I have an assignment in which I need to choose statistical data from the Australian Bureau of Statistics and fit a curve to it.
I've chosen the slaughtering of bulls in NSW (first Excel file, C:143-C:612).
Using MATLAB's fminsearch I came up with the damped oscillation curve
$$ y=A_5+A_1e^{-A(2)x} \sin(A(3)x-A(4)) $$ with parameter values
$$A(1)=50.1759,A(2)=0.0080,A(3)=0.0341,A(4)=-1.0756,A(5)=78.8225 $$
which produced the following picture:
Next, I'm asked to use the Monte-Carlo Method to get further predictions, which I should then average. I can't see how to insert the randomness here, as each data point is only measured once, meaning that the suggested formula
$$newvalue=oldvaluemean+randn()*SEM $$
reduces to
$$newvalues=oldvaluemean=oldvalue $$
Am I doing anything wrong? How can one use the Monte Carlo method here?