Python-生成特定自相关数组 [英] Python - generate array of specific autocorrelation

问题描述

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时表现出特定的自相关.理想情况下，我也想指定均值和方差，并从(多)中提取数据正态分布.但最重要的是，我想指定自相关.我该如何使用numpy或scikit-learn?

I am interested in generating an array(or numpy Series) of length N that will exhibit specific autocorrelation at lag 1. Ideally, I want to specify the mean and variance, as well, and have the data drawn from (multi)normal distribution. But most importantly, I want to specify the autocorrelation. How do I do this with numpy, or scikit-learn?

为了明确和精确，这是我要控制的自相关:

Just to be explicit and precise, this is the autocorrelation I want to control:

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

推荐答案

如果您只对滞后一时的自相关感兴趣，则可以生成维基百科页面上提到了此属性，但这并不难证明这一点.

If you are interested only in the auto-correlation at lag one, you can generate an auto-regressive process of order one with the parameter equal to the desired auto-correlation; this property is mentioned on the Wikipedia page, but it's not hard to prove it.

以下是一些示例代码:

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可让您在滞后一处设置所需的自相关，而可选参数mu和sigma可让您控制所生成信号的均值和标准差.

The parameter corr lets you set the desired auto-correlation at lag one and the optional parameters, mu and sigma, let you control the mean and standard deviation of the generated signal.

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