By Kardi Teknomo, PhD .
The usual way to compute time-variance is given by equation (2). I put here again for your convenient:
Changing to makes equation (2) becomes
Putting out the last term from equation (2) gives
(b) ( why? )
Equation (3) can be rearranged into
The second term of the right hand side of equation (b) can be manipulated as
Put back the second term into equation (b) and replace the third term with equation (a) becomes
Preferable reference for this tutorial is
Teknomo, Kardi. (2006) Recursive Average and Variance.