## Optimization Method for Least Squares

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AbnormalDistribution
Posts: 4
Joined: Fri Feb 09, 2018 12:07 pm

### Optimization Method for Least Squares

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?

EViews Gareth
Fe ddaethom, fe welon, fe amcangyfrifon
Posts: 12036
Joined: Tue Sep 16, 2008 5:38 pm

### Re: Optimization Method for Least Squares

Ols does not have convergence. There is nothing to converge.

AbnormalDistribution
Posts: 4
Joined: Fri Feb 09, 2018 12:07 pm

### Re: Optimization Method for Least Squares

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.

startz
Non-normality and collinearity are NOT problems!
Posts: 3424
Joined: Wed Sep 17, 2008 2:25 pm

### Re: Optimization Method for Least Squares

betaHat=inv(X'X)X'y

EViews Gareth
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### Re: Optimization Method for Least Squares

Its an optimization in the same sense that find the optimal value of X such that X+3=0 is an optimization.

EViews Glenn
EViews Developer
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Joined: Wed Oct 15, 2008 9:17 am

### Re: Optimization Method for Least Squares

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.

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