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I have scanned rigorously on the internet but the information regarding the SURE methodology seems surprisingly very little (at least with regard to its application in finance). I would have imagined if Fama French used this technique then, surely there might information on it out there. However, it's the exact opposite case.

My problem is that I have already calculated all the estimates for intercept terms and respective betas for the 25 portfolios using OLS. Only now I am realizing that I should apparently use this SURE model and not the OLS method.

This was the lecture (https://www.youtube.com/watch?v=Csajx7C3m5M&t=3723s) by Prof. Klaus Grobys I was watching when it occurred to me that I should be using the SURE model because the intercepts would go on to be included in the GRS test statistic.

What is the correct method?

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There unfortunately is no "correct" regression method, all methods will have pros and cons with regards to the goals intended of the model. It is important to note what is often cited in academia aka Fama–MacBeth (time-series) regression is not the standard for the industry aka OLS with Newey West standard errors (cross-sectional) regression.

There's a wealth of knowledge from previous posts below on the topic.

How to build a factor model?

Which approach to estimating fundamental factor models is better, cross-sectional (unobservable) factors or time-series (observable) factors?

When should you build your own equity risk model?

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