title: Why do statsmodels's correlation and autocorrelation functions give different results in Python?
body: <p>I need to obtain the correlation between two different series A and B as well as the autocorrelations of A and B. Using the correlation functions provided by statsmodels I got different results, it's not the same to calculate the autocorrelation of A and to calculate the correlation between A and A, Why are the results different?.</p>
  
  <p>Here is an example of the behavior I'm talking about:</p>
  
  <pre><code>import numpy as np
  from matplotlib import pyplot as plt
  from statsmodels.tsa.stattools import ccf
  from statsmodels.tsa.stattools import acf
  
  #this is the data series that I want to analyze
  A = np.array([np.absolute(x) for x in np.arange(-1,1.1,0.1)])
  
  #This is the autocorrelation using statsmodels's autocorrelation function
  plt.plot(acf(A, fft=True))
  </code></pre>
  
  <p><img src="https://i.stack.imgur.com/hgLd5.png" alt="enter image description here"></p>
  
  <pre><code>#This the autocorrelation using statsmodels's correlation function
  plt.plot(ccf(A, A))
  </code></pre>
  
  <p><img src="https://i.stack.imgur.com/o3Uug.png" alt="enter image description here"></p>