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短程依赖下符号相关积分与 Rényi 二阶熵的极限定理AI 解读

The symbolic correlation integral provides a way to measure the complexity of time series and dynamical systems. In the present article we prove limit results for an estimator of this quantity which is based on U-statistics under the assumption of short-range dependence. To this end, we slightly generalize classical limit results in the framework of 1-approximating functionals. Furthermore, we carefully analyze the limit variance. A simulation study with ARMA and ARCH time…

深度模式及其在动物追踪中的应用AI 解读

We establish a definition of ordinal patterns for multivariate data sets based on the concept of Tukey's halfspace depth. Given the definition of these \emph{depth patterns}, we are interested in the probabilities of observing specific patterns in time series. For this, we consider the relative frequency of depth patterns as natural estimators for their occurrence probabilities. Depending on the choice of reference distribution and the relation between reference and data…

序模式依赖与多元依赖度量AI 解读

Ordinal pattern dependence has been introduced in order to capture co-monotonic behavior between two time series. This concept has several features one would intuitively demand from a dependence measure. It was believed that ordinal pattern dependence satisfies the axioms which Grothe et al. (Journal of Multivariate Analysis 123, 2014) proclaimed for a multivariate measure of dependence. In the present article we show that this is not true and that there is a mistake in the…

长程依赖下的序模式依赖AI 解读

Ordinal pattern dependence is a multivariate dependence measure based on the co-movement of two time series. In strong connection to ordinal time series analysis, the ordinal information is taken into account to derive robust results on the dependence between the two processes. This article deals with ordinal pattern dependence for long-range dependent time series including mixed cases of short- and long-range dependence. We investigate the limit distributions for estimators…