code: def CAT(N, rho, k):
      r
      from numpy import zeros, arange
      cat = zeros(len(rho))
      for p in arange(1, len(rho)+1):
          rho_p = float(N)/(N-p)*rho[p-1]
          s = 0
          for j in range(1, p+1):
              rho_j = float(N)/(N-j)*rho[j-1]
              s = s + 1./rho_j
          #print(s, s/float(N), 1./rho_p)
          cat[p-1] = s/float(N) - 1./rho_p
      return cat
docs: r"""Criterion Autoregressive Transfer Function :
  
      .. math::  CAT(k) = \frac{1}{N} \sum_{i=1}^k \frac{1}{\rho_i} - \frac{\rho_i}{\rho_k}
  
      .. todo:: validation