I have a time series in which each point is constructed manually. I am trying to automate the construction of this curve with a model. This is not a mathematical model but a set of rules for constructing each point along the curve based on various conditions.
I have a manually constructed curve which I regard as the "true" curve and my models will aim to get as close a fit to it as possible.
My question is: what statistic should I use to judge the goodness of fit of a model?
I am currently thinking of using least-squares - minimum mean squared error. This would be the simplest, least sophisticated approach.
Another approach would be to regress the "true" curve against the model curve and then analyse this fit? Would this work? For a perfect fit I'd expect a correlation close to 1 and a R-squared close to 1.
Like I said, the model does not have a mathematical formulation, more of a set of logical rules which produce a number for a particular point in time. The model is deterministic - if the same model with the same parametrisation is run twice it should produce the same output.