{"ID":2891417,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.17625","arxiv_id":"2507.17625","title":"The Joint Asymptotic Distribution of Entropy and Complexity","abstract":"We derive the asymptotic distribution of ordinal-pattern frequencies under weak dependence conditions and investigate the long-run covariance matrix not only analytically for moving-average, Gaussian, and the novel generalized coin-tossing processes, but also approximately by a simulation-based approach. Then, we deduce the asymptotic distribution of the entropy-complexity pair, which emerged as a popular tool for summarizing the time-series dynamics. Here, we make the necessary distinction between a uniform and a non-uniform ordinal pattern distribution and, thus, obtain two different limit theorems. On this basis, we consider a test for serial dependence and check its finite-sample performance. Moreover, we use our asymptotic results to approximate the estimation uncertainty of entropy-complexity pairs.","short_abstract":"We derive the asymptotic distribution of ordinal-pattern frequencies under weak dependence conditions and investigate the long-run covariance matrix not only analytically for moving-average, Gaussian, and the novel generalized coin-tossing processes, but also approximately by a simulation-based approach. Then, we deduc...","url_abs":"https://arxiv.org/abs/2507.17625","url_pdf":"https://arxiv.org/pdf/2507.17625v1","authors":"[\"Angelika Silbernagel\",\"Christian Weiß\"]","published":"2025-07-23T15:53:30Z","proceeding":"math.ST","tasks":"[\"math.ST\",\"math.PR\"]","methods":"[]","has_code":false}