statsmodels.tsa.arima_model.ARIMA.fit

ARIMA.fit(start_params=None, trend='c', method='css-mle', transparams=True, solver='lbfgs', maxiter=50, full_output=1, disp=5, callback=None, **kwargs)

Fits ARIMA(p,d,q) model by exact maximum likelihood via Kalman filter.

Parameters:

start_params : array-like, optional

Starting parameters for ARMA(p,q). If None, the default is given by ARMA._fit_start_params. See there for more information.

transparams : bool, optional

Whehter or not to transform the parameters to ensure stationarity. Uses the transformation suggested in Jones (1980). If False, no checking for stationarity or invertibility is done.

method : str {‘css-mle’,’mle’,’css’}

This is the loglikelihood to maximize. If “css-mle”, the conditional sum of squares likelihood is maximized and its values are used as starting values for the computation of the exact likelihood via the Kalman filter. If “mle”, the exact likelihood is maximized via the Kalman Filter. If “css” the conditional sum of squares likelihood is maximized. All three methods use start_params as starting parameters. See above for more information.

trend : str {‘c’,’nc’}

Whether to include a constant or not. ‘c’ includes constant, ‘nc’ no constant.

solver : str or None, optional

Solver to be used. The default is ‘lbfgs’ (limited memory Broyden-Fletcher-Goldfarb-Shanno). Other choices are ‘bfgs’, ‘newton’ (Newton-Raphson), ‘nm’ (Nelder-Mead), ‘cg’ - (conjugate gradient), ‘ncg’ (non-conjugate gradient), and ‘powell’. By default, the limited memory BFGS uses m=12 to approximate the Hessian, projected gradient tolerance of 1e-8 and factr = 1e2. You can change these by using kwargs.

maxiter : int, optional

The maximum number of function evaluations. Default is 50.

tol : float

The convergence tolerance. Default is 1e-08.

full_output : bool, optional

If True, all output from solver will be available in the Results object’s mle_retvals attribute. Output is dependent on the solver. See Notes for more information.

disp : bool, optional

If True, convergence information is printed. For the default l_bfgs_b solver, disp controls the frequency of the output during the iterations. disp < 0 means no output in this case.

callback : function, optional

Called after each iteration as callback(xk) where xk is the current parameter vector.

kwargs

See Notes for keyword arguments that can be passed to fit.

Returns:

statsmodels.tsa.arima.ARIMAResults class

See also

statsmodels.base.model.LikelihoodModel.fit

for more information on using the solvers.

ARIMAResults

results class returned by fit

Notes

If fit by ‘mle’, it is assumed for the Kalman Filter that the initial unkown state is zero, and that the inital variance is P = dot(inv(identity(m**2)-kron(T,T)),dot(R,R.T).ravel(‘F’)).reshape(r, r, order = ‘F’)