To Do

[eigenfoo]

• Check 4 uses the naive difference of annualizations in order to approximate the actual average. Investigative the math behind this. Why is this approximation good? Does it always hold? Does it get better with increasing n? Why/why not?
  Andre's suggestions: examine the difference of annualizations vs annualization of difference numerically.
  Per Andre's suggestion, we could define Pi-Bi = i*e + b, where e is some number, for all i. Then let e go to zero. Ann(Pi-Bi) should approach b in a continuous manner.
  Then pick some numbers for Bi (or Pi), for all i, and see how Ann(Pi)-Ann(Bi) behaves in the limit that e goes to 0. Plot a graph with [Ann(P-B) - (Ann(P)-Ann(B))] on the y-axis, and e on the x axis.
  Repeat for multiple values of N. Multiple curves on the same set of axes.
• Technical problem with MATLAB Ann, check 2: the following code seems to reject solutions if the min(D) = max(D)...
  indices = find(A_vals < min(D) | A_vals > max(D));
A_vals(indices) = [];
A_vals
• Write up pseudo-code for Ann: useful for multi-language programming.
• Code Ann1 in Python
• Try Ann2 on real data: what kind of numbers do we get? With random numbers (distributed uniformly between 0 and 1), the numbers are very small. Usually, we are lucky to get something that is only on the negative 1-3 order of magnitude,