The Joint Asymptotic Distribution of Entropy and Complexity
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912498405343232 |
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| author | Silbernagel, Angelika Weiß, Christian |
| author_facet | Silbernagel, Angelika Weiß, Christian |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_17625 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Joint Asymptotic Distribution of Entropy and Complexity Silbernagel, Angelika Weiß, Christian Statistics Theory Probability 62M10, 37A35, 60F05, 37M10 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. |
| title | The Joint Asymptotic Distribution of Entropy and Complexity |
| topic | Statistics Theory Probability 62M10, 37A35, 60F05, 37M10 |
| url | https://arxiv.org/abs/2507.17625 |