ARIMA in Econometric Modeler

Hi,

I apologize for the simple question, but I'm very new to econometric analysis in MATLAB and not so experienced in Stata. Essentially, I have a database (attached Excel file) that I'm using to estimate an ARIMA(1,1,4) model for the variable "wpi". I've followed standard procedures in both Stata and MATLAB based on educational videos, but I'm receiving different coefficient estimates. I've made sure that both Stata and MATLAB use the first difference in the dependent variable, but I'm unsure what I'm doing wrong to get different estimates.

In fact, Stata Corp has a video on this exercise (https://www.youtube.com/watch?v=8xt4q7KHfBs), where the author [mistakenly used "wpi" instead of "log(wpi)"] and reports the results at minute 7:26. You can see the coefficient values there. When I fit the exact same model in MATLAB Econometric Modeller, my coefficient estimates are different. For example, the MATLAB constant estimate is 0.15, whereas in Stata it's 0.74, and so on.

Could you please help me diagnose the problem? I'm attaching the dataset here. Thank you very much.

Answer 1

[Subhajyoti]

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.