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I am examining a time series which clearly has two "regimes" (by visual inspection), separated by what appears to be a structural break. I'm trying to get as much information as possible out of the series without relying on parametric models. Is there a way to test for this structural break without having to fit a time series model? I'm aware of the possibility for an $F$-test for equal variances, but this implicitly assumes that the series is Gaussian, which it is not. I'm also aware of the test of Bai and Perron, but this requires a linear model (http://www.econ.nyu.edu/user/baij/econometrica98.pdf).

I'm interested in detecting a change in some (robust) measure of location and scale. Any pointers as to whether and how I can accomplish this "model-free" are much appreciated.

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In the statistical literature there is quite some work on robust change point (aka structural break) tests. For example from the group in Prague/Cologne/... around Hušková, Antoch, Steinebach & Co (see e.g., http://dx.doi.org/10.1007/978-3-642-35494-6_11) or the guys at Dortmund/Bochum/... around Fried, Dehling & Co (see e.g., http://www.birs.ca/workshops/2014/14w5157/files/Dehling.pdf). Both of the links provide numerous references in that literature.

Having said that, if your sample size is large enough for the central limit theorem to kick in, you might still be ok to use standard tests based on linear regressions. The justification for most of these tests (e.g., sup$F$, OLS-based CUSUM, Nyblom-Hansen, etc.) is asymptotic anyway. So you don't rely on the time series being Gaussian but the methods also work if the asymptotic approximations work.

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