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)

$$X_t=X_{t-1}+b_0+(\alpha -1){ϵ}_{t-1}+{ϵ}_t$$

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

$${\tilde{X}}_{t+1}=\alpha X_t+(1-\alpha ){\tilde{X}}_t$$