluctuation (F)')
        plt.tight_layout()
        plt.show()

    return alpha

# 读取Excel数据
data = pd.read_excel('data.xlsx', sheet_name='Sheet1')
X = data['Column1'].values

# 计算Hurst指数
hurst = dfa(X)

print('Hurst指数为:', hurst)

以上代码中的 `dfa()` 函数实现了DFA算法，可以计算出输入时间序列的Hurst指数。您可以将自己的Excel数据文件名替换掉代码中的 `data.xlsx`，并将数据列名替换掉 `X = data['Column1'].values` 中的 `'Column1'`，然后直接运行代码即可得到Hurst指数的计算结果。