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I am trying to approximate the returns of asset A by means of a linear combination of other assets A'=aB0+bB1+c*B2....

I have this quite figured out but I'm not sure what a good metric for goodness of fit would be, so far I am only considering relative error (e=(rA-rA')/rA), and I'm concerned with distortions when rA is close to 0.

What would a better metric could be? Ideally it would penalize sign errors more than absolue value errors (ie, it is worse that rA' is positive when rA is negative).

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Please look up goodness of fit measures such as MSE (mean squared error) , R-squared , and adjusted R squared. There are also a number of others measures that have been developed to penalise complex model to avoid overfitting. These include mallow $C_P$, AIC, and BIC. This note would be a good start:

https://people.duke.edu/~rnau/compare.htm

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  • $\begingroup$ If I'm not mistaken all the measures you mention apply to a linear regression. Even though my model will be a linear one I am planning on evaluating different model choices, most of them not linear, hence I´m not sure such measures as R^2, MSE etc. would apply. $\endgroup$ – amiando Oct 8 '18 at 20:03
  • $\begingroup$ EDIT: MSE would indeed fit the issue, it is non specific to linear regression. Checking wikipedia entry for RMSE I found this paper analyzing error measures for fitted econometric models, very fitting to my application. faculty.weatherhead.case.edu/Fred-Collopy/researchArticles/… $\endgroup$ – amiando Oct 8 '18 at 20:09
  • $\begingroup$ Could you explain what you mean by linear combination please? And how does the model become non linear? $\endgroup$ – Magic is in the chain Oct 8 '18 at 20:12
  • $\begingroup$ Model approximates asset A returns forming the linear combination A'=aB0+bB1+c*B2, where Bi are different assets different from original asset A. The way in which linear weights {a,b,c,...} are chosen does not need to be a linear regression, I am considering things like binning different linear regression by volatility levels, or clustering methods. Hence it is not as simple as checking R^2 for a given LR, or the LR coefficients p-value/t-stat. $\endgroup$ – amiando Oct 8 '18 at 20:19
  • $\begingroup$ Ah ok! Good luck! $\endgroup$ – Magic is in the chain Oct 8 '18 at 20:29

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