Say that the variance of a constant mean scalar stochastic process can take finite number of values. The problem is to detect the the point of break in variance as observation data comes in.
I tried the following: (1)Compute sample variance going forward (Call it Vf(n)), starting from the first data point, (2)Compute the sample variance going backward (Call it Vb(n)), starting from the last data point observed, (3)Compute |Vb(N-n)-Vf(n)|.
Now as I observed from some simulations on MATLAB, |Vb(N-n)-Vf(n)| has a maxima/minima at the break points. But there lots of maximas/minimas around the starting data point and last data point, which have to be filtered out.
Let me know your comments. In particular, is this somehow related to sequential hypothesis testing? What do we do if the mean of the process is not a constant? What about vector random processes?