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The primary is Thiel’s regression. Unfortunately, the assumption of independence is too strong, and so the results should not be considered trustworthy. The second is to take the log of prices, which works in a univariate mannequin, but the issue comes in the multivariate case. The distribution in the multivariate case turns out to be the hyperbolic secant distribution. It lacks a covariance structure, so any squares minimizing tool will generate potentially spurious results. The third case is quantile regression. It is less precise than either of the 2 strategies, but the results wouldn’t be suspect. Quantile regression produces an unbiased estimator, and I believe it could be improved upon by imposing something extra like Rothenberg’s estimator for the Cauchy distribution. Rothenberg, Thomas J.; Fisher, Franklin, M.; Tilanus, C.B. 1964). “A notice on estimation from a Cauchy sample”. Journal of the American Statistical Association. For the next two videos that I am producing, I include some content material from regression.
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