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Optimization Method for Least Squares

Posted: Fri Feb 16, 2018 9:49 pm
I noticed with some methods the convergence method is shown at the estimation output screen, but with OLS the convergence method is omitted. I checked the documentation, but couldn't find details about the convergence method of OLS. Getting OLS to converge is hardly a challenge, but I'm guessing under the hood somewhere there is a convergence method for OLS. If so, what is it?

Re: Optimization Method for Least Squares

Posted: Fri Feb 16, 2018 11:59 pm
Ols does not have convergence. There is nothing to converge.

Re: Optimization Method for Least Squares

Posted: Sat Feb 17, 2018 12:31 am
You are more knowledgeable about this than myself, but from what I understand, technically OLS is still a matter of convergence, it just tends to converge after only 1 iteration. Let me try to rephrase my question.

OLS is a simple method, it doesn't need a fancy convergence method per say. However, OLS is trying to minimize the squared residuals, that can be seen as an optimization problem. The question is, what is the optimization method? What is the method eviews uses to make sure it arrives at the "line of best fit". As simple as OLS is, it still needs to be optimized right? I'm just curious. Maybe it's gradient descent? If the optimization method is in the documentation somewhere, please refer me to that.

Re: Optimization Method for Least Squares

Posted: Sat Feb 17, 2018 8:37 am
betaHat=inv(X'X)X'y

Re: Optimization Method for Least Squares

Posted: Sat Feb 17, 2018 10:52 am
Its an optimization in the same sense that find the optimal value of X such that X+3=0 is an optimization.

Re: Optimization Method for Least Squares

Posted: Tue Feb 20, 2018 3:38 pm
It's an optimization, but because of the linearity of the specification, there is a closed form solution which does not require iteration. You are welcome to think of that as convergence in the sense that given the preliminary estimate, there is no improvement to be gained by perturbing the coefficients, though most people would not view the problem in those terms.