English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The modeling and identification of time series data with a long memory are important in various fields. The streamflow discharge is one such example that can be reasonably described as an aggregated stochastic process of randomized affine processes where the probability measure, we call it reversion measure, for the randomization is not directly observable. Accurate identification of the reversion measure is critical because of its omnipresence in the aggregated stochastic process. However, the modeling accuracy is commonly limited by the available real‐world data. We resolve this issue by proposing the novel upper and lower bounds of a statistic of interest subject to ambiguity of the reversion measure. Here, we use the Tsallis value‐at‐risk (TsVaR) as a convex risk functional to generalize the widely used entropic value‐at‐risk (EVaR) as a sharp statistical indicator. We demonstrate that the EVaR cannot be used for evaluating key statistics, such as mean and variance, of the streamflow discharge due to the blowup of some exponential integrand. We theoretically show that the TsVaR can avoid this issue because it requires only the existence of some polynomial moment, not exponential moment. As a demonstration, we apply the semi‐implicit gradient descent method to calculate the TsVaR and corresponding Radon–Nikodym derivative for time series data of actual streamflow discharges in mountainous river environments.

Statistical evaluation of a long‐memory process using the generalized entropic value‐at‐risk