# statsmodels.tsa.arima_model.ARIMA¶

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

Autoregressive Integrated Moving Average ARIMA(p,d,q) Model

Parameters: endog (array-like) – The endogenous variable. order (iterable) – The (p,d,q) order of the model for the number of AR parameters, differences, and MA parameters to use. exog (array-like, optional) – An optional array 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.

Notes

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 statsmodels.tsa.arima_model.ARIMA.fit. Therefore, for now, css and mle refer to estimation methods only. This may change for the case of the css model in future versions.

Methods

 fit([start_params, trend, method, …]) Fits ARIMA(p,d,q) model by exact maximum likelihood via Kalman filter. from_formula(formula, data[, subset, drop_cols]) Create a Model from a formula and dataframe. geterrors(params) Get the errors of the ARMA process. hessian(params) Compute the Hessian at params, information(params) Fisher information matrix of model initialize() Initialize (possibly re-initialize) a Model instance. 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, typ, dynamic]) ARIMA model in-sample and out-of-sample prediction score(params) Compute the score function at params.

Attributes

 endog_names Names of endogenous variables exog_names