Limit Theorems for the Symbolic Correlation Integral and the Renyi-2 Entropy under Short-range Dependence
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909610715119616 |
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| author | Schnurr, Alexander Silbernagel, Angelika Marin, Manuel Ruiz |
| author_facet | Schnurr, Alexander Silbernagel, Angelika Marin, Manuel Ruiz |
| contents | The symbolic correlation integral provides a way to measure the complexity of time series and dynamical systems. In the present article we prove limit results for an estimator of this quantity which is based on U-statistics under the assumption of short-range dependence. To this end, we slightly generalize classical limit results in the framework of 1-approximating functionals. Furthermore, we carefully analyze the limit variance. A simulation study with ARMA and ARCH time series as well as a real world data example are also provided. In the latter we show how our method could be used to analyze EEG data in the context of epileptic seizures. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_18726 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Limit Theorems for the Symbolic Correlation Integral and the Renyi-2 Entropy under Short-range Dependence Schnurr, Alexander Silbernagel, Angelika Marin, Manuel Ruiz Statistics Theory Probability 62M10, 37A35, 60F05, 37M10 The symbolic correlation integral provides a way to measure the complexity of time series and dynamical systems. In the present article we prove limit results for an estimator of this quantity which is based on U-statistics under the assumption of short-range dependence. To this end, we slightly generalize classical limit results in the framework of 1-approximating functionals. Furthermore, we carefully analyze the limit variance. A simulation study with ARMA and ARCH time series as well as a real world data example are also provided. In the latter we show how our method could be used to analyze EEG data in the context of epileptic seizures. |
| title | Limit Theorems for the Symbolic Correlation Integral and the Renyi-2 Entropy under Short-range Dependence |
| topic | Statistics Theory Probability 62M10, 37A35, 60F05, 37M10 |
| url | https://arxiv.org/abs/2410.18726 |