我对生成长度为N的数组(或numpy系列)感兴趣,该数组将在滞后1时显示出特定的自相关。理想情况下,我也想指定均值和方差,并从(多)正态分布中提取数据。但最重要的是,我想指定自相关。我该如何使用numpy或scikit-learn?

简而言之,这就是我要控制的自相关:

numpy.corrcoef(x[0:len(x) - 1], x[1:])[0][1]

最佳答案

如果您只对滞后一时的自相关感兴趣,则可以生成阶数为auto-regressive process且参数等于所需自相关的Wikipedia page。在上提到了此属性,但并不难证明。

这是一些示例代码:

import numpy as np

def sample_signal(n_samples, corr, mu=0, sigma=1):
    assert 0 < corr < 1, "Auto-correlation must be between 0 and 1"

    # Find out the offset `c` and the std of the white noise `sigma_e`
    # that produce a signal with the desired mean and variance.
    # See https://en.wikipedia.org/wiki/Autoregressive_model
    # under section "Example: An AR(1) process".
    c = mu * (1 - corr)
    sigma_e = np.sqrt((sigma ** 2) * (1 - corr ** 2))

    # Sample the auto-regressive process.
    signal = [c + np.random.normal(0, sigma_e)]
    for _ in range(1, n_samples):
        signal.append(c + corr * signal[-1] + np.random.normal(0, sigma_e))

    return np.array(signal)

def compute_corr_lag_1(signal):
    return np.corrcoef(signal[:-1], signal[1:])[0][1]

# Examples.
print(compute_corr_lag_1(sample_signal(5000, 0.5)))
print(np.mean(sample_signal(5000, 0.5, mu=2)))
print(np.std(sample_signal(5000, 0.5, sigma=3)))


参数corr允许您将所需的自相关设置为滞后一,而可选参数musigma可以控制所生成信号的平均值和标准偏差。

08-25 00:07