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Abstract:
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After reviewing recent work on change point detection in complex data structures, we will then focus on a method for the detection of a change point in a sequence of quantile functions, available through a large number of scalar observations at each time point. Under the null hypothesis, the quantile functions, or equivalently the distributions, are equal. Under the alternative hypothesis, there is a change point such the the distribution changes from one unknown form to another. The change point is unknown and the distributions before and after the potential change point are unknown. No parametric forms of the distributions before and after the change point are assumed. These distribution belong to general classes quantified by tail behavior. The decision about the existence of a change point is made sequentially, as new data arrive. The count of scalar observations available at each time point can increase to infinity. The detection procedure is based on a weighted version of the Wasserstein distance. Its asymptotic and finite sample validity is established. Its performance is illustrated by an application to cross-sectional returns on stocks in the S&P 500 index.
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