This paper introduces rank-based tests for the cointegrating rank in an Error CorrectionModel with i.i.d. elliptical innovations. The tests are asymptotically distribution-free,and their validity does not depend on the actual distribution of the innovations. Thisresult holds despite the fact...

High-dimensional time series may well be the most common type of dataset in the socalled“big data” revolution, and have entered current practice in many areas, includingmeteorology, genomics, chemometrics, connectomics, complex physics simulations, biologicaland environmental research,...

In this paper, we address the problem of dimension reduction for time series of functional data (X_t:t\in \mathbb{Z}). Such functional timeseries frequently arise, e.g. when a continuous-time process is segmented into some smaller natural units, such as days. Then each X_trepresents one intraday...

We propose new concepts of statistical depth, multivariate quantiles,ranks and signs, based on canonical transportation maps between a distributionof interest on IRd and a reference distribution on the d-dimensionalunit ball. The new depth concept, called Monge-Kantorovich depth, specializesto...

We propose a new sequential monitoring scheme for changes in the parameters of a multivariate time series. In contrast to procedures proposed in the literature which compare an estimator from the training sample with an estimator calculated from the remaining data, we suggest to divide the...

Since the introduction by Koenker and Bassett, quantile regression has become increasingly important in many applications. However, many non-parametric conditional quantile estimates yield crossing quantile curves (calculated for various "p"  is an element of  (0, 1)). We propose a new...