statsmodels.tsa.arima_process.ar2arma

statsmodels.tsa.arima_process.ar2arma(ar_des, p, q, n=20, mse='ar', start=None)[source]

Find arma approximation to ar process

This finds the ARMA(p,q) coefficients that minimize the integrated squared difference between the impulse_response functions (MA representation) of the AR and the ARMA process. This does not check whether the MA lag polynomial of the ARMA process is invertible, neither does it check the roots of the AR lag polynomial.

Parameters:
  • ar_des (array_like) – coefficients of original AR lag polynomial, including lag zero
  • p (int) – length of desired AR lag polynomials
  • q (int) – length of desired MA lag polynomials
  • n (int) – number of terms of the impulse_response function to include in the objective function for the approximation
  • mse (string, 'ar') – not used yet,
Returns:

  • ar_app, ma_app (arrays) – coefficients of the AR and MA lag polynomials of the approximation
  • res (tuple) – result of optimize.leastsq

Notes

Extension is possible if we want to match autocovariance instead of impulse response function.