statsmodels.tsa.arima_process.ar2arma

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

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_desarray_like

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

pint

The length of desired AR lag polynomials.

qint

The length of desired MA lag polynomials.

nint

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

msestr, ‘ar’

Not used.

startndarray

Initial values to use when finding the approximation.

Returns:

ar_appndarray

The coefficients of the AR lag polynomials of the approximation.

ma_appndarray

The coefficients of the MA lag polynomials of the approximation.

restuple

The result of optimize.leastsq.

Notes

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