code: def FPE(N,rho, k=None):
      r
      #k #todo check convention. agrees with octave
      fpe = rho * (N + k + 1.) / (N- k -1)
      return fpe
docs: r"""Final prediction error criterion
  
      .. math:: FPE(k) = \frac{N + k + 1}{N - k - 1} \rho_k
  
      :validation: double checked versus octave.