You're right. Traditionally curve fitting is associated with parameters. However I think the price observations you refer to can be measured without parameters, but then maybe I'm mistaken in thinking that fitting parameters from low extremes to high extremes is nonparametric.
As a base, I'll look at what I think about when I see the term "Curve Fitting." If that's different from what others are thinking, then I'll need to see some examples in order to comment.
So here's what I define curve fitting to be.
Let's say we have some share price data for a particular stock.
x1, x2, ..., xm
These provide corresponding returns of y1,y2, ..., ym (where m is the number of prices).
We can now plot these data on a graph. To keep things simple, I'll assume the underlying function is described by
y = ax + b (i.e. a linear function).
Now we need to find the coefficients, a and b such that the function best "fits" the data points.
We can then use the method of least squares to determine the coefficients a and b.
Once we have values for a and b, we can then plug in different values for x (i.e. different price values) and retrieve the corresponding y value (i.e. return).
This allows us to predict the return for an x value that wasn't in the original data set.
However there are a number of assumptions that need to be made as well as a well chosen initial data set. But, in a nutshell, that is what I view as curve fitting.
We can then expand on this to come up with a number of enhancements (which I did in my previous notes).
However I don't believe this is a practical way of doing anything with AI since some of the assumptions might not hold and the underlying function is much more complicated than y = ax + b
I'm not sure what you mean by saying you can change the indicator's length from 30 days to 14 days, but if you provide an example, I'll try to add some comments.
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