method, method='cmle', ic=None, trend='c', transparams=True, start_params=None, solver='lbfgs', maxiter=35, full_output=1, disp=1, callback=None, **kwargs)[source]

Fit the unconditional maximum likelihood of an AR(p) process.


If ic is None, then maxlag is the lag length used in fit. If ic is specified then maxlag is the highest lag order used to select the correct lag order. If maxlag is None, the default is round(12*(nobs/100.)**(1/4.))

methodstr {‘cmle’, ‘mle’}, optional

cmle - Conditional maximum likelihood using OLS mle - Unconditional (exact) maximum likelihood. See solver and the Notes.

icstr {‘aic’,’bic’,’hic’,’t-stat’}

Criterion used for selecting the optimal lag length. aic - Akaike Information Criterion bic - Bayes Information Criterion t-stat - Based on last lag hqic - Hannan-Quinn Information Criterion If any of the information criteria are selected, the lag length which results in the lowest value is selected. If t-stat, the model starts with maxlag and drops a lag until the highest lag has a t-stat that is significant at the 95 % level.

trendstr {‘c’,’nc’}

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

The below can be specified if method is ‘mle’
transparamsbool, optional

Whether or not to transform the parameters to ensure stationarity. Uses the transformation suggested in Jones (1980).

start_paramsarray-like, optional

A first guess on the parameters. Default is cmle estimates.

solverstr or None, optional

Solver to be used if method is ‘mle’. 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’.

maxiterint, optional

The maximum number of function evaluations. Default is 35.


The convergence tolerance. Default is 1e-08.

full_outputbool, 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.

dispbool, optional

If True, convergence information is output.

callbackfunction, optional

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


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


Jones, R.H. 1980 “Maximum likelihood fitting of ARMA models to time

series with missing observations.” Technometrics. 22.3. 389-95.