statsmodels.tsa.forecasting.theta.ThetaModel.fit¶

ThetaModel.fit(use_mle=False, disp=False)[source]¶

Estimate model parameters.

Parameters:¶

use_mlebool, default False

Estimate the parameters using MLE by fitting an ARIMA(0,1,1) with a drift. If False (the default), estimates parameters using OLS of a constant and a time-trend and by fitting a SES to the model data.

dispbool, default True

Display iterative output from fitting the model.

Returns:¶

ThetaModelResult

Model results and forecasting

Notes

When using MLE, the parameters are estimated from the ARIMA(0,1,1)

\[X_t = X_{t-1} + b_0 + (\alpha-1)\epsilon_{t-1} + \epsilon_t\]

When estimating the model using 2-step estimation, the model parameters are estimated using the OLS regression

\[X_t = a_0 + b_0 (t-1) + \eta_t\]

and the SES

\[\tilde{X}_{t+1} = \alpha X_{t} + (1-\alpha)\tilde{X}_{t}\]