Question

Can anyone see if there is something wrong in my matlab code? My objective is to replicate this formula:

q can take value 1,2,3 and 5.
I constructed my vector Xt where each element are a cumulative sum of log(1+return) at each time (t) – for stock returns – first element is normalized to log(1).

Then to compute each element Sq(T,delta t) for the four values of q this is my matlab code:

for j=1:length(dt);
E=Xt(1:dt(j):end);
EE=diff(E(2:end));
EEE=diff(E(1:end-1));
Sqone(j)=sum(abs(EE-EEE).^1);
Sqtwo(j)=sum(abs(EE-EEE).^2);
Sqthree(j)=sum(abs(EE-EEE).^3);
Sqfive(j)=sum(abs(EE-EEE).^5); end;

Is there something wrong in the code above? I am asking this because I know there is something wrong since I am not getting the expected results. I am convinced that it is due to my code posted above.

the vector dt is a vector that goes from 1 to high number – depending on the size of Xt. But my vector dt is not the problem.

Thank you for all your help!

Answer 1

You are taking the difference twice. Once using diff and once using EE-EEE. The correct code is:

for j=1:length(dt);
E=Xt(1:dt(j):end);
EE=abs(diff(E));
Sqone(j)=sum(EE.^1);
Sqtwo(j)=sum(EE.^2);
Sqthree(j)=sum(EE.^3);
Sqfive(j)=sum(EE.^5); end;