# goodness of fit metric

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).

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

• 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. – amiando Oct 8 '18 at 20:03
• 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/… – amiando Oct 8 '18 at 20:09
• Could you explain what you mean by linear combination please? And how does the model become non linear? – Magic is in the chain Oct 8 '18 at 20:12
• 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. – amiando Oct 8 '18 at 20:19
• Ah ok! Good luck! – Magic is in the chain Oct 8 '18 at 20:29