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

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