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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.

 

The structure of power flows in transmission grids is evolving and is likelyto change significantly in the coming years due to the rapid growth ofrenewable energy generation that introduces randomness and bidirectionalpower flows. Another transformative aspect is the increasing penetrationof various smart-meter technologies. Inexpensive measurement devicescan be placed at practically any component of the grid. Using modeldata reflecting smart-meter measurements,we propose a two-stage procedure for detecting a fault in a regional powergrid. In the first stage, a fault is detected in real time. In the second stage,the faulted line is identified with a negligible delay. The approach uses onlythe voltage modulus measured at buses (nodes of the grid) as the input.Our method does not require prior knowledge of thefault type. The method is fully implemented in  R.Pseudo code and complete mathematical formulas are provided. 

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.