Hi Alex,
I fit your data and got an almost similar constant estimate of around 0.15.
The difference in coefficient estimates can be due to:
- Estimation Methods
- Optimization Algorithms
- Convergence Criteria
In MATLAB Econometric Toolbox, the estimate method for ‘arima’ models uses ‘fmincon’ function from Optimization Toolbox as its numerical optimizer to perform maximum likelihood estimation. This optimization function requires initial values to begin the optimization process.
Given that the "fmincon" function primarily focuses on the log-likelihood value, it is possible to have surprisingly significant differences in coefficient values with virtually identical, or very close, log-likelihood values. The optimization summary ('info') and the estimated ‘arima’ model object are returned as a MATLAB structure array.
You may go through the following MathWorks documentation link to learn more about fitting univariate ARIMA models to data:
- 'arima': https://www.mathworks.com/help/econ/arima.estimate.html
- 'fmincon': https://www.mathworks.com/help/optim/ug/fmincon.html
- Optimization summary: https://www.mathworks.com/help/econ/arima.estimate.html
- Initial Values for Conditional Mean Model Estimation: https://www.mathworks.com/help/econ/initial-values-for-arima-estimation.html
I hope this helps.
