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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?

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This type of problem is called change-point analysis. A lot of work has been done on it (and it's more common to look for changes in the mean, rather than changes in the variance), and there are many packages you can use for it in R, Matlab, etc.

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  • $\begingroup$ Thanks for the reply, Douglas. I was just wondering if this would be a decent statistic to detect change-points in piece-wise stationary processes. The same idea may be applied sample mean, in case one is interested in change-point analysis of the mean. $\endgroup$
    – Mohan
    Commented Apr 19, 2013 at 10:47
  • $\begingroup$ @Mohan: It sounds like a reasonable approach, with some problems you have mentioned, plus some others like difficulty identifying multiple change points. You should at least look at the built-in change-point analysis functions in Matlab. $\endgroup$
    – Douglas Zare
    Commented Apr 19, 2013 at 19:47

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