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¶

The coefficients of original AR lag polynomial, including lag zero.

p : int¶

The length of desired AR lag polynomials.

q : int¶

The length of desired MA lag polynomials.

n : int¶

The number of terms of the impulse_response function to include in the objective function for the approximation.

mse : str, 'ar'¶

Not used.

start : ndarray¶

Initial values to use when finding the approximation.

Returns:¶

• ar_app (ndarray) – The coefficients of the AR lag polynomials of the approximation.

• ma_app (ndarray) – The coefficients of the MA lag polynomials of the approximation.

• res (tuple) – The result of optimize.leastsq.

Notes

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