Independent block identification in multivariate time series

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Abstract
In this‐30 work we propose a model selection criterion to estimate the points of independence of a random vector, producing a decomposition of the vector distribution function into independent blocks. The method, based on a general estimator of the distribution function, can be applied for discrete or continuous random vectors, and for i.i.d. data or dependent time series. We prove the consistency of the approach under general conditions on the estimator of the distribution function and we show that the consistency holds for i.i.d. data and discrete time series with mixing conditions. We also propose an efficient algorithm to approximate the estimator and show the performance of the method on simulated data. We apply the method in a real dataset to estimate the distribution of the flow over several locations on a river, observed at different time points.

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