Testing for unspecified periodicities in binary time series
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914971523219456 |
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| author | Schmidtke, Finn Vetter, Mathias |
| author_facet | Schmidtke, Finn Vetter, Mathias |
| contents | Given independent random variables $Y_1, \ldots, Y_n$ with $Y_i \in \{0,1\}$ we test the hypothesis whether the underlying success probabilities $p_i$ are constant or whether they are periodic with an unspecified period length of $r \ge 2$. The test relies on an auxiliary integer $d$ which can be chosen arbitrarily, using which a new time series of length $d$ is constructed. For this new time series, the test statistic is derived according to the classical $g$ test by Fisher. Under the null hypothesis of a constant success probability it is shown that the test keeps the level asymptotically, while it has power for most alternatives, i.e. typically in the case of $r \ge 3$ and where $r$ and $d$ have common divisors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_10203 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Testing for unspecified periodicities in binary time series Schmidtke, Finn Vetter, Mathias Statistics Theory 62M10, 62M15, 62G10 Given independent random variables $Y_1, \ldots, Y_n$ with $Y_i \in \{0,1\}$ we test the hypothesis whether the underlying success probabilities $p_i$ are constant or whether they are periodic with an unspecified period length of $r \ge 2$. The test relies on an auxiliary integer $d$ which can be chosen arbitrarily, using which a new time series of length $d$ is constructed. For this new time series, the test statistic is derived according to the classical $g$ test by Fisher. Under the null hypothesis of a constant success probability it is shown that the test keeps the level asymptotically, while it has power for most alternatives, i.e. typically in the case of $r \ge 3$ and where $r$ and $d$ have common divisors. |
| title | Testing for unspecified periodicities in binary time series |
| topic | Statistics Theory 62M10, 62M15, 62G10 |
| url | https://arxiv.org/abs/2410.10203 |