MATLAB: Tricky formula with cumulative sum

Question

I’m trying to calculate a ”standard deviation series” with a formula that involves a cumulative sum, but my matlab skills apparently aren’t sufficient to figure out how to type the formula in matlab.

The equation I want to write can be seen in step 5. Here: http://en.wikipedia.org/wiki/Rescaled_range

I have a vector “X” and a vector “u” and if I just use the cumulative sum command matlab doesn’t interpret the sum in the way I want it. This is how I want the calculation to look like:

Y(1) = ( X(1)-u(1) )^2

Y(2) = ( X(1)-u(2) )^2 + ( X(2)-u(2) )^2

Y(3) = ( X(1)-u(3) )^2 + ( X(2)-u(3) )^2+ ( X(3)-u(3) )^2

Y(4) = ( X(1)-u(4) )^2 + ( X(2)-u(4) )^2+ ( X(3)-u(4) )^2+ ( X(4)-u(4) )^2

….and so on

So in other words the calculation is increasing in size for each step and keeps X(1), X(2), X(3) and so on but only uses the most current value for “u” in each of the calculations.

This should be pretty simple right? How do I make it happen in matlab, any ideas?

Thanks

Answer 1

To use 'cumsum' you need to get the u's out of the squared expression. Let's assume X and u are row vectors.

 Y = cumsum(X.^2)-2*cumsum(X).*u+(1:size(u,2)).*u.^2;