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The concepts of physical dependence and approximability have been extensively used over the past two decades to quantify nonlinear dependence in time series. We show that most stochastic volatility models satisfy both dependence conditions, even if their realizations take values in abstract Hilbert spaces, thus covering univariate, multi‐variate and functional models. Our results can be used to apply to general stochastic volatility models a multitude of inferential procedures established for Bernoulli shifts.more » « less
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Abstract Localization of faults in a large power system is one of the most important and difficult tasks of power systems monitoring. A fault, typically a shorted line, can be seen almost instantaneously by all measurement devices throughout the system, but determining its location in a geographically vast and topologically complex system is difficult. The task becomes even more difficult if measurements devices are placed only at some network nodes. We show that regression graph neural networks we construct, combined with a suitable statistical methodology, can solve this task very well. A chief advance of our methods is that we construct networks that produce localization without having being trained on data that contain fault localization information. We show that a synergy of statistics and deep learning can produce results that none of these approaches applied separately can achieve.more » « less
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In the context of functional time series, we propose a significance test to distinguish between short memory with a change point and long range dependence. The test is based on coefficients of projections onto an optimal direction that captures the dependence structure of the latent stationary functions that are not observable due to a potential change point. The optimal direction must be estimated as well. The test statistic is constructed using the local Whittle estimator applied to these coefficients. It has standard normal distribution under the null hypothesis (change point) and diverges to infinity under the alternative (long range dependence). The article includes asymptotic theory, a simulation study and an application to curve‐valued time series derived from intraday asset prices.more » « less
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We develop statistical methodology for the quantification of risk of source-destination pairs in an internet network. The methodology is developed within the framework of functional data analysis and copula modeling. It is summarized in the form of computational algorithms that use bidirectional source-destination packet counts as input. The usefulness of our approach is evaluated by an application to real internet traffic flows and via a simulation study.more » « less
