Asymptotic distribution of a robust wavelet-based NKK periodogram
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918268928786432 |
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| author | N'Daam, Manganaw Kpanzou, Tchilabalo Abozou Katchekpele, Edoh |
| author_facet | N'Daam, Manganaw Kpanzou, Tchilabalo Abozou Katchekpele, Edoh |
| contents | This paper investigates the asymptotic distribution of a wavelet-based NKK periodogram constructed from least absolute deviations (LAD) harmonic regression at a fixed resolution level. Using a wavelet representation of the underlying time series, we analyze the probabilistic structure of the resulting periodogram under long-range dependence. It is shown that, under suitable regularity conditions, the NKK periodogram converges in distribution to a nonstandard limit characterized as a quadratic form in a Gaussian random vector, whose covariance structure depends on the memory properties of the process and on the chosen wavelet filters. This result establishes a rigorous theoretical foundation for the use of robust wavelet-based periodograms in the spectral analysis of long-memory time series with heavy-tailed inovations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_00310 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Asymptotic distribution of a robust wavelet-based NKK periodogram N'Daam, Manganaw Kpanzou, Tchilabalo Abozou Katchekpele, Edoh Methodology 62M10, 62G35, 60F05 This paper investigates the asymptotic distribution of a wavelet-based NKK periodogram constructed from least absolute deviations (LAD) harmonic regression at a fixed resolution level. Using a wavelet representation of the underlying time series, we analyze the probabilistic structure of the resulting periodogram under long-range dependence. It is shown that, under suitable regularity conditions, the NKK periodogram converges in distribution to a nonstandard limit characterized as a quadratic form in a Gaussian random vector, whose covariance structure depends on the memory properties of the process and on the chosen wavelet filters. This result establishes a rigorous theoretical foundation for the use of robust wavelet-based periodograms in the spectral analysis of long-memory time series with heavy-tailed inovations. |
| title | Asymptotic distribution of a robust wavelet-based NKK periodogram |
| topic | Methodology 62M10, 62G35, 60F05 |
| url | https://arxiv.org/abs/2601.00310 |