class statsmodels.tsa.arima_model.ARMA(endog, order, exog=None, dates=None, freq=None, missing='none')[source]

Autoregressive Moving Average ARMA(p,q) Model


endog : array-like

The endogenous variable.

order : iterable

The (p,q) order of the model for the number of AR parameters, differences, and MA parameters to use.

exog : array-like, optional

An optional arry of exogenous variables. This should not include a constant or trend. You can specify this in the fit method.

dates : array-like of datetime, optional

An array-like object of datetime objects. If a pandas object is given for endog or exog, it is assumed to have a DateIndex.

freq : str, optional

The frequency of the time-series. A Pandas offset or ‘B’, ‘D’, ‘W’, ‘M’, ‘A’, or ‘Q’. This is optional if dates are given.


If exogenous variables are given, then the model that is fit is

\phi(L)(y_t - X_t\beta) = \theta(L)\epsilon_t

where \phi and \theta are polynomials in the lag operator, L. This is the regression model with ARMA errors, or ARMAX model. This specification is used, whether or not the model is fit using conditional sum of square or maximum-likelihood, using the method argument in Therefore, for now, css and mle refer to estimation methods only. This may change for the case of the css model in future versions.


fit([start_params, trend, method, ...]) Fits ARMA(p,q) model using exact maximum likelihood via Kalman filter.
geterrors(params) Get the errors of the ARMA process.
hessian(params) Compute the Hessian at params,
loglike(params[, set_sigma2]) Compute the log-likelihood for ARMA(p,q) model
loglike_css(params[, set_sigma2]) Conditional Sum of Squares likelihood function.
loglike_kalman(params[, set_sigma2]) Compute exact loglikelihood for ARMA(p,q) model by the Kalman Filter.
predict(params[, start, end, exog, dynamic]) ARMA model in-sample and out-of-sample prediction
score(params) Compute the score function at params.