Matstat Econometrics Matan - page 21
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4) Next time I will describe how the moduli sum minimization method is obtained instead of MNC)
Consider a linear regression model xi = a + b*i + ei over time i=1, 2, ..., n, where the errors ei are white noise with a Laplace distribution. The error density then is p(x,c)=0.5*c*exp(-c*|x|), log(p(x,c))=log(0.5)+log(c)-c*|x|
The likelihood function for noise will be L=p(d1,c)*p(d2,c)*...*p(dn,c), where di=xi-a-b*i is the residual of the model. The 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, so the problem of maximizing LL is solved in two steps
1) Minimizing S (because c>0) by a and b
2) maximizing LL by the parameter c, at a found value of S.
The second item is easily solved (as for exponential distribution) c=n/S
There is a problem with the first item, because in contrast to MNC this problem cannot be solved analytically (on paper) and can only be solved by approximate numerical methods on computer.
I wonder what happens if the ei errors are white noise with Alexei Nikolaev's distribution.
Petrosian's white envy of you.
Petrosian's white envy of you.
He'll be jealous of me when he finds out I mean it.
He would envy me if he knew I meant it.
Stop drinking.
Give up alcohol.
Not relevant.
I wonder what happens if the ei errors are white noise with the Alexei Nikolaev distribution.
Here is the chart for the day when there was a spike.
This is the next day's chart.
Alexey, how would you measure the amount of variance in pair trading? Assuming a linear relationship between the legs.
Is this question not explored within the cool hybrid of cybernetics and mathematics? )
Just a quick look at how the parameters (coefficients and variance of the residuals) of this very linear relationship change over time. Probably, we can only speak of the fact of sliding if the correlation and variance are approximately constant, and the shift fluctuates smoothly around some mean value of its own. Accordingly, one can try to use the parameters of this fluctuation to construct a TC)