mql5

Two traders are talking (taken from this mql5 thread):

Consider a linear regression model xi = a + b * i + ei in time i = 1, 2, ..., n, where the errors ei are white noise with the Laplace distribution. The error density then has the form p (x, c) = 0.5 * c * exp (-c * | x |), log (p (x, c)) = log (0.5) + log (c) -c * | x |

The likelihood function for the noise will have the form L = p (d1, c) * p (d2, c) * ... * p (dn, c), where di = xi-ab * i are the residuals of the model. Logarithm of the likelihood function LL = n * log (0.5) + n * log (c) -c * S, where S = | d1 | + | d2 | + ... + | dn |. S does not depend on the parameter c, therefore the problem of maximizing LL is solved in two stages

and it is the reply:

This is all true. The question is what exactly to take for the sliding between the two rows. For example, there is a traditional opinion that the length of the perpendicular to the regression line. But it seems to me that this is not quite the right way. For it gives a separation not relative to the previous values, but relative to a certain midpoint of them. Such a substance as the "asymmetry" of the opening is lost, and I would like to feel it.

And what do you think?

• minimization of S (since c> 0) with respect to a and b ?
  or
• maximization of LL with respect to the parameter c, with the found value of S ?