# Comparing curve fits

I am experimenting with building a forward curve. I have a piece of code which constructs my prototype curve. I've got a curve sample which was constructed manually and I use it as the baseline - the "true" forward curve I am trying to replicate with my model.

While experimenting with different models and parameterizations, I'm wondering how to evaluate the goodness of fit in this case so that I can answer why prototype curve X is better than prototype curve Y.

At it's most basic, I can use least-squares - MMSE (minimum mean squared error). In such case, I'll take $$y_i$$ from the manual curve and $$\hat{y}_i$$ form my prototype and if $$\frac{1}{n} \sum{(y_i - \hat{y}_i)}$$ from prototype X is smaller than MMSE from prototype Y, then prototype X is a better model.

I am wondering if I can use something like AIC/BIC. However, I'm not sure they apply in this case as the models will have the same input parameters - they just use them differently (i.e. the logic is different).

I'm also wondering if maximum-likelihood would work or if QL (quasi-likelihood) could be used.

How would you compare 2 prototype curves relative to a "true" curve.

• For forward curves I would also consider (good) smoothness and (no) oscillatory behavior as crucial “quality indicators”. – Kermittfrog Nov 8 '20 at 18:03