The bootstrap for testing the equality of two multivariate time series with an application to financial markets

Financiado para publicación en acceso aberto: Universidade da Coruna/CISUG[Abstract]: The problem of testing the equality of the generating processes of two multivariate time series is addressed in this work. To this aim, we construct four tests based on a distance measure between stochastic processes. The metric is defined in terms of the quantile cross-spectral densities of both processes. A proper estimate of this dissimilarity is the cornerstone of the proposed tests. The first test employs the asymptotic distribution of the estimate, which we derive from some standard results on complex random variables and which is useful in its own right. The bad behaviour of this test when compared with alternative ones is shown. The three remaining techniques are based on the bootstrap. Specifically, a particular bootstrap method for spectral densities and extensions of the moving blocks bootstrap and the stationary bootstrap are used for their construction. The approaches are assessed in a broad range of cenarios under the null and the alternative hypothesis. The results from the analyses show that the procedure based on the stationary bootstrap exhibits the best overall performance in terms of both ize and power. The proposed techniques are used to answer the question about whether or not the dotcom bubble crash of 2000s permanently impacted the global market behavior.Ministerio de Economia y Competitividad (MINECO); MTM2017-82724-R, PID2020-113578RB-100Xunta de Galicia; ED431C-2020-14Centro de Investigacion del Sistema Universitario de Galicia "CITIC"; ED431G 2019/0

Hard and soft clustering of categorical time series based on two novel distances with an application to biological sequences

Financiado para publicación en acceso aberto: Universidade da Coruña/CISUG.[Abstract]: Two novel distances between categorical time series are introduced. Both of them measure discrepancies between extracted features describing the underlying serial dependence patterns. One distance is based on well-known association measures, namely Cramer's v and Cohen's κ. The other one relies on the so-called binarization of a categorical process, which indicates the presence of each category by means of a canonical vector. Binarization is used to construct a set of innovative association measures which allow to identify different types of serial dependence. The metrics are used to perform crisp and fuzzy clustering of nominal series. The proposed approaches are able to group together series generated from similar stochastic processes, achieve accurate results with series coming from a broad range of models and are computationally efficient. Extensive simulation studies show that both hard and soft clustering algorithms outperform several alternative procedures proposed in the literature. Two applications involving biological sequences from different species highlight the usefulness of the introduced techniques.Xunta de Galicia; ED431G 2019/01Xunta de Galicia; ED431C-2020-14The research of Ángel López-Oriona and José A. Vilar has been supported by the Ministerio de Economía y Competitividad (MINECO) grants MTM2017-82724-R and PID2020-113578RB-100, the Xunta de Galicia (Grupos de Referencia Competitiva ED431C-2020-14), and the Centro de Investigación del Sistema Universitario de Galicia “CITIC” grant ED431G 2019/01; all of them through the European Regional Development Fund (ERDF). This work has received funding for open access charge by Universidade da Coruña/CISUG. The author Ángel López-Oriona is very grateful to researcher Maite Freire for her lessons about DNA theory