Mark on curve fitting:
You define x as the data variable and y as the yield variable. Then you say(I am analysing your statement without first reading to tyhe end of what yu say):
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..
I would think here that this is possibly unclear as to the purpose of what you are wanting to do: Optimization of the yield function.
If you plot both the input data and the yield data then it would appear that you should do the following:
1) Fit a function on the Yield Data y1, y2, y3,.... and get a function for the Yield as a function of time: F(T)=F(y)
2) Then the question is: How can I maximize the Yield Function F(T) for the investment over a period?(I interpret this is an integration of (F-I) over time, with both F and I=investment being time functions(being dependent on x as well!).
3) To maximise the Yield you should not destroy the original data, as this is the input as this is the independent dataset. What then is the purpose of curve fitting on the x-data?
If you do that then you pollute the input and the fitted-curve-input will change the Yield, possibly in a negative way if you use the new x-data from the x-fit.
4) I would think that a fit on the y-data using the real x-data giving:
y1=F(x1), y2=F(x2),--- yn=F(xn). The real yield is fitted functionally to the real data.
This would keep the real x-data as input unpolluted.
Now I will read on in your statement:
From what you say you might mean more or less the same, as I stated as an objective, but I am not sure. From what you say I interpret that you vary the coefficients in the y=ax+b curve to get a yield function y=F(xn) where y is the yield as a fitted curve(not the y-data points). You do not, as I see now, appear to fit a curve through the x-data as I assumed first you did as well(This was my interpretation from your previous discussions).
In any case, what you propose is, I think, not the same thing! I see Yield as an objective function as an integration over the time-defined instantaneous yields yn=F(xn).
My formulation is not yet rigorously defined, but it more or less fits my view on Yield Optimisation:
The instantaneous value yn of the portfolio as a result of buy/sell triggers from stock prices x(which invoke a buy/sell instruction) and this creates an accumulated Yield Function F=F(yn,tn)over time T.
Is what I mean the same as what you mean?
I see the Yield Function as an accumulation of many yields yn rather than the response curve y=F(xn).
Now, I think this is certainly an OT-Issue(ON TOPIC).
Conrad
